@Preamble{"\input bibnames.sty"
# "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} "
# "\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi"
# "\ifx \undefined \cyr \let \cyr = \relax \fi"
# "\ifx \undefined \cdprime \def \cdprime {''} \fi"
# "\ifx \undefined \k \let \k = \c \fi"
# "\ifx \undefined \erfc \def \erfc #1{{\rm #1}} \fi"
# "\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}} \fi"
# "\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}} \fi"
# "\ifx \undefined \pkg \def \pkg #1{{{\tt #1}}} \fi"
# "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi"
# "\hyphenation{ Rich-ard }"
}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
@String{ack-mv = "Matti Vuorinen,
Department of Mathematics and Statistics,
University of Turku,
Vesilinnantie 5,
20014 Turku, Finland,
e-mail: \path|vuorinen@utu.fi|,
URL: \path|http://users.utu.fi/vuorinen/|"}
@String{ack-nj = "Norbert Juffa,
2445 Mission College Blvd.,
Santa Clara, CA 95054,
USA,
e-mail: \path|norbert@@iit.com|"}
@String{ack-rfb = "Ronald F. Boisvert,
Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA,
Tel: +1 301 975 3812,
e-mail: \path=boisvert@cam.nist.gov="}
@String{inst-ANL = "Argonne National Laboratory"}
@String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL
60439-4801, USA"}
@String{inst-ATT-BELL = "AT\&T Bell Laboratories"}
@String{inst-ATT-BELL:adr = "Murray Hill, NJ, USA"}
@String{inst-BERKELEY-CS = "Department of Computer Science, University
of California"}
@String{inst-BERKELEY-CS:adr = "Berkeley, CA, USA"}
@String{inst-CECM = "Centre for Experimental and Constructive
Mathematics (CECM) at Simon Fraser
University (SFU)"}
@String{inst-CECM:adr = "Burnaby, BC V5A 1S6, Canada"}
@String{inst-CPAM-UCB = "Center for Pure and Applied Mathematics,
University of California, Berkeley"}
@String{inst-CPAM-UCB:adr = "Berkeley, CA, USA"}
@String{inst-CSC = "Center for Scientific Computing,
Department of Mathematics, University of
Utah"}
@String{inst-CSC:adr = "Salt Lake City, UT 84112, USA"}
@String{inst-INST-ADV-STUDY = "Institute for Advanced Study"}
@String{inst-INST-ADV-STUDY:adr = "Princeton, NJ, USA"}
@String{inst-IPTC = "{Institut f{\"u}r Physikalische und
Theoretische Chemie}"}
@String{inst-IPTC:adr = "{Universit{\"a}t Regensburg, D-93040
Regensburg}"}
@String{inst-LASL = "Los Alamos Scientific Laboratory"}
@String{inst-LASL:adr = "Los Alamos, NM, USA"}
@String{inst-LORIA-INRIA-LORRAINE = "LORIA/INRIA Lorraine"}
@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
Nancy-Brabois, 615 rue du jardin
botanique, F-54602
Villers-l{\`e}s-Nancy Cedex, France"}
@String{inst-MATH-NPS = "Department of Mathematics, Naval Postgraduate
School"}
@String{inst-MATH-NPS:adr = "Monterey CA 93943, USA"}
@String{inst-PRINCETON = "Princeton University"}
@String{inst-PRINCETON:adr = "Princeton, NJ, USA"}
@String{inst-STAN-CS = "Stanford University, Department of
Computer Science"}
@String{inst-STAN-CS:adr = "Stanford, CA, USA"}
@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}
@String{j-ACTA-INFO = "Acta Informatica"}
@String{j-ACTA-MATH = "Acta Mathematica"}
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-ADV-APPL-MATH = "Advances in Applied Mathematics"}
@String{j-ADV-COMPUT-MATH = "Advances in Computational Mathematics"}
@String{j-ADV-QUANTUM-CHEM = "Advances in Quantum Chemistry"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANAL-APPL = "Analysis and Applications (Singapore)"}
@String{j-ANN-APPL-STAT = "Annals of Applied Statistics"}
@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of
Statistical Mathematics"}
@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
Intelligence"}
@String{j-ANN-STAT = "Annals of Statistics"}
@String{j-ANZIAM-J = "The ANZIAM Journal"}
@String{j-APPL-COMPUT-HARMON-ANAL = "Applied and Computational Harmonic
Analysis. Time-Frequency and
Time-Scale Analysis, Wavelets,
Numerical Algorithms, and
Applications"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPL-MATH-SCI-RUSE = "Applied Mathematical Sciences (Ruse)"}
@String{j-APPL-NUM-MATH = "Applied Numerical Mathematics: Transactions
of IMACS"}
@String{j-APPL-OPTICS = "Applied Optics"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"}
@String{j-ARCH-RAT-MECH-ANAL = "Archive for Rational Mechanics and Analysis"}
@String{j-ASTROPHYS-SPACE-SCI = "Astrophysics and Space Science"}
@String{j-ATMOS-SCI-LETT = "Atmospheric Science Letters"}
@String{j-AUST-J-STAT = "Australian Journal of Statistics"}
@String{j-AUSTRALIAN-J-PHYS = "Australian Journal of Physics"}
@String{j-AUTOMATICA = "Automatica: the journal of IFAC, the
International Federation of Automatic
Control"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-BIOMETRIKA = "Biometrika"}
@String{j-BIT = "BIT (Nordisk tidskrift for
informationsbehandling)"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BRITISH-J-HIST-MATH = "British Journal for the History of
Mathematics"}
@String{j-BRITISH-J-PHILOS-SCI = "British Journal for the Philosophy of
Science"}
@String{j-BULL-AMS = "Bulletin of the American Mathematical
Society"}
@String{j-C-R-ACAD-BULGARE-SCI = "Comptes rendus de l'Acad{\'e}mie bulgare
des sciences"}
@String{j-CACM = "Communications of the ACM"}
@String{j-CALCOLO = "Calcolo"}
@String{j-CAN-J-MATH = "Canadian Journal of Mathematics =
Journal canadien de
math{\'e}matiques"}
@String{j-CAN-MATH-BULL = "Bulletin canadien de
math\-{\'e}\-mat\-iques = Canadian
Mathematical Bulletin"}
@String{j-CCCUJ = "C/C++ Users Journal"}
@String{j-CELEST-MECH-DYN-ASTR = "Celestial Mechanics and Dynamical Astronomy"}
@String{j-CENTAURUS = "Centaurus: An International Journal of the
History of Science and its Cultural Aspects"}
@String{j-COLLEGE-MATH-J = "College Mathematics Journal"}
@String{j-COMM-PURE-APPL-MATH = "Communications on Pure and Applied
Mathematics (New York)"}
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
and Computation"}
@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
Methods"}
@String{j-COMP-ARCH-NEWS = "ACM SIGARCH Computer Architecture News"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-COMPUT-MATH-APPL = "Computers and Mathematics with Applications"}
@String{j-COMPUT-MATH-MATH-PHYS = "Computational Mathematics and Mathematical
Physics"}
@String{j-COMPUT-PHYS = "Computers in Physics"}
@String{j-COMPUT-PHYS-REP = "Computer Physics Reports"}
@String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"}
@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}
@String{j-COMPUTER = "Computer"}
@String{j-COMPUTING = "Computing: Archiv fur informatik und
numerik"}
@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}
@String{j-CONST-APPROX = "Constructive Approximation"}
@String{j-CYBER = "Cybernetics"}
@String{j-DDJ = "Dr. Dobb's Journal of Software Tools"}
@String{j-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"}
@String{j-DOKL-AKAD-NAUK = "Doklady Akademii nauk SSSR"}
@String{j-EDN = "EDN"}
@String{j-ELECT-LETTERS = "Electronics Letters"}
@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
Computer Science"}
@String{j-ELECTRON-COMMUN-JPN = "Electronics and communications in Japan"}
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
Analysis (ETNA)"}
@String{j-ELECTRONIC-DESIGN = "Electronic Design"}
@String{j-ELECTRONICS = "Electronics"}
@String{j-ELECTRONIK = "Elektronik"}
@String{j-ELEKTRONIKER = "Elektroniker (Switzerland)"}
@String{j-ELEK-RECHENANLAGEN = "Elektronische Rechenanlagen"}
@String{j-EMBED-SYS-PROG = "Embedded Systems Programming"}
@String{j-ENTROPY = "Entropy"}
@String{j-EXP-MATH = "Experimental mathematics"}
@String{j-FIB-QUART = "Fibonacci Quarterly"}
@String{j-FORM-METHODS-SYST-DES = "Formal Methods in System Design"}
@String{j-HEWLETT-PACKARD-J = "Hew\-lett-Pack\-ard Journal: technical
information from the laboratories of
Hew\-lett-Pack\-ard Company"}
@String{j-HIST-MATH = "Historia Mathematica"}
@String{j-HIST-SCI-2 = "Historia Scientiarum. Second Series.
International Journal of the History
of Science Society of Japan"}
@String{j-IBM-JRD = "IBM Journal of Research and Development"}
@String{j-IBM-SYS-J = "IBM Systems Journal"}
@String{j-IBM-TDB = "IBM Technical Disclosure Bulletin"}
@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital Techniques"}
@String{j-IEEE-CGA = "IEEE Computer Graphics and Applications"}
@String{j-IEEE-COMMUN-LET = "IEEE Communications Letters"}
@String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"}
@String{j-IEEE-MICRO = "IEEE Micro"}
@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"}
@String{j-IEEE-SPECTRUM = "IEEE Spectrum"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE Transactions on Circuits and
Systems. 2, Analog and Digital Signal
Processing"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS = "IEEE Transactions on
Circuits and Systems II: Express Briefs"}
@String{j-IEEE-TRANS-COMM = "IEEE Transactions on Communications"}
@String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"}
@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}
@String{j-IEEE-TRANS-EMERG-TOP-COMPUT = "IEEE Transactions on Emerging Topics in
Computing"}
@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}
@String{j-IEEE-TRANS-MICROWAVE-THEORY-TECH = "IEEE Transactions on Microwave
Theory and Techniques"}
@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
Distributed Systems"}
@String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"}
@String{j-IEEE-TRANS-VLSI-SYST = "IEEE Transactions on Very Large Scale
Integration (VLSI) Systems"}
@String{j-IEEE-TRANS-VEH-TECHNOL = "IEEE Transactions on Vehicular Technology"}
@String{j-IEEE-TRANS-WIREL-COMMUN = "IEEE Transactions on Wireless
Communications"}
@String{j-IJQC = "International Journal of Quantum Chemistry"}
@String{j-IJSAHPC = "The International Journal of Supercomputer
Applications and High Performance Computing"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-INFO-PROC-LETT = "Information Processing Letters"}
@String{j-INT-J-COMPUT-INF-SCI = "International Journal of Computer and
Information Sciences"}
@String{j-INT-J-COMPUT-MATH = "International Journal of Computer
Mathematics"}
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
Computing"}
@String{j-INT-J-MATH-EDU-SCI-TECH = "International journal of mathematical
education in science and technology"}
@String{j-INT-J-MATH-MATH-SCI = "International Journal of Mathematics and
Mathematical Sciences"}
@String{j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER = "International Journal on
Software Tools for Technology Transfer (STTT)"}
@String{j-INTEGRATION-VLSI-J = "Integration, the VLSI journal"}
@String{j-INTEL-TECH-J = "Intel Technology Journal"}
@String{j-INTERNET-J-CHEM = "Internet Journal of Chemistry"}
@String{j-INTERVAL-COMP = "Interval Computations = Interval'nye
vychisleniia"}
@String{j-IRE-TRANS-ELEC-COMPUT = "IRE Transactions on Electronic Computers"}
@String{j-ISIS = "Isis"}
@String{j-J-ACM = "Journal of the Association for Computing
Machinery"}
@String{j-J-ACOUST-SOC-AM = "Journal of the Acoustical Society of America"}
@String{j-J-ALG = "Journal of Algorithms"}
@String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical
Association"}
@String{j-J-APPL-STAT = "Journal of Applied Statistics"}
@String{j-J-APPROX-THEORY = "Journal of Approximation Theory"}
@String{j-J-AUSTRAL-MATH-SOC-SER-B = "Journal of the Australian Mathematical
Society: Series B, Applied Mathematics"}
@String{j-J-AUTOM-REASON = "Journal of Automated Reasoning"}
@String{j-J-COMB-THEORY-A = "Journal of Combinatorial Theory (Series A)"}
@String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-J-COMPUT-CHEM = "Journal of Computational Chemistry"}
@String{j-J-COMPUT-GRAPH-STAT = "Journal of Computational and Graphical
Statistics"}
@String{j-J-COMPLEXITY = "Journal of complexity"}
@String{j-J-COMPUT-PHYS = "Journal of Computational Physics"}
@String{j-J-FRANKLIN-INST = "Journal of {The Franklin Institute}"}
@String{j-J-GRAPHICS-GPU-GAME-TOOLS = "Journal of Graphics, GPU, and Game Tools"}
@String{j-J-GRID-COMP = "Journal of Grid Computing"}
@String{j-J-HIGH-ENERGY-PHYS = "Journal of High Energy Physics"}
@String{j-J-INST-MATH-APPL = "Journal of the Institute of Mathematics and
its Applications"}
@String{j-J-KOREA-INFO-SCI-SOCIETY = "Journal of the Korea Information Science
Society = Chongbo Kwahakhoe nonmunji"}
@String{j-J-MATH-ANAL-APPL = "Journal of Mathematical Analysis and
Applications"}
@String{j-J-MATH-CHEM = "Journal of Mathematical Chemistry"}
@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-MATH-PHYS-MIT = "Journal of Mathematics and Physics (MIT)"}
@String{j-J-MOL-STRUCT-THEOCHEM = "Journal of Molecular Structure. Theochem"}
@String{j-J-MULTIVAR-ANAL = "Journal of Multivariate Analysis"}
@String{j-J-NUMBER-THEORY = "Journal of Number Theory"}
@String{j-J-NUMER-METHODS-COMPUT-APPL = "Journal on Numerical Methods and
Computer Applications"}
@String{j-J-OPT-THEORY-APPL = "Journal of Optimization Theory and
Applications"}
@String{j-J-PAR-DIST-COMP = "Journal of Parallel and Distributed
Computing"}
@String{j-J-PHYS-A = "Journal of Physics A (Mathematical and General)"}
@String{j-J-R-STAT-SOC-SER-B-METHODOL = "Journal of the Royal Statistical
Society. Series B (Methodological)"}
@String{j-J-R-STAT-SOC-SER-D-STATISTICIAN = "Journal of the Royal Statistical
Society. Series D (The Statistician)"}
@String{j-J-RES-NATL-BUR-STAND-1934 = "Journal of Research of the National
Bureau of Standards (1934)"}
@String{j-J-RES-NATL-BUR-STAND-B = "Journal of Research of the National Bureau
of Standards. Section B, Mathematics
and Mathematical Physics"}
@String{j-J-SCI-COMPUT = "Journal of Scientific Computing"}
@String{j-J-SOV-MATH = "Journal of Soviet Mathematics"}
@String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and
Simulation"}
@String{j-J-STAT-SOFT = "Journal of Statistical Software"}
@String{j-J-SUPERCOMPUTING = "The Journal of Supercomputing"}
@String{j-J-SYMBOLIC-COMP = "Journal of Symbolic Computation"}
@String{j-J-SYMBOLIC-LOGIC = "Journal of Symbolic Logic"}
@String{j-J-UCS = "J.UCS: The Journal of Universal Computer Science"}
@String{j-J-VLSI-SIGNAL-PROC = "Journal of VLSI Signal Processing"}
@String{j-JETC = "ACM Journal on Emerging Technologies
in Computing Systems (JETC)"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-LECT-NOTES-MATH = "Lecture Notes in Mathematics"}
@String{j-LIN-AND-MULT-ALGEBRA = "Linear and Multilinear Algebra"}
@String{j-LMS-J-COMPUT-MATH = "LMS Journal of Computation and Mathematics"}
@String{j-LOGIN = ";login: the USENIX Association newsletter"}
@String{j-MATH-COMP-SIM = "Mathematics and Computers in Simulation"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-COMPUT-APPL = "Mathematical and Computational Applications"}
@String{j-MATH-COMPUT-SCI = "Mathematics in Computer Science"}
@String{j-MATH-GAZ = "The Mathematical Gazette"}
@String{j-MATH-MAG = "Mathematics Magazine"}
@String{j-MATH-MODEL-NUM-ANA = "Mathematical modelling and numerical
analysis = Modelisation math{\'e}matique et
analyse num{\'e}rique: $M^2AN$"}
@String{j-MATH-OP-RES = "Mathematics of Operations Research"}
@String{j-MATH-PROG = "Mathematical Programming"}
@String{j-MATH-SCI = "The Mathematical Scientist"}
@String{j-MATH-STUDENT = "The Mathematics Student"}
@String{j-MATH-TABLES-AIDS-COMPUT = "Mathematical Tables and Aids to
Computation"}
@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
to Computation"}
@String{j-MATH-Z = "{Mathematische Zeitschrift}"}
@String{j-MATHEMATICA-J = "Mathematica Journal"}
@String{j-METHODS-APPL-ANAL = "Methods and Applications of Analysis"}
@String{j-MICROPROC-MICROPROG = "Microprocessing and Microprogramming"}
@String{j-MICROPROC-MICROSYS = "Microprocessors and Microsystems"}
@String{j-MONAT-MATH = "Monatshefte f{\"u}r Mathematik"}
@String{j-NACH-ELEK = "Nachrichtentechnik Elektronik"}
@String{j-NAMS = "Notices of the American Mathematical
Society"}
@String{j-NEURAL-COMP = "Neural Computation"}
@String{j-NEURAL-NETWORKS = "Neural Networks"}
@String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for
informationsbehandling"}
@String{j-NOTRE-DAME-J-FORM-LOG = "Notre Dame Journal of Formal Logic"}
@String{j-NUCL-INSTR-METH = "Nuclear Instruments and Methods"}
@String{j-NUCL-PHYS-B-PROC-SUPPL = "Nuclear Physics B, Proceedings Supplements"}
@String{j-NUM-MATH = "Numerische Mathematik"}
@String{j-NUMER-ALGORITHMS = "Numerical Algorithms"}
@String{j-OPER-RES = "Operations Research"}
@String{j-PAC-J-MATH = "Pacific Journal of Mathematics"}
@String{j-PACMPL = "Proceedings of the ACM on Programming
Languages (PACMPL)"}
@String{j-PARALLEL-COMPUTING = "Parallel Computing"}
@String{j-PHILOS-MAG = "Philosophical Magazine"}
@String{j-PHILOS-TRANS-R-SOC-LOND = "Philosophical Transactions of the Royal
Society of London"}
@String{j-PHYS-REV-A = "Physical Review A"}
@String{j-PHYS-REV-A-3 = "Physical Review A (3)"}
@String{j-PHYS-REV-E = "Physical Review E (Statistical physics,
plasmas, fluids, and related
interdisciplinary topics)"}
@String{j-PHYS-TODAY = "Physics Today"}
@String{j-PHYSICA-D = "Physica D"}
@String{j-PROBAB-ENGRG-INFORM-SCI = "Probability in the Engineering and
Informational Sciences"}
@String{j-PROC-AM-MATH-SOC = "Proceedings of the American Mathematical
Society"}
@String{j-PROC-CAMBRIDGE-PHIL-SOC = "Proceedings of the Cambridge Philosophical
Society. Mathematical and physical sciences"}
@String{j-PROC-IEEE = "Proceedings of the IEEE"}
@String{j-PROC-LONDON-MATH-SOC-1 = "Proceedings of the London Mathematical
Society. First Series"}
@String{j-PROC-LONDON-MATH-SOC-2 = "Proceedings of the London Mathematical
Society. Second Series"}
@String{j-PROC-LONDON-MATH-SOC-3 = "Proceedings of the London Mathematical
Society. Third Series"}
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS = "Proceedings of the Royal Society of
London. Series A, Containing Papers of a
Mathematical and Physical Character"}
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI = "Proceedings of the Royal
Society of London. Series A, Mathematical
and physical sciences"}
@String{j-PROG-COMP-SOFT = "Programming and Computer Software;
translation of Programmirovaniye (Moscow,
USSR) Plenum"}
@String{j-PROGRAMMIROVANIE = "Programmirovanie"}
@String{j-QUART-APPL-MATH = "Quarterly of Applied Mathematics"}
@String{j-REND-CIRC-MAT = "Rendiconti del Circolo matematico di
Palermo"}
@String{j-REV-MOD-PHYS = "Reviews of Modern Physics"}
@String{j-RUSS-J-MATH-PHYS = "Russian Journal of Mathematical Physics"}
@String{j-SCI-COMPUT-PROGRAM = "Science of Computer Programming"}
@String{j-SCRIPTA-MATH = "Scripta Mathematica"}
@String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"}
@String{j-SIAM-J-COMPUT = "SIAM Journal on Computing"}
@String{j-SIAM-J-CONTROL-OPTIM = "SIAM Journal on Control and Optimization"}
@String{j-SIAM-J-MAT-ANA-APPL = "SIAM Journal on Matrix Analysis and
Applications"}
@String{j-SIAM-J-MATH-ANA = "SIAM journal on mathematical analysis"}
@String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and
Applied Mathematics: Series B, Numerical
Analysis"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"}
@String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and Statistical
Computing"}
@String{j-SIAM-NEWS = "SIAM News"}
@String{j-SIAM-REVIEW = "SIAM Review"}
@String{j-SIGADA-LETTERS = "ACM SIGADA Ada Letters"}
@String{j-SIGCSE = "SIGCSE Bulletin (ACM Special Interest Group
on Computer Science Education)"}
@String{j-SIGNUM = "ACM SIGNUM Newsletter"}
@String{j-SIGPLAN = "ACM SIGPLAN Notices"}
@String{j-SIGSAM = "SIGSAM Bulletin (ACM Special Interest Group
on Symbolic and Algebraic Manipulation)"}
@String{j-SOFTWAREX = "SoftwareX"}
@String{j-SPE = "Soft\-ware\emdash Prac\-tice and Experience"}
@String{j-STAT-PROB-LETT = "Statistics \& Probability Letters"}
@String{j-TECHNIQUE-SCI-INFORMATIQUES = "Technique et Science Informatiques"}
@String{j-TECHNOMETRICS = "Technometrics"}
@String{j-TECS = "ACM Transactions on Embedded Computing
Systems"}
@String{j-TELO = "ACM Transactions on Evolutionary
Learning and Optimization (TELO)"}
@String{j-THEOR-COMP-SCI = "Theoretical Computer Science"}
@String{j-TOKYO-J-MATH = "Tokyo journal of mathematics"}
@String{j-TOMS = "ACM Transactions on Mathematical Software"}
@String{j-TRANS-AM-MATH-SOC = "Transactions of the American Mathematical
Society"}
@String{j-TRANS-INFO-PROCESSING-SOC-JAPAN = "Transactions of the Information
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Singapore 9128"}
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@Article{Horner:1819:XNM,
author = "William George Horner",
title = "{XXI}. {A} new method of solving numerical equations
of all orders, by continuous approximation",
journal = j-PHILOS-TRANS-R-SOC-LOND,
volume = "109",
pages = "308--335",
year = "1819",
CODEN = "PTRSAV",
DOI = "https://doi.org/10.1098/rstl.1819.0023",
ISSN = "0370-2316 (print), 2053-9207 (electronic)",
bibdate = "Sat Oct 21 12:27:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1819.0023",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Transactions of the Royal Society of
London",
journal-URL = "http://rsta.royalsocietypublishing.org/",
keywords = "Horner's nested form; number of multiplications to
evaluate a polynomial",
read = "1 July 1819",
remark-1 = "Communicated by Davies Gilbert, Esq. F.R.S.",
remark-2 = "On page 310 of this paper, Horner gives the steps of
the nested form as a chain of fused multiply-add
operations, and credits this idea to Joseph-Louis
Lagrange (1736--1813) in his 1813 book
\booktitle{Th{\'e}orie des fonctions analytiques}.",
remark-3 = "Knuth \cite[p. 486]{Knuth:1998:SA} gives this paper as
the reference for Horner's nested form, but also
reports that Isaac Newton used it in unpublished notes
150 years earlier, and that it was employed by the
Chinese in the 13th century CE.",
}
@Article{Lovelace:1843:SAE,
author = "Ada Augusta Lovelace",
title = "Sketch of the {Analytical Engine}",
journal = "Scientific Memoirs",
volume = "3",
number = "??",
pages = "666--731",
month = "????",
year = "1843",
bibdate = "Sun Aug 18 09:31:28 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Reprinted in \cite{Lovelace:1989:SAE}.",
acknowledgement = ack-nhfb,
keywords = "Bernoulli numbers",
remark = "This paper contains what some view as possibly the
world's first computer program, a recipe for computing
Bernoulli numbers on Charles Babbage's Analytical
Engine, which was not successfully constructed until
more than a century after their deaths, in 1852 and
1871, respectively. It is not, however, the world's
first computational algorithm: that credit is given to
Euclid's procedure for fast computation of the greatest
common denominator, about 300 BCE, but possibly known a
few hundred years earlier.",
}
@Book{Greenhill:1892:AEF,
author = "Alfred George Greenhill",
title = "The Applications of Elliptic Functions",
publisher = pub-MACMILLAN,
address = pub-MACMILLAN:adr,
pages = "xi + 357",
year = "1892",
bibdate = "Wed Mar 15 08:21:33 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "1847--1927",
remark = "Reprinted in \cite{Greenhill:1959:AEF}.",
}
@Article{Dawson:1897:NV,
author = "H. G. Dawson",
title = "On the Numerical Value of $ \int_0^h e^{x^2} \, d x
$",
journal = j-PROC-LONDON-MATH-SOC-1,
volume = "s1-29",
number = "1",
pages = "519--522",
month = nov,
year = "1897",
CODEN = "PLMTAL",
DOI = "https://doi.org/10.1112/plms/s1-29.1.519",
ISSN = "0024-6115 (print), 1460-244X (electronic)",
ISSN-L = "0024-6115",
bibdate = "Sat Jun 12:08:16 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
fjournal = "Proceedings of the London Mathematical Society. First
Series",
journal-URL = "http://plms.oxfordjournals.org/content/by/year",
remark = "This paper is the origin of Dawson's integral and the
function dawson(x).",
}
@Book{Kennelly:1914:TCH,
author = "Arthur E. (Arthur Edwin) Kennelly",
title = "Tables of Complex Hyperbolic and Circular Functions",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "iii + 212",
year = "1914",
LCCN = "QA342 .K45",
bibdate = "Sat Apr 1 14:49:41 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1861--1939",
subject = "Exponential functions",
}
@Book{Pairman:1919:TDT,
author = "Eleanor Pairman",
title = "Tables of the Digamma and Trigamma Functions",
volume = "I",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "9 + 11",
year = "1919",
LCCN = "QA47 .T7 no.1",
bibdate = "Sat Mar 25 16:17:54 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
series = "Tracts for computers",
acknowledgement = ack-nhfb,
remark = "Edited by Karl Pearson. According to
\cite{Davis:1935:EPF}, the author coined the phrase
`polygamma function' in this booklet. English
dictionaries usually do not include the word
`polygamma'.",
subject = "Gamma functions",
}
@Book{Kennelly:1921:TCH,
author = "Arthur Edwin Kennelly",
title = "Tables of Complex Hyperbolic and Circular Functions",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "iii + 240",
year = "1921",
LCCN = "QA342 .K45 1921",
bibdate = "Sat Apr 1 14:49:41 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1861--",
subject = "Functions, Exponential",
}
@Article{King:1921:SNF,
author = "Louis Vessot King",
title = "On Some New Formulae for the Numerical Calculation of
the Mutual Induction of Coaxial Circles",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS,
volume = "100",
number = "702",
pages = "60--66",
day = "4",
month = oct,
year = "1921",
DOI = "https://doi.org/10.1098/rspa.1921.0070",
ISSN = "0950-1207 (print), 2053-9150 (electronic)",
bibdate = "Wed Feb 03 09:07:10 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
note = "This is the first known publication of the AGM method,
discovered by the author in 1913, for computing
Jacobian elliptic functions. See also
\cite{King:1924:DNC,King:2007:DNC}.",
URL = "http://www.jstor.org/stable/93861",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series A,
Containing Papers of a Mathematical and Physical
Character",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@Book{King:1924:DNC,
author = "Louis Vessot King",
title = "On the Direct Numerical Calculation of Elliptic
Functions and Integrals",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "viii + 42",
year = "1924",
LCCN = "QA343",
bibdate = "Wed Feb 03 08:53:04 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
remark = "The AGM method for Jacobian elliptic functions was
discovered by this book's author at McGill University
in 1913, first published in \cite{King:1921:SNF}, and
then in this monograph (reprinted in
\cite{King:2007:DNC}).",
}
@Article{Ritt:1925:EFT,
author = "J. F. Ritt",
title = "Elementary functions and their inverses",
journal = j-TRANS-AM-MATH-SOC,
volume = "27",
number = "1",
pages = "68--90",
year = "1925",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-1925-1501299-9",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "30A05 (33B10)",
MRnumber = "MR1501299",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/journals/tran/1925-027-01/S0002-9947-1925-1501299-9/",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
}
@Article{Dederick:1926:QDDc,
author = "L. S. Dederick",
title = "Questions and Discussions: Discussions: a Modified
Method for Cube Roots and Fifth Roots",
journal = j-AMER-MATH-MONTHLY,
volume = "33",
number = "9",
pages = "469--472",
month = nov,
year = "1926",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:12 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2299613",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Mahler:1930:NUG,
author = "K. Mahler",
title = "{{\"U}ber die Nullstellen der unvollstaendigen
Gammafunktionen}. ({German}) [{On} the zeros of the
incomplete gamma-functions]",
journal = j-REND-CIRC-MAT,
volume = "54",
number = "??",
pages = "1--41",
month = "????",
year = "1930",
CODEN = "RCMMAR",
ISSN = "0009-725X (print), 1973-4409 (electronic)",
ISSN-L = "0009-725X",
bibdate = "Sat Feb 18 14:57:12 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://carma.newcastle.edu.au/mahler/collected.html;
https://carma.newcastle.edu.au/mahler/docs/002.pdf",
acknowledgement = ack-nhfb,
fjournal = "Rendiconti del Circolo matematico di Palermo",
language = "German",
remark = "Based on doctoral dissertation, Frankfurt, Germany
(1927).",
}
@Book{Hobson:1931:TSE,
author = "Ernest William Hobson",
title = "The Theory of Spherical and Ellipsoidal Harmonics",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xi + 500",
year = "1931",
LCCN = "QA406 .H7",
bibdate = "Sat Apr 1 14:40:56 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1856--1933",
subject = "Spherical harmonics; Lam\'e's functions",
}
@Article{Kalbfell:1934:QDN,
author = "D. C. Kalbfell",
title = "Questions, Discussions and Notes: On a Method for
Calculating Square Roots",
journal = j-AMER-MATH-MONTHLY,
volume = "41",
number = "8",
pages = "504--506",
month = oct,
year = "1934",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:31 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2300417",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{McLachlan:1934:BFE,
author = "N. W. (Norman William) McLachlan",
title = "{Bessel} Functions for Engineers",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xi + 1 + 192",
year = "1934",
LCCN = "QA408 .M3",
bibdate = "Sat Apr 1 14:44:36 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "The Oxford engineering science series",
acknowledgement = ack-nhfb,
author-dates = "1888--",
subject = "Bessel functions",
}
@Article{Davis:1935:EPF,
author = "H. T. Davis",
title = "An extension to polygamma functions of a theorem of
{Gauss}",
journal = j-BULL-AMS,
volume = "41",
number = "4",
pages = "243--248",
month = apr,
year = "1935",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/s0002-9904-1935-06055-0",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Sat Mar 25 16:16:08 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
remark = "A footnote on the first page says ``The name polygamma
is suggested by the paper, \booktitle{Tables of the
Digamma and Trigamma Functions}, by Eleanor Pairman,
Tracts for Computers, No. 1, 1919''
\cite{Pairman:1919:TDT}.",
}
@Article{Airey:1937:CFA,
author = "J. R. Airey",
title = "The ``converging factor'' in asymptotic series and the
calculation of {Bessel}, {Laguerre} and other
functions",
journal = j-PHILOS-MAG,
volume = "24",
number = "162",
pages = "521--552",
month = "????",
year = "1937",
CODEN = "PHMAA4",
DOI = "https://doi.org/10.1080/14786443708565133",
ISSN = "0031-8086",
ISSN-L = "0031-8086",
bibdate = "Thu Dec 01 14:26:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Magazine",
journal-URL = "http://www.tandfonline.com/loi/tphm19",
}
@Article{Escott:1937:QDN,
author = "E. B. Escott",
title = "Questions, Discussions, and Notes: Rapid Method for
Extracting a Square Root",
journal = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2301484",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Ostrowski:1937:KAN,
author = "A. M. Ostrowski",
title = "{{\"U}ber die Konvergenz und die
Abr{\"u}ndungsfestigkeit des Newtonschen Verfahren}.
({German}) [{On} the convergence and rounding strength
of {Newton}'s method]",
journal = "Rec. Math.",
volume = "2",
number = "??",
pages = "1073--1098",
month = "????",
year = "1937",
bibdate = "Mon Oct 23 14:58:35 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Ostrowski:1938:NMA,
author = "A. M. Ostrowski",
title = "On {Newton}'s method of approximation",
journal = "British Association for the Advancement of Science",
volume = "??",
number = "??",
pages = "392--??",
month = "????",
year = "1938",
bibdate = "Mon Oct 23 14:57:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Emde:1940:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "B. T. Teubner",
address = "Leipzig, Germany and Berlin, Germany",
pages = "xii + 181",
year = "1940",
LCCN = "QA47 .E5",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://lccn.loc.gov/45006177",
acknowledgement = ack-nhfb,
author-dates = "1873--1951",
language = "German",
}
@Article{Stoner:1941:FEF,
author = "Paul Matthew Stoner",
title = "Fitting the Exponential Function and the {Gompertz}
Function by the Method of Least Squares",
journal = j-J-AM-STAT-ASSOC,
volume = "36",
number = "216",
pages = "515--518",
month = dec,
year = "1941",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314095;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2278959",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Book{Stratton:1941:ECS,
author = "Julius Adams Stratton and Philip M. (Philip McCord)
Morse and Lan Jen Chu and Reina Albagli Hutner",
title = "Elliptic cylinder and spheroidal wave functions,
including tables of separation constants and
coefficients",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 127",
year = "1941",
LCCN = "QC174.2 .S78",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1901--1994",
remark = "A publication of the Technology Press, Massachusetts
Institute of Technology.",
subject = "Wave mechanics; Mathematics; Tables",
}
@PhdThesis{Dopper:1942:AOV,
author = "Herman Pieter Dopper",
title = "Asymptotische Ontwikkelingen van de Onvolledige
Gammafuncties. ({Dutch}) [{Asymptotic} developments of
the Incomplete Gamma Functions]",
type = "{Ph.D.} thesis",
school = "Rijksuniversiteit Groningen",
address = "Groningen, The Netherlands",
pages = "????",
year = "1942",
bibdate = "Sat Feb 18 14:32:59 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Dutch",
remark = "Cited in \cite{Paris:2016:UAE}.",
}
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Archibald:1943:TTF,
author = "Raymond Clare Archibald",
title = "Tables of Trigonometric Functions in Non-Sexagesimal
Arguments",
journal = j-MATH-TABLES-AIDS-COMPUT,
volume = "1",
number = "2",
pages = "33--44",
month = apr,
year = "1943",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-43-99136-7",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
journal-URL = "http://www.ams.org/mcom/",
remark = "Original journal has only `R. C. A.' as author:
possibly R. C. Archibald. AMS metadata now shows the
full name.",
}
@Book{Tolke:1943:PFE,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 1. Elementare und
elementare transzendente Funktionen, Unterstufe}.
({German}) [{Practical} functional theory. 1.
{Elementary} and elementary transcendental functions,
lower stage]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 261",
year = "1943",
bibdate = "Mon Feb 13 19:15:35 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Turing:1943:MCZ,
author = "A. M. Turing",
title = "A method for the calculation of the zeta-function",
journal = j-PROC-LONDON-MATH-SOC-2,
volume = "48",
pages = "180--197",
year = "1943",
ISSN = "0024-6115 (print), 1460-244X (electronic)",
ISSN-L = "0024-6115",
MRclass = "10.0X",
MRnumber = "MR0009612 (5,173a)",
MRreviewer = "C. L. Siegel",
bibdate = "Sat Nov 19 13:23:32 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/17",
ZMnumber = "0061.08304",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the London Mathematical Society. Second
Series",
received = "7 March 1939",
remark = "According to \cite[page 260]{Newman:1955:AMT},
publication was delayed four years by war-time
difficulties.",
}
@Article{Bateman:1944:GTB,
author = "Harry Bateman and Raymond Clare Archibald",
title = "A Guide to Tables of {Bessel} Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "7",
pages = "205--308",
month = jul,
year = "1944",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1944-0011175-4",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRnumber = "6,132b",
MRreviewer = "G. Szeg{\H{o}}",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lehmer:1944:NCB,
author = "Derrick Henry Lehmer",
title = "Note on the Computation of the {Bessel} Function {$
I_n(X) $}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "5",
pages = "133--135",
month = apr,
year = "1944",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-44-99053-8",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Original journal has only `D. H. L.' as author:
probably D. H. Lehmer. AMS metadata now shows the full
name.",
}
@Book{Lewis:1944:SCH,
author = "Charles J. Lewis",
title = "A survey of the confluent hypergeometric function",
publisher = "????",
address = "Washington, DC, USA",
pages = "155",
year = "1944",
LCCN = "QA351 .L53",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Abramowitz:1945:ZCB,
author = "Milton Abramowitz",
title = "Zeros of certain {Bessel} functions of fractional
order",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "9",
pages = "353--354",
month = jan,
year = "1945",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1945-0011176-7",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "6,132c",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Briggs:1945:TAL,
author = "Lyman J. Briggs and Arnold N. Lowan",
title = "Tables of Associated {Legendre} Functions",
publisher = pub-U-COLUMBIA,
address = pub-U-COLUMBIA:adr,
pages = "xlvi + 303 + 3",
year = "1945",
LCCN = "QA406 .U5 1945",
bibdate = "Sat Apr 1 14:47:02 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Prepared by the Mathematical Tables Project and
conducted under the sponsorship of the National bureau
of Standards. Present volume begun under the auspices
of the Work Projects Administration for the City of New
York and completed with the support of the Office of
Scientific Research and Development. Lyman J. Briggs,
Director, National Bureau of Standards and official
sponsor. Arnold N. Lowan, Project Director,
Mathematical Tables Project. Reproduced by a photo
offset process.",
subject = "Legendre's functions",
}
@Book{Emde:1945:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "Edwards Bros.",
address = "Ann Arbor, MI, USA",
pages = "xii + 181",
year = "1945",
LCCN = "????",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Original edition published in 1940.",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Anonymous:1946:MZC,
author = "Anonymous",
title = "More Zeros of Certain {Bessel} Functions of Fractional
Order",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "2",
number = "15",
pages = "118--119",
month = jul,
year = "1946",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1946-0016689-0",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Anonymous:1948:TBF,
author = "Anonymous",
title = "Tables of the {Bessel} Functions {$ Y_0 (x) $}, {$ Y_1
(x) $}, {$ K_0 (x) $}, {$ K_1 (x) $}, $ 0 \leq x \leq 1
$",
volume = "1",
publisher = pub-US-GPO,
address = pub-US-GPO:adr,
pages = "ix + 60",
year = "1948",
LCCN = "QA3 .U5 no. 1",
bibdate = "Sat Nov 04 16:47:30 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = ser-APPL-MATH-SER-NBS,
acknowledgement = ack-nhfb,
}
@Book{Emde:1948:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
edition = "Second",
pages = "xii + 181",
year = "1948",
LCCN = "QA55 .E5 1948",
MRclass = "65.0X",
MRnumber = "11,263k",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the square-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Wise:1948:IBF,
author = "M. E. Wise",
title = "The Incomplete Beta Function and the Incomplete Gamma
Function: An Acknowledgment",
journal = j-J-R-STAT-SOC-SER-B-METHODOL,
volume = "10",
number = "2",
pages = "264--264",
month = "????",
year = "1948",
CODEN = "JSTBAJ",
DOI = "https://doi.org/10.2307/2983781",
ISSN = "0035-9246",
ISSN-L = "0035-9246",
bibdate = "Fri Jan 23 11:53:21 MST 2015",
bibsource = "http://www.jstor.org/stable/i349688;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-b.bib",
URL = "http://www.jstor.org/stable/2983781",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series B
(Methodological)",
journal-URL = "http://www.jstor.org/journals/00359246.html",
}
@Article{Hartree:1949:NIP,
author = "D. R. Hartree",
title = "Notes on iterative processes",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "45",
number = "2",
pages = "230--236",
month = apr,
year = "1949",
CODEN = "PCPSA4",
DOI = "https://doi.org/10.1017/s0305004100024762",
ISSN = "0008-1981",
ISSN-L = "0008-1981",
MRclass = "65.0X",
MRnumber = "29268",
MRreviewer = "E. Bodewig",
bibdate = "Thu Aug 3 09:15:52 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Correction: in equation (29) at the bottom of page
233, replace the denominator term $ 2 y_0 $ by $ 2 y_1
$, matching the denominator in equation (32) on page
234.",
URL = "https://ui.adsabs.harvard.edu/abs/1949PCPS...45..230H",
ZMnumber = "0033.19003",
acknowledgement = ack-nhfb,
author-dates = "Douglas Rayner Hartree (27 March 1897--12 February
1958)",
fjournal = "Proceedings of the Cambridge Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
keywords = "$1/p$-th root; iterative process; reciprocal square
root; square root",
ZBmath = "3051117",
}
@Article{Lowan:1949:CLN,
author = "Arnold N. Lowan",
title = "The {Computation Laboratory of the National Bureau of
Standards}",
journal = j-SCRIPTA-MATH,
volume = "15",
number = "??",
pages = "33--63",
month = "????",
year = "1949",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0034.07002",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
ZBmath = "3052129",
}
@Book{Magnus:1949:FTS,
author = "Wilhelm Magnus and Fritz Oberhettinger",
title = "Formulas and theorems for the special functions of
mathematical physics",
publisher = "Chelsea Pub. Co.",
address = "New York, NY, USA",
pages = "172",
year = "1949",
LCCN = "QA41 M19e",
bibdate = "Sat Oct 30 18:44:51 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translated from the German by John Wermer.",
acknowledgement = ack-nhfb,
}
@Article{Mitchell:1949:TFA,
author = "K. Mitchell",
title = "Tables of the function $ \int_0^z - \log |1 - y| / y
\, d y $ with an account of some properties of this and
related functions",
journal = j-PHILOS-MAG,
volume = "40",
number = "302",
pages = "351--368",
year = "1949",
CODEN = "PHMAA4",
DOI = "https://doi.org/10.1080/14786444908561256",
ISSN = "0031-8086",
bibdate = "Sat Jun 17 17:47:16 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.tandfonline.com/doi/abs/10.1080/14786444908561256",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Magazine",
journal-URL = "http://www.tandfonline.com/loi/tphm19",
received = "9 April 1948",
}
@InProceedings{Polya:1949:RCP,
author = "G. P{\'o}lya",
editor = "J. Neyman",
booktitle = "Proceedings of the First Berkeley Symposium on
Mathematical Statistics and Probability",
title = "Remarks on computing the probability integral in one
and two dimensions",
publisher = pub-U-CALIFORNIA-PRESS,
address = pub-U-CALIFORNIA-PRESS:adr,
pages = "63--78",
year = "1949",
bibdate = "Sat Dec 16 17:23:49 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{USNBSCL:1949:TCH,
author = "{United States National Bureau of Standards
Computation Laboratory }",
title = "Tables of the confluent hypergeometric function {$ F(n
/ 2, 1 / 2, x) $ and related functions}",
volume = "3",
publisher = pub-US-GPO,
address = pub-US-GPO:adr,
pages = "xxii + 73",
year = "1949",
LCCN = "QA3 .U5 no. 3",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Applied mathematics series",
URL = "http://openlibrary.org/works/OL1218358W/Tables_of_the_confluent_hypergeometric_function_F%28n_2_1_2_x%29_and_related_functions",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions; Mathematics; Tables",
}
@Article{Norlund:1950:HF,
author = "Niels Erik N{\o}rlund",
title = "Hypergeometric functions",
journal = "Mat. Tidsskr. B.",
volume = "1950",
number = "??",
pages = "18--21",
year = "1950",
MRclass = "33.0X",
MRnumber = "MR0045259 (13,554e)",
MRreviewer = "S. C. van Veen",
bibdate = "Thu Dec 01 12:41:44 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0067.29402",
acknowledgement = ack-nhfb,
language = "Danish",
}
@TechReport{Stanley:1950:TRG,
author = "John Pearson Stanley and Maurice V. Wilkes",
title = "Table of the reciprocal of the gamma function for
complex argument",
type = "Report",
institution = "Computation Centre, University of Toronto",
address = "Toronto, ON, Canada",
pages = "????",
year = "1950",
MRclass = "65.0X",
MRnumber = "48144",
MRreviewer = "S. C. van Veen",
bibdate = "Sat Sep 07 16:52:05 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0040.06903",
abstract = "Toronto, ON, Canada",
acknowledgement = ack-nhfb,
author-dates = "Sir Maurice Vincent Wilkes (26 June 1913--29 November
2010)",
RSBM-number = "22",
ZBmath = "3060432",
}
@Book{Tolke:1950:PFE,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 1. Elementare und
elementare transzendente Funktionen}. ({German})
[{Practical} functional theory. 1. {Elementary} and
elementary transcendental functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 440",
year = "1950",
bibdate = "Mon Feb 13 19:12:35 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Tricomi:1950:AEU,
author = "F. G. Tricomi",
title = "{Asymptotische Eigenschaften der unvollst{\"a}ndigen
Gammafunktion}. ({German}) [{Asymptotic} properties of
the incomplete gamma function]",
journal = j-MATH-Z,
volume = "53",
number = "2",
pages = "136--148",
month = apr,
year = "1950",
CODEN = "MAZEAX",
DOI = "https://doi.org/10.1007/BF01162409",
ISSN = "0025-5874 (print), 1432-1823 (electronic)",
ISSN-L = "0025-5874",
bibdate = "Sat Feb 18 14:47:24 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/BF01162409",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Zeitschrift",
journal-URL = "http://link.springer.com/journal/209",
language = "German",
}
@Article{Cadwell:1951:BNI,
author = "J. H. Cadwell",
title = "The Bivariate Normal Integral",
journal = j-BIOMETRIKA,
volume = "38",
number = "3/4",
pages = "475--479",
month = dec,
year = "1951",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2332596",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
MRclass = "60.0X",
MRnumber = "0045960 (13,662h)",
MRreviewer = "G. E. Noether",
bibdate = "Sat Jun 21 14:32:38 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315418;
https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2332596",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://biomet.oxfordjournals.org/content/by/year;
http://www.jstor.org/journals/00063444.html",
}
@Article{Fogel:1951:FTE,
author = "{\`E}. K. Fogel'",
title = "A finite theory of elementary functions. {I}.
{Logarithmic} and exponential functions. ({Russian})",
journal = "Latvijas PSR Zin\=at{\c{n}}u Akad. V\=estis",
volume = "5",
number = "46",
pages = "801--813",
year = "1951",
MRclass = "33.0X",
MRnumber = "15,218b",
MRreviewer = "H. N. Shapiro",
bibdate = "Sat Apr 25 13:05:19 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@InProceedings{Gellman:1951:CCH,
author = "Harvey Gellman",
booktitle = "Proceedings of a Computation Seminar [{IBM Department
of Education, Endicot, NY, from December 5 to 9,
1949}]",
title = "The Calculation of Complex Hypergeometric Functions
with the {IBM Type 602-A} Calculating Punch",
publisher = "IBM",
address = "New York, NY, USA",
pages = "161--168",
year = "1951",
bibdate = "Mon Jun 18 06:09:24 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "A Computation Seminar, sponsored by the International
Business Machines Corporation, was held in the IBM
Department of Education, Endicot, NY, from December 5
to 9, 1949. Attending the Seminar were one hundred and
seven research engineers and scientists who are
experienced both in applying mathematical methods to
the solution of physical problems and in the associated
punched card methods of computation.",
}
@Article{Rutishauser:1951:BAK,
author = "Heinz Rutishauser",
title = "{Bemerkungen zur Arbeit von K. Emden ``Eine L{\"o}sung
f{\"u}r $ \int e^{b(x + a \cos x)} \, d x $}''.
({German}) [{Remarks} on the work by {K. Emden, ``A
solution for $ \int e^{b (x + a \ cos x)} \, d x
$''}]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "2",
number = "4",
pages = "292--293",
month = jul,
year = "1951",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/bf02579691",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRclass = "26.1X",
MRnumber = "44598",
MRreviewer = "F. J. Murray",
bibdate = "Mon Aug 24 21:56:15 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Heinz Rutishauser (30 January 1918--10 November
1970)",
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
ZAMP. Journal of Applied Mathematics and Physics.
Journal de Math\'{e}matiques et de Physique
Appliqu\'{e}es",
journal-URL = "http://link.springer.com/journal/33",
language = "German",
}
@Article{Salzer:1951:FCE,
author = "H. E. Salzer",
title = "Formulas for Calculating the Error Function of a
Complex Variable",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "34",
pages = "67--70",
month = apr,
year = "1951",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1951-0048150-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Salzer:1951:RTT,
author = "H. E. Salzer",
title = "Radix Table for Trigonometric Functions and their
Inverses to High Accuracy",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "33",
pages = "9--11",
month = jan,
year = "1951",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-51-99447-1",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Wilkes:1951:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
pages = "167",
year = "1951",
LCCN = "QA76.5 .W55 1951",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also second edition \cite{Wilkes:1957:PPE}, and
reprint \cite{Wilkes:1982:PPE}.",
acknowledgement = ack-nhfb,
tableofcontents = "Part I \\
Chapter 1. The Design of Programs for Electronic
Computing Machines / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machines / 2 \\
1-3 Description of the EDSAC / 3 \\
1-4 The EDSAC order code / 5 \\
1-5 Notes on the order code / 6 \\
1-6 The use of conditional orders / 7 \\
1-7 Modification of orders by the program / 8 \\
1-8 Multiaddress codes / 11 \\
1-9 Binary--decimal conversion / 12 \\
1-10 Checking facilities / 14 \\
Chapter 2. Input of Orders / 15 \\
2-1 Initial orders / 15 \\
2-2 Pseudo-orders / 17 \\
2-3 Examples / 17 \\
2-4 Control combinations / 17 \\
2-5 Starting the program / 18 \\
2-6 Use of code letters / 19 \\
2-7 Constants / 20 \\
2-8 Notation / 20 \\
Chapter 3. Subroutines and Parameters / 22 \\
3-1 Open subroutines / 22 \\
3-2 closed subroutines / 22 \\
3-3 preset parameters / 23 \\
3-4 program parameters / 23 \\
Chapter 4. Library Subroutines and their Use in
Constructing Programs / 25 \\
4-1 Library catalog / 25 \\
4-2 Input and output subroutines / 25 \\
4-3 Division subroutines / 27 \\
4-4 Trigonometrical and other functions / 27 \\
4-5 Quadrature / 27 \\
4-6 Assembly subroutines / 27 \\
4-7 Integration of differential equations / 32 \\
4-8 Processes, Interpretive subroutines / 34 \\
Chapter 5. Pitfalls / 38 \\
5-1 Proofreading of programs, points to be checked / 38
\\
5-2 Location of mistakes in a program / 39 \\
5-3 Counting operations / 41 \\
Chapter 6. Use of the EDSAC \& Its Associated Equipment
/ 42 \\
6-1 Tape Punching \& editing facilities / 42 \\
6-2 Storage of library subroutines / 43 \\
6-3 EDSAC organization / 43 \\
6-4 EDSAC controls / 43 \\
Chapter 7. Examples / 45 \\
7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
7-2 Example 2. Calculation of $\pi$ by evaluation of
definite integral / 48 \\
7-3 Alternative method for Example 2 / 52 \\
7-4 Example 2, with extra print orders for checking /
53 \\
7-5 Application of checking subroutine C11 to Example 2
/ 54 \\
7-6 Example of integration of an ordinary differential
equation / 46 \\
7-7 Evaluation of a definite integral / 61 \\
7-8 Program to facilitate the solution of algebraic
equation / 66 \\
Part II. Specifications of Library Subroutines / 72 \\
A. Subroutines to carry out floating point arithmetic /
73 \\
B. Subroutines to carry out arithmetical operations on
complex numbers / 78 \\
C. Checking subroutines / 79 \\
D. Division subroutines / 82 \\
E. Exponential subroutines / 83 \\
F. General routines relating to functions / 84 \\
G. Subroutines for integration of ordinary differential
equations / 86 \\
J. Subroutines for calculating special functions
[Legendre polynomials] / 88 \\
K. Subroutines for the summation of power series / 88
\\
L. Subroutines for evaluating logarithms / 91 \\
M. Miscellaneous subroutines / 91 \\
P. Print subroutines / 92 \\
Q. Quadrature subroutines / 95 \\
R. Input subroutines / 96 \\
S. Subroutines for evaluation of fractional powers / 98
\\
T. Subroutines for calculating trigonometrical
functions / 99 \\
U. Subroutines for counting operations / 101 \\
V1. Multiplication of vector by symmetric matrix / 102
\\
V2. Addition and subtraction of $n$ dimensional vectors
/ 103 \\
Part III. Programs of Selected Library Subroutines /
104 \\
Appendix A. Keyboard perforator code, etc. / 158 \\
Appendix B. The initial orders / 159 \\
Appendix C. Control combinations / 161 \\
Appendix D. Interpretive subroutines: example of
packing of orders / 162 \\
Appendix E. Methods of counting in a simple cycle / 164
\\
Index",
}
@Book{Anonymous:1952:BFP,
author = "Anonymous",
title = "{Bessel} Functions, {Part II}",
volume = "10",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "????",
year = "1952",
bibdate = "Tue Nov 14 14:59:31 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "British Association Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: was Leslie Fox a co-author?? Who were the
authors?? Page count??",
}
@InBook{Goncarov:1952:EFC,
author = "V. L. Gon{\v{c}}arov",
booktitle = "Encyclopaedia of elementary mathematics. {Book III}.
{Functions} and limits (the foundations of analysis)",
title = "Elementary functions of a complex variable",
publisher = "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
address = "Moscow-Leningrad, USSR",
pages = "491--552",
year = "1952",
MRclass = "30.0X",
MRnumber = "14,1073c",
MRreviewer = "R. P. Boas, Jr.",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Goncarov:1952:EFR,
author = "V. L. Gon{\v{c}}arov",
booktitle = "Encyclopaedia of elementary mathematics. {Book III}.
{Functions} and limits (the foundations of analysis)",
title = "Elementary functions of a real variable. Limits of
sequences and functions. {The} general concept of a
function",
publisher = "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
address = "Moscow-Leningrad, USSR",
pages = "9--296",
year = "1952",
MRclass = "27.2X",
MRnumber = "14,1070d",
MRreviewer = "R. P. Boas, Jr.",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Kuipers:1952:PSE,
author = "L. Kuipers",
title = "Properties of some elementary functions",
journal = "Nederl. Akad. Wetensch. Proc. Ser. A. = Indagationes
Math.",
volume = "55",
number = "14",
pages = "388--393",
year = "1952",
MRclass = "27.0X",
MRnumber = "14,360e",
MRreviewer = "E. Frank",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Bowman:1953:IEF,
author = "Frank Bowman",
title = "Introduction to Elliptic Functions with Applications",
publisher = "English Universities Press",
address = "London, UK",
pages = "115",
year = "1953",
LCCN = "QA343 .B76 1953",
bibdate = "Wed Mar 15 06:50:49 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
subject = "Elliptic functions; Elliptische functies",
}
@InProceedings{Lovelace:1953:AET,
author = "Ada Augusta Lovelace",
title = "{Appendix 1}: {Extracts} From {{\booktitle{Taylor's
Scientific Memoirs}}, Vol. III}",
crossref = "Bowden:1953:FTT",
pages = "341--408",
year = "1953",
bibdate = "Fri Jun 08 08:33:30 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Reprint of \cite{Lovelace:1843:SAE}. Pages 400--408
describe the computation of the Bernoulli numbers.",
acknowledgement = ack-nhfb,
}
@Article{Salzer:1953:RTO,
author = "Herbert E. Salzer",
title = "Radix Table for Obtaining Hyperbolic and Inverse
Hyperbolic Functions to Many Places",
journal = j-J-MATH-PHYS-MIT,
volume = "32",
number = "1--4",
pages = "197--202",
month = apr,
year = "1953",
CODEN = "JMPHA9",
DOI = "https://doi.org/10.1002/sapm1953321197",
ISSN = "0097-1421",
ISSN-L = "0097-1421",
bibdate = "Sat Aug 19 13:35:59 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib",
URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1953321197",
acknowledgement = ack-nhfb,
ajournal = "J. Math. Phys. (MIT)",
fjournal = "Journal of Mathematics and Physics (MIT)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590",
onlinedate = "April 1953",
}
@Article{Scherberg:1953:ACP,
author = "Max G. Scherberg and John F. Riordan",
title = "Analogue Calculation of Polynomial and Trigonometric
Expansions (in {Other Aids to Computation})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "7",
number = "41",
pages = "61--65",
month = jan,
year = "1953",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-53-99373-9",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Stiefel:1953:ITF,
author = "E. Stiefel",
title = "{Zur Interpolation von tabellierten Funktionen durch
Exponentialsummen und zur Berechnung von Eigenwerten
aus den Schwarzschen Konstanten}. ({German}) [{On}
interpolation of tabulated functions by exponential
sums and on the calculation of eigenvalues from the
{Schwarz}'s constants]",
journal = j-Z-ANGE-MATH-MECH,
volume = "33",
pages = "260--262",
year = "1953",
CODEN = "ZAMMAX",
DOI = "https://doi.org/10.1002/zamm.19530330806",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
MRclass = "65.0X",
MRnumber = "59061",
MRreviewer = "D. C. Gilles",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
fjournal = "Zeitschrift f{\"{u}}r Angewandte Mathematik und
Mechanik. Ingenieurwissenschaftliche
Forschungsarbeiten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
language = "German",
}
@Article{Turing:1953:SCR,
author = "A. M. Turing",
title = "Some calculations of the {Riemann} zeta-function",
journal = j-PROC-LONDON-MATH-SOC-3,
volume = "3",
number = "3",
pages = "99--117",
year = "1953",
CODEN = "PLMTAL",
ISSN = "0024-6115 (print), 1460-244X (electronic)",
ISSN-L = "0024-6115",
MRclass = "65.0X",
MRnumber = "MR0055785 (14,1126e)",
MRreviewer = "D. H. Lehmer",
bibdate = "Sat Nov 19 13:23:32 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See corrections and improvements
\cite{Lehman:1970:DZR}, and \cite{Trudgian:2011:ITM}.
The latter comments: ``Turing's Method has become the
standard technique used in modern verification of the
Riemann hypothesis.'' See also
\cite{Lehmer:1956:RRZ}.",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/21",
ZMnumber = "0050.08101",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the London Mathematical Society. Third
Series",
}
@Article{Aaboe:1954:AKI,
author = "Asger Aaboe",
title = "{Al-K{\=a}sh{\v{\i}}}'s iteration method for the
determination of $ \sin 1^\circ $",
journal = j-SCRIPTA-MATH,
volume = "20",
number = "??",
pages = "24--29",
month = "????",
year = "1954",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
MRclass = "01.0X",
MRnumber = "62046",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0055.00104",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
ZBmath = "3086736",
}
@Article{Atta:1954:CGH,
author = "Susie E. Atta and Ward C. Sangren",
title = "Calculation of Generalized Hypergeometric Series",
journal = j-J-ACM,
volume = "1",
number = "4",
pages = "170--172",
month = oct,
year = "1954",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320783.320785",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 08 21:50:00 1994",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Cahill:1954:PCH,
author = "W. F. Cahill",
title = "Programs for Computing the Hypergeometric Series (in
Automatic Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
number = "45",
pages = "36--37",
month = jan,
year = "1954",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-54-99344-8",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Clenshaw:1954:PAE,
author = "C. W. Clenshaw",
title = "Polynomial approximations to elementary functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
number = "47",
pages = "143--147",
month = jul,
year = "1954",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1954-0063487-2",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "41.1X",
MRnumber = "16,128f",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Fox:1954:STB,
author = "L. Fox",
title = "A Short Table for {Bessel} Functions of Integer Orders
and Large Arguments",
volume = "3",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "28",
year = "1954",
MRclass = "65.0X",
MRnumber = "65245",
MRreviewer = "R. C. Archibald",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Royal Society Shorter Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@TechReport{Franklin:1954:CARa,
author = "J. Franklin and B. Friedman",
title = "A convergent asymptotic representation for integrals",
institution = "Division of Electromagnetic Research, Institute of
Mathematical Sciences, New York University",
address = "New York, NY, USA",
pages = "i + 17",
year = "1954",
MRclass = "40.0X",
MRnumber = "0068019",
MRreviewer = "J. G. van der Corput",
bibdate = "Tue Feb 06 15:03:36 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Res. Rep. No. BR-9",
acknowledgement = ack-nhfb,
remark = "See applications in
\cite{Temme:2015:AMI,Navas-Palencia:2018:HPC}.",
}
@Article{LaFara:1954:MCI,
author = "Robert L. LaFara",
title = "A Method for Calculating Inverse Trigonometric
Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
number = "47",
pages = "132--139",
month = jul,
year = "1954",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1954-0063150-8",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InCollection{Ostrowski:1954:TPA,
author = "A. M. Ostrowski",
title = "On two problems in abstract algebra connected with
{Horner}'s rule",
crossref = "Birkhoff:1954:SMM",
pages = "40--48",
year = "1954",
bibdate = "Fri Oct 20 10:13:10 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "number of multiplications to evaluate a polynomial",
remark = "TO DO: Find copy of this book section.",
}
@Article{Shenton:1954:INI,
author = "L. R. Shenton",
title = "Inequalities for the Normal Integral Including a New
Continued Fraction",
journal = j-BIOMETRIKA,
volume = "41",
number = "1/2",
pages = "177--189",
month = jun,
year = "1954",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2333015",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
MRclass = "62.0X",
MRnumber = "0061785 (15,884e)",
MRreviewer = "E. Lukacs",
bibdate = "Sat Jun 21 14:32:43 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315422;
https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2333015",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://biomet.oxfordjournals.org/content/by/year;
http://www.jstor.org/journals/00063444.html",
}
@InProceedings{Todd:1954:MWN,
author = "John Todd",
editor = "????",
booktitle = "Transactions of {2nd Symposium on Applied Mathematics,
29 April 1954, University of Chicago}",
title = "Motivation for working on numerical analysis",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "????",
year = "1954",
bibdate = "Fri Oct 20 13:28:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Sponsored by the American Mathematical Society and the
Office of Ordnance Research",
}
@Article{Booth:1955:NAP,
author = "A. D. Booth",
title = "A note on approximating polynomials for trigonometric
functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
number = "49",
pages = "21--23",
month = jan,
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1955-0069579-7",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "69579",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@TechReport{Carlson:1955:RAF,
author = "Bengt Carlson and Max Goldstein",
title = "Rational Approximations of Functions",
type = "Report",
number = "LA-1943",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "iv + 46",
month = aug,
year = "1955",
DOI = "https://doi.org/10.2172/4374577",
bibdate = "Sat Dec 27 09:41:36 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.osti.gov/scitech/biblio/4374577-0deJO9/;
http://www.osti.gov/scitech/servlets/purl/4374577",
acknowledgement = ack-nhfb,
keywords = "$-\ln(x)/(1 - x)$; $\art(x) / x$; $\cos(x)$;
$\exp(-x)$; $\sin(x) / x$; $\tan(x) / x$; $x \cot(x)$;
$x**(1/2)$; $x**(1/3)$; $x**(1/4)$; $x**(1/5)$;
$x**(1/6)$; $x**(1/7)$; continued fractions; rational
approximations",
remark = "Cited in \cite[page 71]{Abramowitz:1964:HMF}.",
}
@Article{Clenshaw:1955:NSC,
author = "C. W. Clenshaw",
title = "A Note on the Summation of {Chebyshev} Series",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
number = "51",
pages = "118--120",
month = jul,
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "0071856",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Chebyshev series; Clenshaw algorithm; Clenshaw
summation; Horner polynomial evaluation",
remark = "Hidden inside \cite{Brenner:1955:TNS}, but important
in its own right for commentary on the recursive
algorithm for summation of Chebyshev series, and a
brief analysis of its accuracy.",
}
@Article{Froberg:1955:NTC,
author = "Carl-Erik Fr{\"o}berg",
title = "Numerical Treatment of {Coulomb} Wave Functions",
journal = j-REV-MOD-PHYS,
volume = "27",
number = "4",
pages = "399--411",
month = oct,
year = "1955",
CODEN = "RMPHAT",
DOI = "https://doi.org/10.1103/RevModPhys.27.399",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
bibdate = "Tue May 22 16:36:44 MDT 2012",
bibsource = "http://rmp.aps.org/toc/RMP/v27/i4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/revmodphys1950.bib",
URL = "http://link.aps.org/doi/10.1103/RevModPhys.27.399;
http://rmp.aps.org/abstract/RMP/v27/i4/p399_1",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
}
@Book{Hastings:1955:ADC,
author = "Cecil {Hastings, Jr.}",
title = "Approximations for Digital Computers",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "viii + 201",
year = "1955",
ISBN = "0-691-07914-5",
ISBN-13 = "978-0-691-07914-1",
LCCN = "QA76 .H37",
bibdate = "Mon Oct 01 15:59:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
note = "Assisted by Jeanne T. Hayward and James P. Wong, Jr.",
series = "The Rand series",
acknowledgement = ack-nhfb,
remark-1 = "Reprinted 1957, 1959, 1962, 1966, and 1970. I have
fourth printing (1962).",
remark-2 = "Hastings gives a polynomial approximation for
computing random numbers from a normal distribution.",
subject = "Electronic digital computers; Numerical analysis",
tableofcontents = "Preface / v \\
Part I \\
1: Concerning Best Fit / 3 \\
2: Linear Weights / 19 \\
3: An Iterative Procedure / 27 \\
4: Solution of Equations / 35 \\
5: Chebyshev Polynomials / 47 \\
6: Concerning Weights / 65 \\
7: Function With a Peak / 75 \\
8: Rates of Convergence / 83 \\
9: Choice of Form / 95 \\
10: A Scoring-Camera Problem / 115 \\
Part II \\
1: $\log_{10} x$ / 125 \\
5: $\phi(x) = (1 - e^{-x}) / x$ / 129 \\
8: $\arctan x$ / 132 \\
14: $\sin (\pi/2) x$ / 138 \\
17: $10^x$ / 141 \\
21: $W(x) = e^{-x} / (1 + e^{-x})^2$ / 145 \\
24: $P_k(x) = 1.72 + 42 x^2$ or $0.136 / x^2$ / 148 \\
27: $E'(x) = (1 / \sqrt{2 \pi}) e^{-(1/2)x^2}$ / 151
\\
30: ``Total Klein-Nishina Cross Section'' Function /
154 \\
31: $\Gamma(1 + x)$ / 155 \\
35: $\arcsin x$ / 159 \\
40: $\log_2 x$ / 164 \\
43: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \,
dt$ / 167 \\
46: $K(k) = \int_0^{\pi/2} (1 / \sqrt{1 - k^2 \sin^2
\phi}) \, d\phi$ / 170 \\
49: $E(k) = \int_0^{\pi/2} (\sqrt{1 - k^2 \sin^2 \phi})
\, d\phi$ / 173 \\
52: $\ln(1 + x)$ / 176 \\
57: $e^{-x}$ / 181 \\
61: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \,
dt$ / 185 \\
64: $-{\rm Ei}(-x) = \int_x^\infty (e^{-t} / t) \, dt$
/ 188 \\
67: $q = (1 / \sqrt{2 \pi}) \int_{x(q)}^\infty
e^{-(1/2)t^2} \, dt$ / 191 \\
69: $W(z) = \int_0^\infty (e^(-u z) / (K_1^2(u) + \pi^2
I_1^2(u))) (1/u) \, du$ / 193 \\
71: $P(x) = \int_x^\infty (\sin(t - x) / t) \, dt$ /
195 \\
74: $Q(x) = \int_x^\infty (\cos(t - x) / t) \, dt$ /
195 \\
References for Part II / 201",
}
@Book{Hobson:1955:TSE,
author = "Ernest William Hobson",
title = "The Theory of Spherical and Ellipsoidal Harmonics",
publisher = "Chelsea Pub. Co.",
address = "New York, NY, USA",
pages = "500",
year = "1955",
LCCN = "QA406 .H7 1955",
bibdate = "Sat Apr 1 14:40:56 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1856--1933",
subject = "Spherical harmonics; Lam{\'e}'s functions",
}
@Book{McLachlan:1955:BFE,
author = "N. W. (Norman William) McLachlan",
title = "{Bessel} Functions for Engineers",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
edition = "Second",
pages = "xii + 239",
year = "1955",
LCCN = "QA408 .M3 1955",
bibdate = "Sat Apr 1 14:44:36 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "The Oxford engineering science series",
acknowledgement = ack-nhfb,
author-dates = "1888--",
subject = "Bessel functions",
}
@Article{Motzkin:1955:EP,
author = "T. S. Motzkin",
title = "Evaluation of polynomials",
journal = j-BULL-AMS,
volume = "61",
number = "2",
pages = "163--163",
month = mar,
year = "1955",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Fri Oct 20 09:06:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
issue = "635",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
keywords = "number of multiplications to evaluate a polynomial",
received = "12 November 1954",
remark = "One-paragraph abstract only, with reference-less
mention of Ostrowski.",
}
@Article{Motzkin:1955:ERF,
author = "T. S. Motzkin",
title = "Evaluation of rational functions",
journal = j-BULL-AMS,
volume = "61",
number = "2",
pages = "163--163",
month = mar,
year = "1955",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Fri Oct 20 09:06:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
issue = "635",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
keywords = "number of multiplications to evaluate a polynomial",
received = "12 November 1954",
remark = "One-paragraph abstract only, with reference to
Ostrowski.",
}
@Article{Norlund:1955:HF,
author = "Niels Erik N{\o}rlund",
title = "Hypergeometric functions",
journal = j-ACTA-MATH,
volume = "94",
number = "??",
pages = "289--349",
month = "????",
year = "1955",
CODEN = "ACMAA8",
DOI = "https://doi.org/10.1007/BF02392494",
ISSN = "0001-5962 (print), 1871-2509 (electronic)",
ISSN-L = "0001-5962",
MRclass = "33.0X",
MRnumber = "MR0074585 (17,610d)",
MRreviewer = "A. Erd{\'e}lyi",
bibdate = "Thu Dec 01 10:09:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Acta Mathematica",
journal-URL = "http://link.springer.com/journal/11511",
}
@Article{Preston:1955:ACS,
author = "F. S. Preston",
title = "An Analog Computer for the Solution of Tangents",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-4",
number = "3",
pages = "101--106",
month = "????",
year = "1955",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/IRETELC.1955.507908",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407908",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Robinson:1955:EAC,
author = "A. S. Robinson",
title = "An Electronic Analog Computing Technique for the
Solution of Trigonometric Problems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-4",
number = "3",
pages = "95--101",
month = "????",
year = "1955",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/IRETELC.1955.5407907",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407907",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Salzer:1955:CZE,
author = "Herbert E. Salzer",
title = "Complex zeros of the error function",
journal = j-J-FRANKLIN-INST,
volume = "260",
number = "3",
pages = "209--211",
month = sep,
year = "1955",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(55)90732-8",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "65.1X",
MRnumber = "71880",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Franklin Institute",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Todd:1955:MWN,
author = "John Todd",
title = "Motivation for working in numerical analysis",
journal = j-COMM-PURE-APPL-MATH,
volume = "8",
number = "1",
pages = "97--116",
month = feb,
year = "1955",
CODEN = "CPAMAT, CPMAMV",
DOI = "https://doi.org/10.1002/cpa.3160080107",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
MRclass = "65.0X",
MRnumber = "70251",
MRreviewer = "G. E. Forsythe",
bibdate = "Fri Oct 20 08:38:37 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0064.37402",
acknowledgement = ack-nhfb,
ajournal = "Comm. Pure Appl. Math.",
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
keywords = "characteristic roots (eigenvalues) of finite matrices;
game theory; integral equations; modified differences;
Monte Carlo; number of multiplications to evaluate a
polynomial; polynomial evaluation; quadrature; recent
activity in numerical analysis; sequence convergence
acceleration; theory of machines (automata)",
remark-1 = "This may be the earliest paper to note that a
polynomial of degree $n$ can be evaluated with fewer
than $n$ multiplications, but requiring more than $n$
additions. The normal Horner form requires $n$ multiply
and $n$ add operations: $ h = a_n $, $ h = x h + a_k $
(for $ k = n - 1 $ to $0$), and on modern hardware can
be conveniently evaluated in $n$ consecutive fused
multiply-add operations. However, the evaluation of the
altered forms often has terms of differing signs, and
may be subject to catastrophic leading digit loss, when
the original polynomial, if it had coefficients of the
same sign, might have been computed stably for $ x >
0$. In some cases, the new coefficients are complex,
even when those of the original polynomial are real
numbers. See also related publications
\cite{Ostrowski:1954:TPA, Todd:1954:MWN,
Motzkin:1955:EP, Motzkin:1955:ERF, Belaga:1958:SPI,
Pan:1959:CSC, Pan:1959:SCP, Floyd:1961:ACE,
Dorn:1962:GHR, Knuth:1962:EPC, Eisman:1963:PER,
Eve:1964:EP, Rice:1965:CPR, Winograd:1970:NMN,
Rabin:1972:FEP, Miller:1975:CCN, Knuth:1998:EP,
Kusterer:1979:SEP, Ceberio:2002:HRI, Cameron:2024:AHM}.
Rice reports extreme numerical instability of the
Belaga and Motzkin forms, and moderate instability of
the Pan forms, while the Chebyshev form is never
unstable. Todd cites Motzkin's work as ``to appear'',
and those two one-paragraph abstracts were received 12
November 1954 and published in March 1955, but Todd's
paper has no received date, so we cannot determine
their relative priority. Entry
\cite{Ostrowski:1954:TPA} may be prior art, but a copy
of that work has not yet been located. The quotation in
entry \cite{Eve:1964:E} summarizes the bounds on the
number of add and multiply operations.",
remark-2 = "Knuth's treatment (Knuth:1962:EPC) concentrates on
operation counts, because the polynomial variable need
not be a real scalar floating-point number: it could be
complex, multiple precision, matrix, series, ..., where
multiplication is relatively expensive. Knuth remarks
on page 485 that ``numerical analysis of the accuracy
achieved \ldots{} is beyond the scope of this book: the
reader should be careful to investigate the accuracy of
any calculations undertaken with floating-point
arithmetic.'' On page 486, Knuth notes that the nested
form is often attributed to Horner:1819:XNM, but that
Isaac Newton used it in unpublished notes 150 years
earlier, and it was employed by the Chinese in the 13th
century CE.",
remark-3 = "The year of this paper is erroneously cited in
reference lists of several sources as 1951, rather than
the correct 1955.",
ZBmath = "3109832",
}
@Book{Achieser:1956:TA,
author = "N. I. Achieser",
title = "Theory of Approximation",
publisher = "Frederick Ungar Publishing Company",
address = "New York, NY, USA",
pages = "x + 307",
year = "1956",
LCCN = "QA221 .A533 1956",
bibdate = "Fri Oct 20 08:06:59 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Translation of Russian original, Lek{\"e}t{\`\i}sii po
teorii approksima{\"e}t{\`\i}sii. Reprinted in
\cite{Achieser:1992:TA}.",
subject = "Mathematical analysis",
tableofcontents = "Approximation Problems in Linear Normalized Spaces
\\
Formulation of the Principal Problem in the Theory of
Approximation / 1 \\
The Concept of Metric Space / 1 \\
The Concept of Linear Normalized Space / 2 \\
Examples of Linear Normalized Spaces / 3 \\
The Inequalities of Holder and Minkowski / 4 \\
Additional Examples of Linear Normalized Spaces / 7 \\
Hilbert Space / 8 \\
The Fundamental Theorem of Approximation Theory in
Linear Normalized Spaces / 10 \\
Strictly Normalized Spaces / 11 \\
An Example of Approximation in the Space $L^p$ / 12 \\
Geometric Interpretation / 13 \\
Separable and Complete Spaces / 14 \\
Approximation Theorems in Hilbert Space / 15 \\
An Example of Approximation in Hilbert Space / 19 \\
More About the Approximation Problem in Hilbert Space /
21 \\
Orthonormalized Vector Systems in Hilbert Space / 22
\\
Orthogonalization of Vector Systems / 23 \\
Infinite Orthonormalized Systems / 25 \\
An Example of a Non-Separable System / 29 \\
Weierstrass' First Theorem / 29 \\
Weierstrass' Second Theorem / 32 \\
The Separability of the Space C / 33 \\
The Separability of the Space $L^p$ / 34 \\
Generalization of Weierstrass' Theorem to the Space
$L^p$ / 37 \\
The Completeness of the Space $L^p$ / 38 \\
Examples of Complete Orthonormalized Systems in
L[superscript 2] / 40 \\
Muntz's Theorem / 43 \\
The Concept of the Linear Functional / 46 \\
F. Riesz's Theorem / 47 \\
A Criterion for the Closure of a Set of Vectors in
Linear Normalized Spaces / 49 \\
P. L. Tchebysheff's Domain of Ideas \\
Statement of the Problem / 51 \\
A Generalization of the Theorem of de la Vallee-Poussin
/ 52 \\
The Existence Theorem / 53 \\
Tchebysheff's Theorem / 55 \\
A Special Case of Tchebysheff's Theorem / 57 \\
The Tchebysheff Polynomials of Least Deviation from
Zero / 57 \\
A Further Example of P. Tchebysheff's Theorem / 58 \\
An Example for the Application of the General Theorem
of de la Vallee-Poussin / 60 \\
An Example for the Application of P. L. Tchebysheff's
General Theorem / 62 \\
The Passage to Periodic Functions / 64 \\
An Example of Approximating with the Aid of Periodic
Functions / 66 \\
The Weierstrass Function / 66 \\
Haar's Problem / 67 \\
Proof of the Necessity of Haar's Condition / 68 \\
Proof of the Sufficiency of Haar's Condition / 69 \\
An Example Related to Haar's Problem / 72 \\
P. L. Tchebysheff's Systems of Functions / 73 \\
Generalization of P. L. Tchebysheff's Theorem / 74 \\
On a Question Pertaining to the Approximation of a
Continuous Function in the Space $L$ / 76 \\
A. A. Markoff's Theorem / 82 \\
Special Cases of the Theorem of A. A. Markoff / 85 \\
Elements of Harmonic Analysis \\
The Simplest Properties of Fourier Series / 89 \\
Fourier Series for Functions of Bounded Variation / 93
\\
The Parseval Equation for Fourier Series / 97 \\
Examples of Fourier Series / 98 \\
Trigonometric Integrals / 101 \\
The Riemann--Lebesgue Theorem / 103 \\
Plancherel's Theory / 104 \\
Watson's Theorem / 106 \\
Plancherel's Theorem / 108 \\
Fejer's Theorem / 110 \\
Integral-Operators of the Fejer Type / 113 \\
The Theorem of Young and Hardy / 116 \\
Examples of Kernels of the Fejer Type / 118 \\
The Fourier Transformation of Integrable Functions /
120 \\
The Faltung of two Functions / 122 \\
V. A. Stekloff's Functions / 123 \\
Multimonotonic Functions / 125 \\
Conjugate Functions / 126 \\
Certain Extremal Properties of Integral Transcendental
Functions of the Exponential Type \\
Integral Functions of the Exponential Type / 130 \\
The Borel Transformation / 132 \\
The Theorem of Wiener and Paley / 134 \\
Integral Functions of the Exponential Type which are
Bounded along the Real Axis / 137 \\
S. N. Bernstein's Inequality / 140 \\
B. M. Levitan's Polynomials / 146 \\
The Theorem of Fejer and Riesz. A Generalization of
This Theorem / 152 \\
A Criterion for the Representation of Continuous
Functions as Fourier--Stieltjes Integrals / 154 \\
Questions Regarding the Best Harmonic Approximation of
Functions Preliminary Remarks / 160 \\
The Modulus of Continuity / 161 \\
The Generalization to the Space $L^p$ ($p \geq 1$) /
162 \\
An Example of Harmonic Approximation / 165 \\
Some Estimates for Fourier Coefficients / 169 \\
More about V. A. Stekloff's Functions / 173 \\
Two Lemmas / 175 \\
The Direct Problem of Harmonic Approximation / 176 \\
A Criterion due to B. Sz.-Nagy / 183 \\
The Best Approximation of Differentiable Functions /
187 \\
Direct Observations Concerning Periodic Functions / 195
\\
Jackson's Second Theorem / 199 \\
The Generalized Fejer Method / 201 \\
Berstein's Theorem / 206 \\
Priwaloff's Theorem / 210 \\
Generalizations of Bernstein's Theorems to the Space
$L^p$ ($p \geq 1$) / 211 \\
The Best Harmonic Approximation of Analytic Functions /
214 \\
A Different Formulation of the Result of the Preceding
Section / 218 \\
The Converse of Bernstein's Theorem / 221 \\
Wiener's Theorem on Approximation \\
Wiener's Problem / 224 \\
The Necessity of Wiener's Condition / 224 \\
Some Definitions and Notation / 225 \\
Several Lemmas / 227 \\
The Wiener--Levy Theorem / 230 \\
Proof of the Sufficiency of Wiener's Condition / 233
\\
Wiener's General Tauber Theorem / 234 \\
Weakly Decreasing Functions / 235 \\
Remarks on the Terminology / 237 \\
Ikehara's Theorem / 238 \\
Carleman's Tauber Theorem / 241 \\
Various Addenda and Problems \\
Elementary Extremal Problems and Certain Closure
Criteria / 243 \\
Szego's Theorem and Some of Its Applications / 256 \\
Further Examples of Closed Sequences of Functions / 267
\\
The Caratheodory--Fejer Problem and Similar Problems /
270 \\
Solotareff's Problems and Related Problems / 280 \\
The Best Harmonic Approximation of the Simplest
Analytic Functions / 289 \\
Notes / 296 \\
Index / 306",
}
@InProceedings{Haynes:1956:EIE,
author = "John G. Haynes",
editor = "????",
booktitle = "{ACM'56: Proceedings of the 1956 11th ACM national
meeting}",
title = "Evaluation of incomplete elliptic integrals by
{Gaussian} integration",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "56--59",
year = "1956",
DOI = "https://doi.org/10.1145/800258.808948",
bibdate = "Fri Dec 21 08:53:15 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=808948",
acknowledgement = ack-nhfb,
}
@Book{Jeffreys:1956:MMP,
author = "Harold Jeffreys and Bertha {Swirles Jeffreys}",
title = "Methods of Mathematical Physics",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Third",
pages = "714",
year = "1956",
LCCN = "QA401 .J4 1956",
bibdate = "Thu Aug 17 10:48:45 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://en.wikipedia.org/wiki/Bertha_Swirles;
https://en.wikipedia.org/wiki/Harold_Jeffreys",
acknowledgement = ack-nhfb,
author-dates = "Sir Harold Jeffreys (22 April 1891--18 March 1989);
Lady Bertha Swirles Jeffreys (22 May 1903--18 December
1999)",
remark = "References to Douglas Hartree in",
remark-1 = "First edition 1946, second edition 1950, third edition
1956, first paperback edition 1972, reprinted 1978,
1980, 1988, 1992, 1999, 2001. Third edition preface is
dated April 1953. Second edition preface is dated 15
November 1948. First edition preface is dated 1946.
Reprinted in \cite{Jeffreys:1999:MMP}.",
subject-dates = "Douglas Rayner Hartree (27 March 1897--12 February
1958)",
tableofcontents = "Preface \\
Authors' Notes \\
1: The Real Variable \\
2: Scalars and Vectors \\
3: Tensors \\
4: Matrices \\
5: Multiple Integrals \\
6: Potential Theory \\
7: Operational Methods \\
8: Physical Applications of the Operational Method \\
9: Numerical Methods \\
10: Calculus of Variations \\
11: Functions of a Complex Variable \\
12: Contour Integration and Bromwich's Integral \\
13: Conformal Representation \\
14: Fourier's Theorem \\
15: The Factorial and Related Functions \\
16: Solution of Linear Differential Equation \\
17: Asymptotic Expansions \\
18: The Equations of Potential, Waves, and Heat
Conduction \\
19: Waves in One Dimension and Waves With Spherical
Symmetry \\
20: Conduction of Heat in One and Three Dimensions \\
21: Bessel Functions \\
22: Applications of Bessel Functions \\
23: The Confluent Hypergeometric Function \\
24: Legendre Functions and Associated Functions \\
25: Elliptic Functions \\
Notes \\
Appendix on Notation \\
Index",
}
@Article{Lehmer:1956:RRZ,
author = "D. H. Lehmer",
title = "On the roots of the {Riemann} zeta-function",
journal = j-ACTA-MATH,
volume = "95",
number = "1",
pages = "291--298",
month = dec,
year = "1956",
CODEN = "ACMAA8",
DOI = "https://doi.org/10.1007/BF02401102",
ISSN = "0001-5962 (print), 1871-2509 (electronic)",
ISSN-L = "0001-5962",
MRclass = "10.1X",
MRnumber = "0086082 (19,121a)",
MRreviewer = "L. Schoenfeld",
bibdate = "Mon Sep 28 16:18:23 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Acta Mathematica",
journal-URL = "http://link.springer.com/journal/11511",
remark-1 = "See \cite[references 38--39, page
54]{Bullynck:2015:CPT} for Turing's role in this work,
published two years after Turing's death in 1954.
Turing's incomplete work appears in
\cite{Turing:1953:SCR}.",
remark-2 = "From page 293: ``Plans to extend the work of
Titchmarsh [on the zeros of the Riemann zeta function]
by use of a differential analyzer were made in 1939 by
the late A. M. Turing. These were interrupted by the
war and later rendered obsolete by the advent of the
electronic digital computers.''",
remark-3 = "From page 293: ``In 1947 the writer programmed an
extension of the work of Titchmarsh [on the zeros of
the Riemann zeta function] for the ENIAC, the only
electronic computer then in operation. However, before
the program could be run, the ENIAC was drastically
modified thus rendering it useless for the problem.''",
remark-4 = "From page 293: ``In June 1950, Turing used the
Manchester University Mark 1 electronic digital
computer to examine the zeta-function for $24,937.96 <
t < 25,735.93$ (that is for $63 < \sqrt{\tau} < 6.4$)
and found in this region of the critical strip that
there are about 1070 simple zeros all with $a = 1/2$.
In another short run the validity of the Riemann
Hypothesis was verified between Titchmarsh's upper
limit of $t = 1468$ and $t = 1540$. Only some twenty
hours of machine time was used. Unfortunately no
further time was made available and these incomplete
results were published in 1953.''",
}
@InProceedings{Luke:1956:RFAa,
author = "Yudell L. Luke",
editor = "????",
booktitle = "{ACM'56: Proceedings of the 1956 11th ACM national
meeting}",
title = "On rational function approximations to the exponential
function with application to the practical solution of
linear differential difference equations with constant
coefficients",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "13--16",
year = "1956",
DOI = "https://doi.org/10.1145/800258.808937",
bibdate = "Fri Dec 21 08:53:15 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See errata and addenda \cite{Luke:1956:RFAb}.",
URL = "https://dl.acm.org/ft_gateway.cfm?id=808937",
acknowledgement = ack-nhfb,
}
@InProceedings{Luke:1956:RFAb,
author = "Yudell L. Luke",
editor = "????",
booktitle = "{ACM'56: Proceedings of the 1956 11th ACM national
meeting}",
title = "On rational function approximations to the exponential
function with application to the practical solution of
linear differential difference equations with constant
coefficients: Errata and addenda",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "177--178",
year = "1956",
DOI = "https://doi.org/10.1145/800258.808979",
bibdate = "Fri Dec 21 08:53:15 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Luke:1956:RFAa}.",
URL = "https://dl.acm.org/ft_gateway.cfm?id=808979",
acknowledgement = ack-nhfb,
}
@Book{Sneddon:1956:SFM,
author = "Ian Naismith Sneddon",
title = "Special Functions of Mathematical Physics and
Chemistry",
volume = "19",
publisher = "Oliver and Boyd",
address = "Edinburgh, UK",
edition = "Third",
pages = "viii + 164",
year = "1956",
LCCN = "QA1 U588 v. 19",
bibdate = "Sat Oct 30 18:41:48 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "University mathematical texts",
acknowledgement = ack-nhfb,
remark = "See second edition \cite{Sneddon:1961:SFM} and third
edition \cite{Sneddon:1980:SFM}.",
subject = "Functions, Special",
}
@Book{Stratton:1956:SWF,
author = "Julius Adams Stratton",
title = "Spheroidal Wave Functions, Including Tables of
Separation Constants and Coefficients",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 613",
year = "1956",
LCCN = "QA405 .S8",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1901--1994",
subject = "Wave mechanics; Spheroidal functions",
}
@Book{Flammer:1957:SWF,
author = "Carson Flammer",
title = "Spheroidal Wave Functions",
publisher = pub-STANFORD,
address = pub-STANFORD:adr,
pages = "ix + 220",
year = "1957",
LCCN = "QA405 .F55",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "A Stanford Research Institute monograph",
acknowledgement = ack-nhfb,
remark = "The basis for this monograph was work done at Stanford
Research Institute for the United States Air Force
Cambridge Research Center under Contract AF 19
(604)-1296.",
subject = "Spheroidal functions",
}
@Article{Franklin:1957:CARb,
author = "Joel Franklin and Bernard Friedman",
title = "A convergent asymptotic representation for integrals",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "53",
pages = "612--619",
year = "1957",
CODEN = "PCPSA4",
ISSN = "0008-1981",
MRclass = "42.1X",
MRnumber = "0090691",
MRreviewer = "P. Henrici",
bibdate = "Tue Feb 06 15:03:36 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2F167020D3A1F98182882E99549E7751/S0305004100032667a.pdf/a-convergent-asymptotic-representation-for-integrals.pdf",
abstract = "This paper represents a new method for obtaining an
asymptotic representation for integrals of the form $
\int_0^\infty e^{-p x} x^{c - 1} f(x) \, d x $ when $p$
is large. It is shown that if $ f(x)$ satisfies certain
conditions this representation is also convergent.
Numerical calculations seem to show that the first term
of the representation gives a close approximation to
the value of the integral for a wide range of values of
$p$.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
remark = "See applications in
\cite{Temme:2015:AMI,Navas-Palencia:2018:HPC}.",
}
@Article{Hitchcock:1957:PAB,
author = "A. J. M. Hitchcock",
title = "Polynomial Approximations to {Bessel} Functions of
Order Zero and One and to Related Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "86--88",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kogbetliantz:1957:CEN,
author = "E. G. Kogbetliantz",
title = "Computation of {$ e^N $} for $ - \infty < {N} < +
\infty $ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "110--115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.12.0110",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "68.0X",
MRnumber = "19,775d",
bibdate = "Tue Sep 06 20:55:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "W. F. Freiberger",
}
@Article{Linskii:1957:CEF,
author = "V. S. Linski{\u{\i}}",
title = "Calculation of elementary functions on automatic
digital machines. ({Russian})",
journal = "Vy{\v{c}}isl. Mat.",
volume = "2",
pages = "90--119",
year = "1957",
MRclass = "68.00",
MRnumber = "21 \#982",
MRreviewer = "J. W. Carr, III",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Luke:1957:C,
author = "Yudell L. Luke",
title = "On the Computation of $ \log {Z} $ and $ \operatorname
{arc} \tan {Z} $",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "57",
pages = "16--18",
month = jan,
year = "1957",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1957-0084855-1",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Miller:1957:NGS,
author = "J. C. P. Miller",
title = "Note on the General Solution of the Confluent
Hypergeometric Equation",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "97--99",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Southard:1957:ATW,
author = "Thomas H. Southard",
title = "Approximation and Table of the {Weierstrass} $ \wp $
Function in the Equianharmonic Case for Real Argument",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "99--100",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Stegun:1957:GBF,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Generation of {Bessel} Functions on High Speed
Computers",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "60",
pages = "255--257",
month = oct,
year = "1957",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1957-0093939-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{T:1957:CHS,
author = "C. B. T.",
title = "Comment: {T. H. Southard, \booktitle{Approximation and
table of the Weierstrass $ \wp $ function in the
equianharmonic case for real argument}. [MTAC, this
issue, p. 99--100]}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "110--110",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002157",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Wilkes:1957:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xiv + 238",
year = "1957",
LCCN = "QA76.5 .W52 1957",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also first edition \cite{Wilkes:1951:PPE}.",
URL = "https://b-ok.org/book/3668116/b363ff",
acknowledgement = ack-nhfb,
remark-1 = "According to \cite{Anderson:2019:SAM}, this book
discusses the computation of integer population counts
on the Electronic Delay Storage Automatic Calculator
(EDSAC) computer using a recursive divide-and-conquer
algorithm. See also somewhat negative 1958 review by
Fernando J. Corbat{\'o}
\cite{https://doi.org/10.1063/1.3062687}.
Floating-point arithmetic is discussed on pages 60,
90--91, and 135--137.",
remark-2 = "From page 5: ``Each storage location in the EDSAC
holds 17 binary digits. In words representing numbers,
the binary point is regarded as being to the right of
the extreme left-hand digit; this digit (the most
significant digit) is used as a sign indicator and is
referred to as the sign digit. \ldots{} the capacity of
the accumulator is 70 digits; there is, therefore,
plenty of room to hold the full 33-digit product of two
17-digit numbers. \ldots{} A negative number $-x$
(where $O < x \leq 1$) is represented by a $1$ in the
sign-digit position, followed by the digits of $(1 -
x)$; for example, $1.1100\ldots{}$ represents $-(1 -
3/4) = -1/4$. \ldots{}. Another way of explaining the
representation of negative numbers is to regard the
sign digit as an ordinary numerical digit, and to say
that $-x$ is stored as the number $(2 - x)$. Note in
particular that $1.0000\ldots{}$ represents $-1$.''
[Page 59 calls this a {\em True complements}
representation, distinguished from one's complement.]",
remark-3 = "From page 35: ``The EDSAC has a facility which enables
an even-numbered storage location and the following
odd-numbered storage to be used as a single storage
location holding 35 binary digits.'' [This suggests the
word size in 18, not 17 as page 5 suggests. The
Wikipedia article on the EDSAC reports: ``The EDSAC's
main memory consisted of 1024 locations, though only
512 locations were initially installed. Each contained
18 bits, but the topmost bit was always unavailable due
to timing problems, so only 17 bits were used.'']",
remark-4 = "From page 36: ``The multiplier register of the
arithmetical unit is of sufficient capacity to hold a
long number, and the accumulator is of sufficient
capacity to hold the complete (69) binary digit
[including the sign bit] product of two long
numbers.''",
remark-5 = "From page 36: ``In some calculations, long numbers may
not provide sufficient precision. In such cases, the
programmer may make use of what is known as
double-length or double-precision working, in which two
long storage locations are used to hold the digits of a
single number.'' [this would be a quad-word number
holding 69 bits, including the sign bit.].",
remark-6 = "From page 60: ``\ldots{} two double-length numbers,
each stored in two locations, can be added and the
result put in two locations in the store, by means of
six orders''.",
remark-7 = "From page 90: ``Each number is expressed in the form
$a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
p < 63$ and is represented in the store by $a \cdot
2^{-11} + p \cdot 2^{-6}$.''",
remark-8 = "From page 91: ``Numbers are expressed in the form $a
\cdot 10^p$, where $a$ and $p$ are packed into a single
storage location. The number of digits defining $p$ may
be varied from 4 to 15 by means of a preset parameter,
so that a suitable value for the permissible range of
variation of numbers may be selected for a given
calculation.''",
remark-9 = "From page 91: ``Although the use of floating-point
operation can simplify the programmer's task by
relieving him of undue preoccupation with scaling, it
must not be thought that it solves all his
difficulties. In particular, the loss of significant
digits resulting from the subtraction of a number from
a nearly equal number can have serious consequences
unless proper precautions are taken.''",
tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machine / 1 \\
1-3 The EDSAC / 3 \\
1-4 Store / 5 \\
1-5 Arithmetical unit / 5 \\
1-6 Form of numbers in the machine / 5 \\
1-7 Form of orders in the machine / 6 \\
1-8 Storage of orders / 6 \\
1-9 Written form of orders / 7 \\
1-10 Some simple examples / 7 \\
Exercises A / 9 \\
1-11 Jump orders / 9 \\
Exercises B / 11 \\
1-12 Repeated groups of orders / 11 \\
1-13 The use of the B-register / 15 \\
Exercises C / 18 \\
1-14 Equivalence between orders and numbers;
pseudo-orders / 18 \\
1-15 Use of the arithmetical unit for constructing or
modifying orders / 20 \\
1-16 The mix order / 23 \\
Exercises D / 24 \\
CHAPTER 2. SUBROUTINES / 25 \\
2-1 Introduction / 25 \\
2-2 Relative numbering of addresses / 25 \\
2-3 Internal and external forms of orders / 26 \\
2-4 Reading of orders from the input tape / 28 \\
2-5 Open and closed subroutines / 29 \\
2-6 Entering and leaving a closed subroutine / 29 \\
2-7 Closed B subroutines / 30 \\
2-8 Closed A subroutines / 31 \\
2-9 Use of library subroutines / 32 \\
Exercises E / 33 \\
2-10 Long numbers / 35 \\
2-11 Some further orders in the order code / 36 \\
2-12 Scale factors / 38 \\
2-13 Control combinations / 39 \\
Exercises F / 40 \\
2-14 Relative addresses in control combinations / 41
\\
2-15 Extension of the use of relative addresses / 41
\\
2-16 Setting of the constants to be added by terminal
code letters / 43 \\
2-17 Complete table of terminal code letters / 44 \\
2-18 Parameters / 45 \\
2-19 Preset parameters / 46 \\
2-20 Program parameters / 46 \\
2-21 Standard procedure for setting preset parameters /
46 \\
2-22 Interpretive subroutines / 47 \\
Exercises G / 49 \\
CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
3-1 Introduction / 51 \\
3-2 Single-address codes / 52 \\
3-3 Multi-address codes / 53 \\
3-4 Multiplication and division / 56 \\
3-5 Source-destination codes / 57 \\
3-6 Representation of negative numbers / 59 \\
3-7 Miscellaneous facilities / 60 \\
3-8 Minimum-access coding / 61 \\
3-9 The evaluation of an order code / 63 \\
3-10 Use of an auxiliary store / 64 \\
CHAPTER 4. INPUT AND OUTPUT / 66 \\
4-1 Introduction / 66 \\
4-2 Input of numbers / 66 \\
4-3 Output of numbers / 67 \\
4-4 Input of orders / 69 \\
4-5 Recognition of the code letter S / 72 \\
4-6 Economy of input and output time / 72 \\
4-7 Some features of input systems used with other
machines / 73 \\
4-8 Punched tape / 73 \\
4-9 Punched cards / 75 \\
CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
5-1 Introduction / 80 \\
5-2 Library catalog / 80 \\
5-3 Input subroutines / 81 \\
5-4 Output subroutines / 81 \\
5-5 Division subroutines / 82 \\
5-6 Trigonometric and other functions / 82 \\
5-7 The economization of a power series by the use of
Chebyshev polynomials / 83 \\
5-8 Quadrature / 86 \\
5-9 Integration of ordinary differential equations / 87
\\
5-10 Library subroutines Gl2 and G13: Runge--Kutta
processes / 88 \\
5-11 The independent variable / 88 \\
5-12 Definition of the Runge--Kutta--Gill process / 89
\\
5-13 Taylor-series method / 90 \\
5-14 Interpretive subroutines / 90 \\
5-15 Floating-point subroutines / 90 \\
CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
6-1 Introduction / 92 \\
6-2 Proofreading of programs / 93 \\
6-3 Punching / 93 \\
6-4 Locating mistakes in a program- / 94 \\
6-5 Subroutines for checking programs / 96 \\
6-6 The development of a program / 97 \\
CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
/ 99 \\
EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
EXAMPLE 2 The evaluation of a definite integral / 102
\\
EXAMPLE 3 Integration of an ordinary differential
equation / 108 \\
EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
EXAMPLE 5 Evaluation of a definite integral / 118 \\
CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
8-1 Introduction / 126 \\
8-2 Conversion versus interpretation / 127 \\
8-3 Assembly of a program / 127 \\
8-4 Floating addresses / 129 \\
8-5 Formula recognition / 136 \\
Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
139 \\
CATEGORY A. Subroutines to carry out floating-point
arithmetic / 140 \\
CATEGORY B. Subroutines to perform arithmetical
operations on complex numbers / 142 \\
CATEGORY C. Error-diagnosis subroutines / 144 \\
CATEGORY D. Division subroutines / 146 \\
CATEGORY E. Exponential subroutines / 148 \\
CATEGORY F. General subroutines relating to functions /
148 \\
CATEGORY G. Subroutines for the integration of
differential equations / 150 \\
CATEGORY L. Subroutines for evaluating logarithms / 153
\\
CATEGORY M. Miscellaneous subroutines / 154 \\
CATEGORY N. Operations on double-length numbers / 156
\\
CATEGORY P. Print subroutines / 158 \\
CATEGORY Q. Quadrature subroutines / 162 \\
CATEGORY R. Input subroutines / 164 \\
CATEGORY s. Subroutines for evaluating fractional
powers / 168 \\
CATEGORY T. Subroutines for calculating trigonometric
functions / 169 \\
CATEGORY Z. Post-mortem routines / 170 \\
PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
SUBROUTINES / 173 \\
APPENDIX 1. Input and output codes of the EDSAC / 212
\\
APPENDIX 2. Order code and controls of the EDSAC / 214
\\
APPENDIX 3. The initial input routine of the EDSAC /
218 \\
APPENDIX 4. Control combinations / 221 \\
APPENDIX 5. Specimen solutions to programming exercises
/ 223 \\
BIBLIOGRAPHY / 233 \\
INDEX / 237",
}
@Article{Beattie:1958:TFZ,
author = "Curtis L. Beattie",
title = "Table of First 700 Zeros of {Bessel} Functions --- {$
J_l(x) $} and {$ J^{\prime }_l(x) $}",
journal = j-BELL-SYST-TECH-J,
volume = "37",
number = "3",
pages = "689--697",
month = may,
year = "1958",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "65.00",
MRnumber = "0093928 (20 \#448)",
MRreviewer = "J. C. P. Miller",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1958/BSTJ.1958.3703.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol37/bstj37-3-689.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Belaga:1958:SPI,
author = "{\`E}. G. Belaga",
title = "Some problems involved in the calculation of
polynomials",
journal = j-DOKL-AKAD-NAUK,
volume = "123",
pages = "775--777",
year = "1958",
CODEN = "DANKAS",
ISSN = "0002-3264",
MRclass = "65.00",
MRnumber = "105192",
MRreviewer = "John Todd",
bibdate = "Fri Oct 20 10:34:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii Nauk SSSR",
journal-URL = "http://istina.msu.ru/journals/366838/",
keywords = "number of multiplications to evaluate a polynomial",
}
@Book{Bowman:1958:IBF,
author = "Frank Bowman",
title = "Introduction to {Bessel} Functions",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 135",
year = "1958",
LCCN = "QA408 .B68i 1958",
bibdate = "Sat Jan 15 17:24:26 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "An unabridged and unaltered republication of the first
edition.",
subject = "Bessel functions",
}
@Article{Dingle:1958:AEC,
author = "R. B. Dingle",
title = "Asymptotic Expansions and Converging Factors. {III}.
Gamma, Psi and Polygamma Functions, and {Fermi--Dirac}
and {Bose--Einstein} Integrals",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "244",
number = "1239",
pages = "484--490",
day = "22",
month = apr,
year = "1958",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
bibdate = "Mon Jun 18 07:22:24 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/100264",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series A,
Mathematical and physical sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/content/current",
}
@Article{Goldstein:1958:BFL,
author = "M. Goldstein and R. M. Thaler",
title = "{Bessel} Functions for Large Arguments",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "12",
number = "61",
pages = "18--26",
month = jan,
year = "1958",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1958-0102906-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kogbetliantz:1958:CANa,
author = "E. G. Kogbetliantz",
title = "Computation of Arctan {N} for $ - \infty < {N} < +
\infty $ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "1",
pages = "43--53",
month = jan,
year = "1958",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.21.0043",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65.3X",
MRnumber = "19,982e",
bibdate = "Wed Aug 31 13:40:00 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. B. Haselgrove",
}
@Article{Kogbetliantz:1958:CANb,
author = "E. G. Kogbetliantz",
title = "Computation of Arcsin {N} for $ 0 < {N} < 1 $ Using an
Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "3",
pages = "218--222",
month = jul,
year = "1958",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.23.0218",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65.3X",
MRnumber = "19,1197c",
bibdate = "Wed Aug 31 13:41:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. B. Haselgrove",
}
@Book{Lewin:1958:DAF,
author = "Leonard Lewin",
title = "Dilogarithms and Associated Functions",
publisher = "Macdonald",
address = "London, UK",
pages = "353",
year = "1958",
LCCN = "QA351 .L5",
bibdate = "Fri Jun 16 13:51:36 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "22-Jul-1919--13-Aug-2007",
author-url = "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
remark = "Foreword by J. C. P. Miller",
subject = "Dilogarithms",
}
@TechReport{Miller:1958:LNN,
author = "J. C. P. Miller",
title = "Lecture Notes on Numerical Analysis",
type = "Report",
institution = "Cambridge University",
address = "Cambridge, England",
year = "1958",
bibdate = "Fri Sep 20 14:46:35 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.youtube.com/watch?v=81YrRSeReKo",
acknowledgement = ack-nhfb,
remark-1 = "Cited in \cite[Reference 21]{Agarwal:1986:NSV} in
elefunt.bib and fparith.bib.",
remark-2 = "Page 135 of the Agarwal paper says ``Kahan has also
informed us that Miller [21] wrote about the
extra-accurate table idea in 1958.'' William M. Kahan
spent 1958--1960 in Cambridge, as a pro-forma student
of J. C. P. Miller --- Kahan already had a Ph.D. from
the University of Toronto, but it was not recognized by
Cambridge University! See the video interview in the
URL.",
}
@Article{Sugai:1958:ERR,
author = "Iwao Sugai",
title = "Extraction of Roots by Repeated Subtractions for
Digital Computers",
journal = j-CACM,
volume = "1",
number = "12",
pages = "6--8",
month = dec,
year = "1958",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/377924.377928",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sugai58;
https://www.math.utah.edu/pub/tex/bib/cacm1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Sugai58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sugai58",
}
@Article{Wadey:1958:TSR,
author = "W. G. Wadey",
title = "Two Square-Root Approximations",
journal = j-CACM,
volume = "1",
number = "11",
pages = "13--14",
month = nov,
year = "1958",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368932.368936",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Wadey58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}
@Article{Corbato:1959:GSB,
author = "Fernando J. Corbat{\'o} and Jack L. Uretsky",
title = "Generation of Spherical {Bessel} Functions in Digital
Computers",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "366--375",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Mon Dec 05 20:07:17 1994",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Davis:1959:LEI,
author = "Philip J. Davis",
title = "{Leonhard Euler}'s Integral: a Historical Profile of
the Gamma Function: In Memoriam: {Milton Abramowitz}",
journal = j-AMER-MATH-MONTHLY,
volume = "66",
number = "10",
pages = "849--869",
month = dec,
year = "1959",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2309786",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "00 (33.00)",
MRnumber = "MR0106810 (21 #5540)",
bibdate = "Mon Jun 28 12:39:33 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amermathmonthly1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2309786",
acknowledgement = ack-nhfb,
author-dates = "Philip J. Davis (2 January 1923--14 March 2018)",
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{DiDonato:1959:NFC,
author = "A. R. DiDonato and A. V. Hershey",
title = "New Formulas for Computing Incomplete Elliptic
Integrals of the First and Second Kind",
journal = j-J-ACM,
volume = "6",
number = "4",
pages = "515--526",
month = oct,
year = "1959",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320998.321005",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.00",
MRnumber = "0107353",
MRreviewer = "F. Stallmann",
bibdate = "Mon Dec 05 20:10:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Book{Emde:1959:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "B. T. Teubner",
address = "Leipzig, Germany and Berlin, Germany",
edition = "Third",
pages = "xii + 181",
year = "1959",
LCCN = "QA47 .E5",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://lccn.loc.gov/61020314",
acknowledgement = ack-nhfb,
author-dates = "1873--1951",
language = "German",
}
@Article{Gautschi:1959:EIL,
author = "W. Gautschi",
title = "Exponential integral $ \int_1^\infty e^{-x t} t^{-n}
\, d t $ for large values of $n$",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "62",
number = "3",
pages = "123--125",
month = mar,
year = "1959",
DOI = "https://doi.org/10.6028/jres.062.022",
ISSN = "0091-0635",
bibdate = "Sat Feb 18 14:39:27 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
}
@Article{Goldstein:1959:RTC,
author = "M. Goldstein and R. M. Thaler",
title = "Recurrence Techniques for the Calculation of {Bessel}
Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "66",
pages = "102--108",
month = apr,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1959-0105794-5",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Greenhill:1959:AEF,
author = "Alfred George Greenhill",
title = "The Applications of Elliptic Functions",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xi + 357",
year = "1959",
bibdate = "Wed Mar 15 08:21:33 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Greenhill:1892:AEF}.",
acknowledgement = ack-nhfb,
author-dates = "1847--1927",
remark = "Reprint of \cite{Greenhill:1892:AEF}.",
}
@Article{Kogbetliantz:1959:CSC,
author = "E. G. Kogbetliantz",
title = "Computation of $ \sin {N} $, $ \cos {N} $, and $ {M} $
th Root of $ {N} $ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "3",
number = "2",
pages = "147--152",
month = apr,
year = "1959",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.32.0147",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65.00",
MRnumber = "21 \#964",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "B. A. Chartres",
}
@Article{Kreyszig:1959:RUE,
author = "Erwin Kreyszig and John Todd",
title = "The radius of univalence of the error function",
journal = j-NUM-MATH,
volume = "1",
pages = "78--89",
month = dec,
year = "1959",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 20:47:18 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Longman:1959:STT,
author = "I. M. Longman",
title = "A Short Table of $ \int^\infty_x {J}_0 (t)t^{-n} d t $
and $ \int^\infty_x {J}_1 (t) t^{-n} d t $ (in
{Technical Notes and Short Papers})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "306--311",
month = oct,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1959-0108892-5",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 6-digit values for $ n = 1, 2, \ldots {},
22 $ and for $ x = 1, 2, \ldots {}, 10 $.",
}
@Article{Luke:1959:ECH,
author = "Yudell L. Luke",
title = "Expansion of the Confluent Hypergeometric Function in
Series of {Bessel} Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "261--271",
month = oct,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1959-0107027-2",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Pan:1959:CSC,
author = "V. Ya. Pan",
title = "Certain schemes for the calculation of values of
polynomials with real coefficients",
journal = "Problemy Kibernetiki",
volume = "5",
number = "??",
pages = "17--29",
month = "????",
year = "1959",
bibdate = "Fri Oct 20 10:40:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Also available as English translation JPRS No.
11045.",
acknowledgement = ack-nhfb,
ajournal = "Probl. Kibernetiki",
keywords = "number of multiplications to evaluate a polynomial",
language = "Russian",
remark = "Check: MathSciNet does not cover this volume, or
record this paper, and the year may be wrong (based on
available volume/year list entries). Cited in
\cite[ref. 5, p. 178]{Fike:1967:MEP}.",
}
@Article{Pan:1959:SCP,
author = "V. Ya. Pan",
title = "Schemes for the computation of polynomials with real
coefficients",
journal = j-DOKL-AKAD-NAUK,
volume = "127",
number = "2",
pages = "266--269",
month = "????",
year = "1959",
CODEN = "DANKAS",
ISSN = "0002-3264",
bibdate = "Fri Oct 20 10:38:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii nauk SSSR",
journal-URL = "http://istina.msu.ru/journals/366838/",
keywords = "number of multiplications to evaluate a polynomial",
language = "Russian",
}
@Article{Sarafyan:1959:NMC,
author = "Diran Sarafyan",
title = "A New Method of Computation of Square Roots Without
Using Division",
journal = j-CACM,
volume = "2",
number = "11",
pages = "23--24",
month = nov,
year = "1959",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368481.368511",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}
@Article{Sherry:1959:CGF,
author = "M. E. Sherry and S. Fulda",
title = "Calculation of Gamma Functions to High Accuracy (in
{Technical Notes and Short Papers})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "314--315",
month = oct,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1959-0108891-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Stiefel:1959:NMT,
author = "Eduard L. Stiefel",
title = "Numerical methods of {Tchebycheff} approximation",
crossref = "Langer:1959:NAP",
pages = "217--232",
year = "1959",
MRclass = "65.00 (41.00)",
MRnumber = "0107961",
MRreviewer = "M. R. Hestenes",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
}
@Article{Strachey:1959:TSR,
author = "C. Strachey",
title = "On taking the square root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Volder:1959:CCT,
author = "Jack Volder",
title = "The {CORDIC} Computing Technique",
journal = "Proceedings of the Western Joint Computer Conference",
pages = "257--261",
year = "1959",
DOI = "https://doi.org/10.1145/1457838.1457886",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Article{Volder:1959:CTC,
author = "Jack E. Volder",
title = "The {CORDIC} Trigonometric Computing Technique",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "3",
pages = "330--334",
month = sep,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222693",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222693",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Anonymous:1960:BFP,
author = "Anonymous",
title = "{Bessel} Functions. {Part III}: {Zeros} and Associated
Values",
volume = "7",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "lx + 79",
year = "1960",
MRclass = "65.00",
MRnumber = "119441",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Prepared under the direction of the Bessel Functions
Panel of the Mathematical Tables Committee",
series = "Royal Society Mathematical Tables",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Anonymous:1960:EFG,
author = "Anonymous",
title = "Errata to {Fisher} and {Gupta}",
journal = j-TECHNOMETRICS,
volume = "2",
number = "4",
pages = "523--524",
month = nov,
year = "1960",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266462",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:29 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254224;
https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
note = "See \cite{Fisher:1960:PPD,Gupta:1960:OSG}.",
URL = "http://www.jstor.org/stable/1266462",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
subject-dates = "Sir Ronald Aylmer Fisher (17 February 1890--29 July
1962)",
}
@Article{Beam:1960:ACE,
author = "A. Beam",
title = "{Algorithm 14}: {Complex} exponential integral",
journal = j-CACM,
volume = "3",
number = "7",
pages = "406--406",
month = jul,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367349.367351",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:27 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Ei(z)$; special functions",
remark = "Fullerton: 30-line Algol procedure incorrectly
labelled algorithm 13.",
}
@Article{Fisher:1960:PPD,
author = "Ronald A. Fisher and E. A. Cornish",
title = "The Percentile Points of Distributions Having Known
Cumulants",
journal = j-TECHNOMETRICS,
volume = "2",
number = "2",
pages = "209--225",
month = may,
year = "1960",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266546",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:27 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254222;
https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
note = "See errata \cite{Anonymous:1960:EFG}.",
URL = "http://www.jstor.org/stable/1266546",
acknowledgement = ack-nhfb,
author-dates = "Sir Ronald Aylmer Fisher (17 February 1890--29 July
1962)",
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Book{Fox:1960:TWP,
author = "L. Fox",
title = "Tables of {Weber} Parabolic Cylinder Functions and
Other Functions for Large Arguments",
volume = "4",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "iii + 40",
year = "1960",
MRclass = "65.00 (33.00)",
MRnumber = "120778",
MRreviewer = "L. J. Slater",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Department of Scientific and Industrial Research",
series = "National Physical Laboratory Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Gupta:1960:OSG,
author = "Shanti S. Gupta",
title = "Order Statistics from the Gamma Distribution",
journal = j-TECHNOMETRICS,
volume = "2",
number = "2",
pages = "243--262",
month = may,
year = "1960",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266548",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
MRclass = "62.00",
MRnumber = "0112225 (22 \#3079)",
MRreviewer = "S. S. Wilks",
bibdate = "Sat Jun 21 13:17:27 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254222;
https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
note = "See errata \cite{Anonymous:1960:EFG}.",
URL = "http://www.jstor.org/stable/1266548",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Haimovici:1960:MRE,
author = "Corina Haimovici",
title = "A method of representing elementary functions in
algebras of finite order. ({Romanian})",
journal = "An. {\c{S}}ti. Univ. ``Al. I. Cuza'' Ia{\c{s}}i
Sec{\c{t}} I. (N.S.)",
volume = "6",
pages = "507--515",
year = "1960",
MRclass = "26.00",
MRnumber = "24 \#A1342",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Harumi:1960:VTN,
author = "Kasabur{\^o} Harumi and Shigetoshi Katsura and John W.
{Wrench, Jr.}",
title = "Values of {$ \frac {2}{\pi } \int^\infty_0 \Big (\frac
{\sin t}{t} \Big)^n d t $} (in {Technical Notes and
Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "72",
pages = "379--379",
month = oct,
year = "1960",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1960-0122010-7",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 10-digit table for $ n = 1, 2, \ldots {},
30 $.",
}
@InCollection{Kogbetliantz:1960:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of elementary functions",
crossref = "Ralston:1960:MMD",
pages = "7--35",
year = "1960",
MRclass = "68.00 (65.00)",
MRnumber = "22 \#8681",
MRreviewer = "J. C. P. Miller",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Lang:1960:ECC,
author = "H. A. Lang",
title = "On the Evaluation of Certain Complex Elliptic
Integrals (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "70",
pages = "195--199",
month = apr,
year = "1960",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1960-0112241-4",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Lebedev:1960:GMT,
author = "A. V. (Aleksandr Vasil'evich) Lebedev and R. M. (Rimma
Maksimova) Fedorova and Nina Mikhollovna Burunova",
title = "A Guide to Mathematical Tables",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xlvi + 586",
year = "1960",
LCCN = "Z6654.T3 L42",
bibdate = "Mon Feb 13 17:12:14 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "English edition prepared by D. G. Fry from the Russian
original.",
acknowledgement = ack-nhfb,
subject = "Mathematics; Tables; Indexes",
tableofcontents = "Front Cover \\
A Guide to Mathematical Tables \\
Copyright Page \\
Translator's Preface \\
Preface \\
Index to the Section Headings in the Table of Contents
of the Guide and the Supplement \\
Table of Contents \\
Part One: Description of the Tables \\
1. Powers, Rational and Algebraic Functions \\
Positive Whole Powers \\
Fractional Positive Powers \\
Reciprocals (Negative Whole and Fractional Powers) \\
Rational Functions \\
Algebraic Functions \\
Complex Numbers and Their Powers \\
2. Trigonometric Functions. Various Values Connected
With the Circle and the Sphere \\
Natural Values of Trigonometric Functions \\
Various Expressions Containing Trigonometric Functions
\\
Derivatives and Powers of Trigonometric Functions \\
Reciprocal Trigonometric Functions of A Complex
Variable \\
Geometric Quantities \\
Tables For Converting From One Angular Measure to
Another \\
3. Exponential and Hyperbolic Functions \\
Exponential Functions \\
Hyperbolic Functions \\
Expressions Containing Trigonometric and Hyperbolic
Functions \\
Inverse Hyperbolic Functions \\
4. Logarithms \\
Common Logarithms and Antilogarithms \\
Natural Logarithms \\
Logarithms to Base 2 \\
5. Factorials, Euler Integrals and Related Functions
\\
Factorials \\
the Gamma Function \\
the Psi Function and Its Derivatives \\
the Beta Function \\
Certain Constants \\
6. Sine and Cosine Integrals, Exponential and
Logarithmic Integrals and Related Functions \\
Sine and Cosine Integrals \\
Hyperbolic Sine and Cosine Integrals \\
Exponential Integral \\
Logarithmic Integral \\
Generalised and Composite Integral Functions \\
Integral Functions of Complex Argument \\
7. Probability Integrals and Related Functions \\
Functions of the Distribution of Probability and
Related Functions \\
Probability Integrals and Expressions Containing
Probability Integrals \\
Tables in Which the Integral Serves As the Argument \\
Probability Integrals of Complex Argument \\
Derivatives of Various Orders of Probability
Distribution Functions \\
Zeros of Probability Integrals \\
Logarithms of Probability Integrals \\
Fresnel Integrals and Related Functions \\
8. Elliptic Integrals and Elliptic Functions \\
Moduli of the Integrals \\
Complete Elliptic Integrals \\
Incomplete Elliptic Integrals \\
Elliptic Functions \\
Theta Functions \\
9. Legendre Functions and Polynomials \\
Legendre Polynomials and Legendre Functions of the
First Kind \\
Associated Legendre Functions of the First Kind \\
Roots of Legendre Functions \\
Various Expressions Containing Legendre Functions \\
10. Cylinder Functions \\
Cylinder Functions of the First and Second Kinds of
Real Argument \\
Riccati--Bessel Functions \\
Lommel Functions of Two Real Variables \\
Cylinder Functions of the Third Kind (Hankel Functions)
\\
Cylinder Functions of the First and Second Kinds of
Imaginary Argument \\
Lommel Functions of Two Imaginary Variables \\
Cylinder Functions of Complex Argument \\
Thomson Functions",
}
@Manual{Maehly:1960:ACD,
author = "Hans J. Maehly",
title = "Approximations for the {Control Data 1604}",
organization = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "ii + 44",
day = "15",
month = jan,
year = "1960",
bibdate = "Tue Nov 06 00:39:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.bitsavers.org/pdf/cdc/1604/Approximations_For_The_Control_Data_1604_Mar60.pdf",
acknowledgement = ack-nhfb,
keywords = "$\arctan(x)$; $\cos(x)$; $\exp(x)$; $\log(x)$;
$\sin(x)$; $\sqrt(x)$; $\tan(x)$; CDC 1604",
}
@Article{Philip:1960:FI,
author = "J. R. Philip",
title = "The function $ \operatorname {inverfc} \theta $",
journal = j-AUSTRALIAN-J-PHYS,
volume = "13",
number = "1",
pages = "13--20",
month = mar,
year = "1960",
CODEN = "AUJPAS",
DOI = "https://doi.org/10.1071/PH600013",
ISSN = "0004-9506 (print), 1446-5582 (electronic)",
ISSN-L = "0004-9506",
MRnumber = "22 9626",
bibdate = "Tue Sep 11 20:53:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "135.28302",
abstract = "The function inverfc $ \theta $ arises in certain
differential equations when concentration is taken as
an independent variable. It enters into a general
method of exact solution of the concentration-dependent
diffusion equation. An account is given of the
properties of this function, and of its derivatives and
integrals. The function\par
$$ B(\theta) = (2 / \pi^{1 / 2}) \exp [ - (\operatorname {inverfc} \theta)^2] $$
\noindent is intimately connected with the first
integral of inverfc $ \theta $ and with its
derivatives. Tables of $ \operatorname {inverfc} \theta
$ and $ B(\theta) $ are given.",
acknowledgement = ack-nhfb,
fjournal = "Australian Journal of Physics",
journal-URL = "http://www.publish.csiro.au/ph/content/allissues",
}
@Book{Rainville:1960:SF,
author = "Earl David Rainville",
title = "Special Functions",
publisher = pub-MACMILLAN,
address = pub-MACMILLAN:adr,
pages = "xii + 365",
year = "1960",
ISBN = "0-8284-0258-2",
ISBN-13 = "978-0-8284-0258-3",
LCCN = "QA331 R15; QA351 .R3 1971",
bibdate = "Mon Sep 3 16:04:28 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Reprinted in 1971.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Based upon the lectures on special functions which
\ldots{} [the author has] been giving at the University
of Michigan since 1946. Fullerton: All traditional
functions and polynomials are discussed in some
detail.",
shorttableofcontents = "1: Infinite Products \\
2: The Gamma and Beta Functions \\
3: Asymptotic Series \\
4: The Hypergeometric Function \\
5: Generalized Hypergeometric Functions \\
6: Bessel Functions \\
7: The Confluent Hypergeometric Function \\
8: Generating Functions \\
9: Orthogonal Polynomials \\
10: Legendre Polynomials \\
11: Hermite Polynomials \\
12: Laguerre Polynomials \\
13: The Sheffer Classification and Related Topics \\
14: Pure Recurrence Relations \\
15: Symbolic Relations \\
16: Jacobi Polynomials \\
17: Ultraspherical and Gegenbauer Polynomials \\
18: Other Polynomial Sets \\
19: Elliptic Functions \\
20: Theta Functions \\
21: Jacobian Elliptic Functions \\
Bibliography \\
Index",
subject = "Functions, Special",
tableofcontents = "1: Infinite Products \\
1. Introduction / 1 \\
2. Definition of an infinite product / 1 \\
3. A necessary condition for convergence . / 2 \\
4. The associated series of logarithms / 2 \\
5. Absolute convergence / 3 \\
6. Uniform convergence / 5 \\
\\
2: The Gamma and Beta Functions \\
7. The Euler or Mascheroni constant $\gamma$ / 8 \\
8. The Gamma function / 9 \\
9. A series for $\Gamma'(z) / \Gamma(z)$ / 10 \\
10. Evaluation of $\Gamma(1)$ and $\Gamma'(1)$ / 10 \\
11. The Euler product for $\Gamma(z)$ / 11 \\
12. The difference equation $\Gamma(z + 1) = z
\Gamma(z)$ / 12 \\
13. The order symbols $o$ and $O$ / 12 \\
14. Evaluation of certain infinite products / 13 \\
15. Euler's integral for $\Gamma(z)$ / 15 \\
16. The Beta function / 18 \\
17. The value of $\Gamma(z) \Gamma(1 - z)$ / 19 \\
18. The factorial function / 22 \\
19. Legendre's duplication formula / 23 \\
20. Gauss' multiplication theorem / 24 \\
21. A summation formula due to Euler / 26 \\
22. The behavior of $\log \Gamma(z)$ for large $|z|$ /
29 \\
\\
3: Asymptotic Series \\
23. Definition of an asymptotic expansion / 33 \\
24. Asymptotic expansions about infinity / 36 \\
25. Algebraic properties / 38 \\
26. Term-by-term integration / 39 \\
27. Uniqueness / 40 \\
28. Watson's lemma / 41 \\
\\
4: The Hypergeometric Function \\
29. The function $F(a, b; c; z)$ / 45 \\
30. A simple integral form / 47 \\
31. $F(a, b; c; 1)$ as a function of the parameters /
48 \\
32. Evaluation of $F(a, b; c; 1)$ / 48 \\
33. The contiguous function relations / 50 \\
34. The hypergeometric differential equation / 53 \\
35. Logarithmic solutions of the hypergeometric
equation / 54 \\
36. $F(a, b; c; 2)$ as a function of its parameters /
55 \\
37. Elementary series manipulations / 56 \\
38. Simple transformations / 58 \\
39. Relation between functions of $z$ and $1 - z$ / 61
\\
40. A quadratic transformation / 63 \\
41. Other quadratic transformations / 65 \\
42. A theorem due to Kummer / 68 \\
43. Additional properties / 68 \\
\\
5: Generalized Hypergeometric Functions \\
44. The function $_pF_q$ / 73 \\
45. The exponential and binomial functions / 74 \\
46. A differential equation / 74 \\
47. Other solutions of the differential equation / 76
\\
48. The contiguous function relations / 80 \\
49. A simple integral / 85 \\
50. The $_pF_q$ with unit argument / 85 \\
51. Saalsch{\"u}tz' theorem / 86 \\
52. Whipple's theorem / 88 \\
53. Dixon's theorem / 92 \\
54. Contour integrals of Barnes' type / 94 \\
55. The Barnes integrals and the function $_pF_q$ / 98
\\
56. A useful integral / 102 \\
\\
6: Bessel Functions \\
57. Remarks / 108 \\
58. Definition of $J_n(z)$ / 108 \\
59. Bessel's differential equation / 109 \\
60. Differential recurrence relations / 110 \\
61. A pure recurrence relation / 111 \\
62. A generating function / 112 \\
63. Bessel's integral / 114 \\
64. Index half an odd integer 114 , \\
65. Modified Bessel functions / 116 \\
66. Neumann polynomials / 116 \\
67. Neumann series / 119 \\
\\
7: The Confluent Hypergeometric Function \\
68. Basic properties of the $_1F_1$ / 123 \\
69. Kummer's first formula / 124 \\
70. Kummer's second formula / 125 \\
\\
8: Generating Functions \\
71. The generating function concept / 129 \\
72. Generating functions of the form $G(2 x t - t^2)$ /
131 \\
73. Sets generated by $e^t \psi(x t)$ / 132 \\
74. The generating functions $A(t) \exp[-x t / (1 -
t)]$ / 135 \\
75. Another class of generating functions / 137 \\
76. Boas and Buck generating functions / 140 \\
77. An extension / 143 \\
\\
9: Orthogonal Polynomials \\
78. Simple sets of polynomials / 147 \\
79. Orthogonality / 147 \\
80. An equivalent condition for orthogonality / 148 \\
81. Zeros of orthogonal polynomials / 149 \\
82. Expansion of polynomials / 150 \\
83. The three-term recurrence relation / 151 \\
84. The Christoffel--Darboux formula / 153 \\
85. Normalization; Bessel's inequality / 155 \\
\\
10: Legendre Polynomials \\
86. A generating function / 157 \\
87. Differential recurrence relations / 158 \\
88. The pure recurrence relation / 159 \\
89. Legendre's differential equation / 160 \\
90. The Rodrigues formula / 161 \\
91. Bateman's generating function / 162 \\
92. Additional generating functions / 163 \\
93. Hypergeometric forms of $P_n(x)$ / 163 \\
94. Brafman's generating functions / 167 \\
95. Special properties of $P_n(x)$ / 168 \\
96. More generating functions / 169 \\
97. Laplace's first integral form / 171 \\
98. Some bounds on $P_n(z)$ / 172 \\
99. Orthogonality / 173 \\
100. An expansion theorem / 176 \\
101. Expansion of $x^n$ / 179 \\
102. Expansion of analytic functions / 181 \\
\\
11: Hermite Polynomials \\
103. Definition of $H_n(x)$ / 187 \\
104. Recurrence relations / 188 \\
105. The Rodrigues formula / 189 \\
106. Other generating functions / 190 \\
107. Integrals / 190 \\
108. The Hermite polynomial as a $_2F_0$ / 191 \\
109. Orthogonality / 191 \\
110. Expansion of polynomials / 193 \\
111. More generating functions / 196 \\
\\
12: Laguerre Polynomials \\
112. The polynomial $L_n^{(\alpha)}(x)$ / 200 \\
113. Generating functions / 201 \\
114. Recurrence relations / 202 \\
115. The Rodrigues formula / 203 \\
116. The differential equation / 204 \\
117. Orthogonality / 204 \\
118. Expansion of polynomials / 206 \\
119. Special properties / 209 \\
120. Other generating functions / 211 \\
121. The simple Laguerre polynomials / 213 \\
\\
13: The Sheffer Classification and Related Topics \\
122. Differential operators and polynomial sets / 218
\\
123. Sheffer's $A$-type classification / 221 \\
124. Polynomials of Sheffer $A$-type zero / 222 \\
195. An extension of Sheffer's classification / 226 \\
126. Polynomials of $\sigma$-type zero / 228 \\
\\
14: Pure Recurrence Relations \\
127. Sister Celine's technique / 233 \\
128. A mild extension / 240 \\
\\
15: Symbolic Relations \\
129. Notation / 246 \\
130. Symbolic relations among classical polynomials /
247 \\
131. Polynomials of symbolic form $L_n(y(x))$ / 249 \\
\\
16: Jacobi Polynomials \\
132. The Jacobi polynomials / 254 \\
133. Bateman's generating function / 256 \\
134. The Rodrigues formula / 257 \\
135. Orthogonality / 258 \\
136. Differential recurrence relations / 261 \\
137. The pure recurrence relation / 263 \\
138. Mixed relations / 263 \\
139. Appell's functions of two variables / 265 \\
140. An elementary generating function / 269 \\
141. Brafman's generating functions / 271 \\
142. Expansion in series of polynomials / 272 \\
\\
17: Ultraspherical and Gegenbauer Polynomials \\
143. Definitions / 276 \\
144. The Gegenbauer polynomials / 277 \\
145. The ultraspherical polynomials / 283 \\
\\
18: Other Polynomial Sets \\
146. Bateman's $Z_n(x)$ / 285 \\
147. Rice's $H_n(\zeta, p, v)$ / 287 \\
148. Bateman's $F_n(z)$ / 289 \\
149. Sister Celine's polynomials / 290 \\
150. Bessel polynomials / 293 \\
151. Bedient's polynomials / 297 \\
152. Shively's pseudo-Laguerre and other polynomials /
298 \\
153. Bernoulli polynomials / 299 \\
154. Euler polynomials / 300 \\
155. Tchebicheff polynomials / 301 \\
\\
19: Elliptic Functions \\
156. Doubly periodic functions / 305 \\
157. Elliptic functions / 306 \\
158. Elementary properties / 306 \\
159. Order of an elliptic function / 308 \\
160. The Weierstrass function $P(z)$ / 309 \\
161. Other elliptic functions / 311 \\
162. A differential equation for $P(z)$ / 311 \\
163. Connection with elliptic integrals / 313 \\
\\
20: Theta Functions \\
164. Definitions / 314 \\
165. Elementary properties / 315 \\
166. The basic property table / 316 \\
167. Location of zeros / 319 \\
168. Relations among squares of theta functions / 322
\\
169. Pseudo addition theorems / 325 \\
170. Relation to the heat equation / 328 \\
171. The relation $\theta_1' = \theta_2 \theta_3
\theta_4$ / 329 \\
172. Infinite products / 332 \\
173. The value of $G$ / 334 \\
\\
21: Jacobian Elliptic Functions \\
174. A differential equation involving theta functions
/ 339 \\
175. The function $\sn(u)$ / 342 \\
176. The functions $\cn(u)$ and $\dn(u)$ / 343 \\
177. Relations involving squares / 344 \\
178. Relations involving derivatives / 345 \\
179. Addition theorems / 347 \\
\\
Bibliography / 349 \\
\\
Index / 359",
}
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367236.367267",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "M. Lotkin",
}
@Article{Sholander:1960:AEE,
author = "Marlow Sholander",
title = "Analytical expressions and elementary functions",
journal = j-AMER-MATH-MONTHLY,
volume = "67",
number = "3",
pages = "213--214",
month = mar,
year = "1960",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "26.00",
MRnumber = "22 \#9553",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2309678",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{Slater:1960:CHF,
author = "Lucy Joan Slater",
title = "Confluent hypergeometric functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "247",
year = "1960",
LCCN = "QA351 .S56",
bibdate = "Sat Oct 30 21:01:55 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Discussion of properties and 7 decimal
place tables of $_1 F_1 (a; b; x)$.",
subject = "Hypergeometric functions",
}
@Article{Traub:1960:CNM,
author = "J. F. Traub",
title = "Comments on a recent paper [{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = j-CACM,
volume = "3",
number = "2",
pages = "86--86",
month = feb,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366959.366989",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
abstract = "Mr. Diran Sarafyan, in his paper \booktitle{A New
Method of Computation of Square Roots Without Using
Divisions} (Communications, Nov. 1959) gave a way of
computing square roots which converges faster than the
standard Newton method. His technique can be
generalized as follows.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}
@Article{Ward:1960:CCE,
author = "Morgan Ward",
title = "The Calculation of the Complete Elliptic Integral of
the Third Kind",
journal = j-AMER-MATH-MONTHLY,
volume = "67",
number = "3",
pages = "205--213",
month = mar,
year = "1960",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2309677",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Tue Feb 6 16:32:27 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2309677",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
}
@Book{Warmus:1960:TEF,
author = "Mieczys{\l}aw Warmus",
title = "Tables of elementary functions",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "vii + 567",
year = "1960",
LCCN = "QA55 .W3 1960",
MRclass = "65.05",
MRnumber = "23 \#B1141",
MRreviewer = "J. C. P. Miller",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Pa{\'n}stwowe Wydawnictwo Naukowe, Warsaw. Separately
bound table of proportional parts, 30 pp.",
acknowledgement = ack-nhfb,
}
@Article{Wynn:1960:RAF,
author = "Peter Wynn",
title = "The Rational Approximation of Functions which are
Formally Defined by a Power Series Expansion",
journal = j-MATH-COMPUT,
volume = "14",
number = "70",
pages = "147--186",
month = apr,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Barakat:1961:EIG,
author = "Richard Barakat",
title = "Evaluation of the Incomplete Gamma Function of
Imaginary Argument by {Chebyshev} Polynomials",
journal = j-MATH-COMPUT,
volume = "15",
number = "73",
pages = "7--11",
month = jan,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Boersma:1961:TFR,
author = "J. Boersma",
title = "Two Formulas Relating to Elliptic Integrals of the
Third Kind (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "296--298",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Bowman:1961:IEF,
author = "Frank Bowman",
title = "Introduction to Elliptic Functions with Applications",
volume = "922",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "115",
year = "1961",
LCCN = "QA343 .B76 1961",
bibdate = "Wed Mar 15 06:50:49 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Unabridged and corrected republication of
\cite{Bowman:1953:IEF}.",
}
@Article{Cheney:1961:TNA,
author = "E. W. Cheney and H. L. Loeb",
title = "Two new algorithms for rational approximation",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "72--75",
month = dec,
year = "1961",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386002",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Corrington:1961:ACE,
author = "Murlan S. Corrington",
title = "Applications of the Complex Exponential Integral",
journal = j-MATH-COMPUT,
volume = "15",
number = "73",
pages = "1--6",
month = jan,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Ehrling:1961:NCI,
author = "G. Ehrling",
title = "On the Numerical Computation of Incomplete Elliptic
Integrals",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "1",
pages = "8--14",
month = mar,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01961946",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:06 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=1&spage=8",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Fields:1961:EHF,
author = "Jerry L. Fields and Jet Wimp",
title = "Expansions of Hypergeometric Functions in
Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "390--395",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Floyd:1961:ACE,
author = "Robert W. Floyd",
title = "An algorithm for coding efficient arithmetic
operations",
journal = j-CACM,
volume = "4",
number = "1",
pages = "42--51",
month = jan,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366062.366082",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:30 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/Compiler.Lins.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Robert W. Floyd (8 June 1936--25 September 2001)",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Description of binary subdivision method for computing
$n$-th powers in $ O(\log_2 (n))$ operations, as
referenced in \cite{Knuth:1962:EPC}.",
}
@Article{Froberg:1961:RCA,
author = "Carl-Erik Fr{\"o}berg",
title = "Rational {Chebyshev} Approximations of Elementary
Functions",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "4",
pages = "256--262",
month = dec,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933243",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See erratum \cite{Froberg:1963:ERC}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "elementary functions",
}
@Article{Gautschi:1961:RCR,
author = "Walter Gautschi",
title = "Recursive Computation of the Repeated Integrals of the
Error Function",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "227--232",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gray:1961:BFI,
author = "Marion C. Gray",
title = "{Bessel} functions of integral order and complex
argument",
journal = j-CACM,
volume = "4",
number = "4",
pages = "169--169",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366318",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "33.25",
MRnumber = "27\#1636",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The FORTRAN II source language [1, 2] places rather
severe restrictions on the form a subscript may take,
primarily because of the manner in which indices are
incremented in iterative loops. In the process of
constructing a compiler for a medium-sized (8008-word
memory) computer which will accept the FORTRAN II
source language, it became clear that the ``recursive
address calculation'' scheme, as used in the FORTRAN
compilers to minimize object-program running time, was
probably not the best one to use. This system,
described in some detail by Samelson and Bauer [3],
requires that the subscript expression be a linear
function of the subscripting variable. The alternative,
which requires complete evaluation of the ``storage
mapping function'', is usually rejected because of the
time required for the object program to perform the
necessary address calculation.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Bessel functions; special functions",
}
@Article{Herndon:1961:ABF,
author = "John R. Herndon",
title = "{Algorithm 57}: {Ber} or {Bei} Function",
journal = j-CACM,
volume = "4",
number = "4",
pages = "181--181",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366476",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "bei functions; ber functions; special functions",
remark = "Fullerton: 20-line Algol procedure that only sums
series.",
}
@Article{Herndon:1961:ACEa,
author = "John R. Herndon",
title = "{Algorithm 55}: {Complete} elliptic integral of the
first kind",
journal = j-CACM,
volume = "4",
number = "4",
pages = "180--180",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366454",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Herndon:1961:ACEb,
author = "John R. Herndon",
title = "{Algorithm 56}: {Complete} elliptic integral of the
second kind",
journal = j-CACM,
volume = "4",
number = "4",
pages = "180--181",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366474",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Herndon:1961:AEC,
author = "John R. Herndon",
title = "{Algorithm 46}: {Exponential} of a Complex Number",
journal = j-CACM,
volume = "4",
number = "4",
pages = "178--178",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366356",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\exp(z)$; $e^z$; elementary functions",
}
@Article{Herndon:1961:AGF,
author = "John R. Herndon",
title = "{Algorithm 54}: {Gamma} function for range $1$ to
$2$",
journal = j-CACM,
volume = "4",
number = "4",
pages = "180--180",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366453",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Gamma(x)$; special functions",
}
@Article{Herndon:1961:ASN,
author = "J. R. Herndon",
title = "{Algorithm 49}: {Spherical} {Neumann} Function",
journal = j-CACM,
volume = "4",
number = "4",
pages = "179--179",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.355579",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Coleman:1978:RSN}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Neumann functions; special functions",
}
@Book{Hochstadt:1961:SFM,
author = "Harry Hochstadt",
title = "Special functions of mathematical physics",
publisher = pub-HRW,
address = pub-HRW:adr,
pages = "viii + 81",
year = "1961",
ISBN = "0-236-73011-8",
ISBN-13 = "978-0-236-73011-7",
LCCN = "QA351 H65 1961",
bibdate = "Sat Oct 30 18:01:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Reprinted 1966.",
}
@Article{L:1961:BRF,
author = "Y. L. L.",
title = "Book Review: {L. Fox, \booktitle{Tables of Weber
Parabolic Cylinder Functions and Other Functions for
Large Arguments}, National Physical Laboratory
Mathematical Tables Volume 4, Her Majesty's Stationery
Office, London, 1960, iii + 40 p., 28 cm.
(Paperback)}",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "310--311",
month = jul,
year = "1961",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-61-99215-8",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Nov 15 11:07:36 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2002928;
https://www.ams.org/journals/mcom/1961-15-075/S0025-5718-61-99215-8/S0025-5718-61-99215-8.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Y. L. L. == Yudell L. Luke",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Landau:1961:PSW,
author = "H. J. Landau and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {II}",
journal = j-BELL-SYST-TECH-J,
volume = "40",
number = "1",
pages = "65--84",
month = jan,
year = "1961",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.27",
MRnumber = "0140733 (25 \#4147)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-65.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Luke:1961:EHF,
author = "Yudell L. Luke and Richard L. Coleman",
title = "Expansion of Hypergeometric Functions in Series of
Other Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "233--237",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Rader:1961:CAC,
author = "P. J. Rader and Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 14 [not 13]}: {Complex}
exponential integral",
journal = j-CACM,
volume = "4",
number = "2",
pages = "105--105",
month = feb,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:30 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Ei(z)$; special functions",
remark = "Fullerton: It's accurate but sometimes slow.",
}
@Article{Slepian:1961:PSW,
author = "D. Slepian and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {I}",
journal = j-BELL-SYST-TECH-J,
volume = "40",
number = "1",
pages = "43--63",
month = jan,
year = "1961",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.27",
MRnumber = "0140732 (25 \#4146)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-43.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Book{Sneddon:1961:SFM,
author = "Ian Naismith Sneddon",
title = "Special Functions of Mathematical Physics and
Chemistry",
publisher = "Oliver and Boyd",
address = "Edinburgh, UK",
edition = "Ssecond",
pages = "184",
year = "1961",
LCCN = "QA331 .S65 1961",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "University mathematical texts",
acknowledgement = ack-nhfb,
remark = "See first edition \cite{Sneddon:1956:SFM} and third
edition {Sneddon:1980:SFM}",
}
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "409--417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.20",
MRnumber = "MR0134842 (24 \#B894)",
MRreviewer = "M. E. Rose",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "399--403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Weingarten:1961:TGC,
author = "Harry Weingarten and A. R. {Di Donato}",
title = "A Table of Generalized Circular Error",
journal = j-MATH-COMPUT,
volume = "15",
number = "74",
pages = "169--173",
month = apr,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Werner:1961:CAG,
author = "Helmut Werner and Robert Collinge",
title = "{Chebyshev} Approximations to the Gamma Function (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "15",
number = "74",
pages = "195--197",
month = apr,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wojcicki:1961:ABF,
author = "Maria E. Wojcicki",
title = "{Algorithm 44}: {Bessel} Functions Computed
Recursively",
journal = j-CACM,
volume = "4",
number = "4",
pages = "177--178",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366341",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Bessel functions; special functions",
}
@Article{Albrecht:1962:FKM,
author = "J. Albrecht",
title = "{Fehlerschranken und Konvergenzbeschleunigung bei
einer monotonen oder alternierenden Iterationsfolge}.
({German}) [{Error} Bounds and Convergence Acceleration
with a Monotone or Alternating Iteration Sequence]",
journal = j-NUM-MATH,
volume = "4",
pages = "196--208",
month = dec,
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration",
language = "German",
}
@Article{Arscott:1962:BRI,
author = "F. M. Arscott",
title = "Book Review: {{\booktitle{Introduction to Elliptic
Functions with Applications}} (F. Bowman)}",
journal = j-SIAM-REVIEW,
volume = "4",
number = "4",
pages = "408--408",
month = "????",
year = "1962",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1004109",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:04:56 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/4/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1962",
}
@TechReport{Blanch:1962:TRR,
author = "Gertrude Blanch and Donald S. Clemm",
title = "Tables Relating to the Radial {Mathieu} Functions,
Vols. 1 \& 2",
type = "Report",
institution = "Aeronautical Research Labs. U. S. Government Printing
Office",
address = "Washington, DC, USA",
year = "1962",
bibdate = "Fri Oct 29 21:37:53 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Gertrude Blanch (1897--1996)",
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 7-place tables.",
}
@Article{Boersma:1962:CLF,
author = "J. Boersma",
title = "On the Computation of {Lommel}'s Functions of Two
Variables (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "16",
number = "78",
pages = "232--238",
month = apr,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Lommel's functions are infinite sums
involving Bessel functions $ J_{\nu - 2m}(x) $.",
}
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "155--164",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219348",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Christiansen:1962:APC,
author = "S{\o}ren Christiansen",
title = "{Algol} Programming: Contribution no. 3: Calculation
of complementary {Fresnel} integrals",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "3",
pages = "192--194",
year = "1962",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:34:20 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: A 50-line Algol procedure is given. It
calculates $ \int_x^\infty \cos (t) / \sqrt {2 \pi t}
\, d t $ and $ \int_x^\infty \sin (t) / \sqrt {2 \pi t}
\, d t $.",
}
@Article{Cundiff:1962:AEA,
author = "John L. Cundiff",
title = "{Algorithm 88}: {Evaluation} of Asymptotic Expression
for the {Fresnel} Sine and Cosine Integrals",
journal = j-CACM,
volume = "5",
number = "5",
pages = "280--280",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: Can be used with algorithms 89 and 90.
30-line Algol procedure.",
}
@Article{Cundiff:1962:AEFa,
author = "John L. Cundiff",
title = "{Algorithm 89}: {Evaluation} of the {Fresnel} Sine
Integral",
journal = j-CACM,
volume = "5",
number = "5",
pages = "280--280",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "S(x); special functions",
remark = "Fullerton: 20-line Algol procedure that must be used
with algorithm 88.",
}
@Article{Cundiff:1962:AEFb,
author = "John L. Cundiff",
title = "{Algorithm 90}: {Evaluation} of the {Fresnel} Cosine
Integral",
journal = j-CACM,
volume = "5",
number = "5",
pages = "281--281",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); special functions",
remark = "Fullerton: 20-line Algol procedure that must be used
with algorithm 88.",
}
@Article{DiDonato:1962:MCC,
author = "A. R. DiDonato and M. P. Jarnagin",
title = "A Method for Computing the Circular Coverage
Function",
journal = j-MATH-COMPUT,
volume = "16",
number = "79",
pages = "347--355",
month = jul,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{DiDonato:1962:MCG,
author = "A. R. DiDonato and M. P. Jamagin",
title = "A Method for Computing the Generalized Circular Error
Function and the Circular Coverage Function",
type = "NWL Report",
number = "1768",
institution = "Naval Surface Weapons Center",
address = "Dahlgren, VA 22448, USA",
day = "23",
month = jan,
year = "1962",
bibdate = "Wed Nov 12 15:56:35 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Dorn:1962:GHR,
author = "William S. Dorn",
title = "Generalizations of {Horner}'s rule for polynomial
evaluation",
journal = j-IBM-JRD,
volume = "6",
number = "2",
pages = "239--245",
month = apr,
year = "1962",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.62.0239",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65.50",
MRnumber = "24 \#B2541",
bibdate = "Tue Sep 11 16:10:28 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392358",
ZMnumber = "128.37202",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "D. H. Lehmer",
}
@Article{Fraser:1962:CRA,
author = "W. Fraser and J. F. Hart",
title = "On the computation of rational approximations to
continuous functions",
journal = j-CACM,
volume = "5",
number = "7",
pages = "401--403",
month = jul,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368273.368578",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:39 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
elementary functions; Remes algorithm; special
functions",
remark = "This paper outlines the Remes algorithm for ``for
finding polynomial approximations to the determination
of `best' rational approximations.''. It also gives
approximations for starting values of Newton--Raphson
iterations for $ \abs (x) $, $ \cos (x) $, $ \Gamma (1
+ x) $, and $ \sin (x) $.",
}
@Article{Hansen:1962:SRV,
author = "Eldon R. Hansen and Merrell L. Patrick",
title = "Some Relations and Values for the Generalized
{Riemann} Zeta Function",
journal = j-MATH-COMPUT,
volume = "16",
number = "79",
pages = "265--274",
month = jul,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Jefferson:1962:RAI,
author = "David K. Jefferson",
title = "Remark on {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "5",
number = "10",
pages = "514--514",
month = oct,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:41 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Knuth:1962:ECP,
author = "Donald E. Knuth",
title = "{Euler}'s Constant to $ 1271 $ Places",
journal = j-MATH-COMPUT,
volume = "16",
number = "79",
pages = "275--281",
month = jul,
year = "1962",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1962-0148255-X",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "10.41",
MRnumber = "26 #5763",
bibdate = "Fri Mar 22 18:03:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database; MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Knuth:1962:EPC,
author = "Donald E. Knuth",
title = "Evaluation of polynomials by computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355580.369074",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00 (12.00)",
MRnumber = "27 #970",
bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "The author reports that Motzkin (1962) showed that
Horner's rule for polynomial evaluation may not be
optimal, and develops the idea further for arbitrary
polynomials, but also observes that the coefficients of
the revised polynomials may be difficult to find. He
also asks about, but does not answer, the question of
error analysis of the various methods.",
}
@Article{Landau:1962:PSW,
author = "H. J. Landau and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {III}. {The} dimension of the space of
essentially time- and band-limited signals",
journal = j-BELL-SYST-TECH-J,
volume = "41",
number = "4",
pages = "1295--1336",
month = jul,
year = "1962",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.28 (94.10)",
MRnumber = "0147686 (26 \#5200)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1962/BSTJ.1962.4104.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol41/bstj41-4-1295.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Merner:1962:AAC,
author = "J. N. Merner",
title = "{ACM Algorithm 149}: Complete Elliptic Integral",
journal = j-CACM,
volume = "5",
number = "12",
pages = "605",
month = dec,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Skovgaard:1978:RCE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Thacher:1962:CAB,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 57}: {$ \operatorname
{ber} $} or {$ \operatorname {bei} $} function",
journal = j-CACM,
volume = "5",
number = "8",
pages = "438--438",
month = aug,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:40 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "bei functions; ber functions; special functions",
remark = "Fullerton: The algorithm is inaccurate for large
$x$.",
}
@Article{Thacher:1962:CAH,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithms 191 and 192,
Hypergeometric and Confluent Hypergeometric
Functions}",
journal = j-CACM,
volume = "7",
number = "4",
pages = "244--244",
month = apr,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 11:27:28 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: An error in a comment is noted.",
}
@Article{Wimp:1962:PEB,
author = "Jet Wimp",
title = "Polynomial Expansions of {Bessel} Functions and Some
Associated Functions",
journal = j-MATH-COMPUT,
volume = "16",
number = "80",
pages = "446--458",
month = oct,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
note = "See corrigendum \cite{Wimp:1972:CPE}.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wynn:1962:AAP,
author = "P. Wynn",
title = "An Arsenal of {ALGOL} Procedures for Complex
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "4",
pages = "232--255",
month = dec,
year = "1962",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940171",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "ALGOL; complex arithmetic; confluence hypergeometric
function; continued fractions; incomplete beta
function; incomplete gamma function; Stieltjes
$S$-fractions; Weber parabolic cylinder function",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Barakat:1963:CES,
author = "Richard Barakat and Agnes Houston",
title = "{Chebyschev} Expansion of the Sine and Cosine
Integrals",
journal = j-J-MATH-PHYS-MIT,
volume = "42",
number = "1--4",
pages = "331--333",
month = apr,
year = "1963",
CODEN = "JMPHA9",
DOI = "https://doi.org/10.1002/sapm1963421331",
ISSN = "0097-1421",
ISSN-L = "0097-1421",
bibdate = "Sat Aug 19 13:36:07 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib",
URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1963421331",
acknowledgement = ack-nhfb,
ajournal = "J. Math. Phys. (MIT)",
fjournal = "Journal of Mathematics and Physics (MIT)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590",
onlinedate = "April 1963",
}
@Article{Burgoyne:1963:AKF,
author = "F. D. Burgoyne",
title = "Approximations to {Kelvin} Functions (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "17",
number = "83",
pages = "295--298",
month = jul,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 9-digit approximations.",
}
@Article{Carlitz:1963:IEF,
author = "L. Carlitz",
title = "The Inverse of the Error Function",
journal = j-PAC-J-MATH,
volume = "13",
number = "2",
pages = "459--470",
year = "1963",
CODEN = "PJMAAI",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
bibdate = "Thu Sep 13 21:30:05 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://pjm.math.berkeley.edu/pjm;
http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
}
@Article{Clenshaw:1963:ASF,
author = "C. W. Clenshaw and G. F. Miller and M. Woodger",
title = "Algorithms for Special Functions {I}",
journal = j-NUM-MATH,
volume = "4",
pages = "403--419",
month = dec,
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:21:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
remark = "Fullerton: ALGOL 60 procedures with accuracy $ \approx
10^{-15} $ for $ \exp $, $ \ln $, $ \sin $, $ \cos $, $
\tan $, $ \arcsin $, $ \arctan $, $ \gamma $, $ \Ei $
and $ \erf $. See G. F. Miller (1965) for
corrections.",
}
@Article{Eisman:1963:PER,
author = "S. H. Eisman",
title = "Polynomial Evaluation Revisited",
journal = j-CACM,
volume = "6",
number = "7",
pages = "384--385",
month = jul,
year = "1963",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366663.366668",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Erdelyi:1963:AEC,
author = "A. Erd{\'e}lyi and M. Wyman",
title = "The asymptotic evaluation of certain integrals",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "14",
number = "1",
pages = "217--260",
month = jan,
year = "1963",
CODEN = "AVRMAW",
DOI = "https://doi.org/10.1007/BF00250704",
ISSN = "0003-9527 (print), 1432-0673 (electronic)",
ISSN-L = "0003-9527",
bibdate = "Sat Feb 18 14:53:08 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/BF00250704",
acknowledgement = ack-nhfb,
fjournal = "Archive for rational mechanics and analysis",
journal-URL = "http://link.springer.com/journal/205",
keywords = "incomplete gamma function",
}
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting Approximations for the Iterative Calculation
of Square Roots",
journal = j-COMP-J,
volume = "6",
number = "3",
pages = "274--276",
month = nov,
year = "1963",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/6.3.274",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:30 MST 2012",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://comjnl.oxfordjournals.org/content/6/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Several starting approximations are given which, in
conjunction with a well-known iterative process, lead
to square root approximations, with a relative error in
the range $ (2^{-55}, 2^{-45}) $, at the expense of
three divisions. More accurate approximations are given
which require in addition a single multiplication.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fettis:1963:AMH,
author = "Henry E. Fettis",
title = "{Algorithm 163}: {Modified} {Hankel} function",
journal = j-CACM,
volume = "6",
number = "4",
pages = "161--162",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Hankel functions; special functions",
remark = "Fullerton: A 25-line Algol procedure for $ e^x K_p(x)
$.",
}
@Article{Froberg:1963:APC,
author = "Carl-Erik Fr{\"o}berg",
title = "{Algol} Programming: Contribution no. 5: Computation
of the {Fermi} function",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "3",
number = "2",
pages = "141--142",
year = "1963",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: The Fermi function depends on several
physical parameters of the atomic nucleus.",
}
@Article{Froberg:1963:ERC,
author = "C.-E. Fr{\"o}berg",
title = "Erratum: {``Rational Chebyshev Approximations of
Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261,
line 12]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "3",
number = "1",
pages = "68--68",
month = mar,
year = "1963",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01963538",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Froberg:1961:RCA}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "elementary functions",
}
@InProceedings{Gautschi:1963:RCS,
author = "Walter Gautschi",
editor = "????",
booktitle = "{The University of Michigan Engineering Summer
Conferences, Numerical Analysis, Summer 1963}",
title = "Recursive computation of special functions",
publisher = "????",
address = "????",
pages = "??--??",
year = "1963",
bibdate = "Fri Aug 21 11:08:35 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gray:1963:AFI,
author = "Malcolm D. Gray",
title = "{Algorithm 213}: {Fresnel} Integrals",
journal = j-CACM,
volume = "6",
number = "10",
pages = "617--617",
month = oct,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:49 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Gray:1964:CAF} and related
remark \cite{Gray:1963:RAE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); S(x); special functions",
}
@Article{Gray:1963:RAE,
author = "Malcolm D. Gray",
title = "Remark on Algorithms 88, 89, and 90 evaluation of the
{Fresnel} integrals",
journal = j-CACM,
volume = "6",
number = "10",
pages = "618--618",
month = oct,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:49 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: An error is noted.",
}
@Article{Hofsommer:1963:NCE,
author = "D. J. Hofsommer and R. van de Riet",
title = "On the numerical calculation of elliptic integrals of
the first and second kind and the elliptic functions of
{Jacobi}",
journal = j-NUM-MATH,
volume = "5",
pages = "291--302",
month = dec,
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Ibbetson:1963:AG,
author = "D. Ibbetson",
title = "{Algorithm 209}: {Gauss}",
journal = j-CACM,
volume = "6",
number = "10",
pages = "616--616",
month = oct,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:49 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Knuth:1963:LEE,
author = "Donald E. Knuth",
title = "Letter to the {Editor}: {Evaluation} of polynomials by
computer",
journal = j-CACM,
volume = "6",
number = "2",
pages = "51--51",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Dec 26 16:31:38 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Knuth:1962:EPC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Lee-Whiting:1963:EFC,
author = "G. E. Lee-Whiting",
title = "Erratum: ``{Formulas} for Computing Incomplete
Elliptic Integrals of the First and Second Kinds''",
journal = j-J-ACM,
volume = "10",
pages = "412--412",
year = "1963",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Dec 10 15:59:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Lee-Whiting:1963:FCI}.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
xxmonth = "none",
xxnumber = "none",
}
@Article{Lee-Whiting:1963:FCI,
author = "G. E. Lee-Whiting",
title = "Formulas for Computing Incomplete Elliptic Integrals
of the First and Second Kinds",
journal = j-J-ACM,
volume = "10",
number = "2",
pages = "126--130",
month = apr,
year = "1963",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Nov 05 22:55:28 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Lee-Whiting:1963:EFC}.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Book{Ljusternik:1963:MVF,
author = "L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R.
Janpol{\'s}ki{{\u{\i}}}",
title = "{{\cyr Matematicheski{\u{\i}}analiz. Vychislenie
{\`e}lementarnykh funktsi{\u{\i}}}}. [Mathematical
analysis. {Computation} of the elementary functions]",
publisher = "Gosudarstv. Izdat. Fiz-Mat. Lit.",
address = "Moscow, USSR",
pages = "247",
year = "1963",
MRclass = "65.25",
MRnumber = "28 \#1733",
MRreviewer = "John Todd",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ludwig:1963:AIB,
author = "Oliver G. Ludwig",
title = "{Algorithm 179}: {Incomplete} beta ratio",
journal = j-CACM,
volume = "6",
number = "6",
pages = "314--314",
month = jun,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Pike:1976:RIB,Bosten:1974:RAI}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: This algorithm is the basis for a modern
treatment by Bosten and Battiste.",
}
@Article{Meyer:1963:CAI,
author = "Noelle A. Meyer",
title = "Certification of {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "6",
number = "2",
pages = "69--69",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:44 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Newman:1963:ICS,
author = "J. N. Newman and W. Frank",
title = "An Integral Containing the Square of a {Bessel}
Function",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "64--70",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: The integral $ I_n^m(x) = \int_0^{\pi / 2}
\frac {J_n^2(x \cos (\theta))}{(x \cos (\theta))^{2m}}
\, d \theta $, where $m$ and $n$ are either integers or
half integers, is considered.",
}
@Article{Peuizulaev:1963:AEF,
author = "{\v{S}}. I. Pe{\u{\i}}zulaev",
title = "An approximation by elementary functions.
({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
volume = "3",
pages = "769--770",
year = "1963",
MRclass = "41.30",
MRnumber = "28 \#398",
MRreviewer = "D. D. Stancu",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Relph:1963:AAH,
author = "A. P. Relph",
title = "{ACM Algorithm 191}: Hypergeometric",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--389",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:32:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Koppelaar:1974:CRA}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Relph:1963:ACH,
author = "A. P. Relph",
title = "{Algorithm 192}: {Confluent} hypergeometric",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--388",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: 30-line Algol procedure for complex args.
The work of Luke supersedes this.",
}
@Article{Relph:1963:AH,
author = "A. P. Relph",
title = "{Algorithm 191}: {Hypergeometric}",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--388",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Koppelaar:1974:CRA}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: 30-line Algol procedure. The work of Luke
is better.",
}
@Article{Rutishauser:1963:BQG,
author = "H. Rutishauser",
title = "{Betrachtungen zur Quadratwurzeliteration}. ({German})
[{Considerations} on square root iteration]",
journal = j-MONAT-MATH,
volume = "67",
pages = "452--464",
year = "1963",
CODEN = "MNMTA2",
DOI = "https://doi.org/10.1007/BF01295091",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
MRclass = "65.50",
MRnumber = "158532",
MRreviewer = "A. S. Householder",
bibdate = "Mon Aug 24 21:56:15 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Heinz Rutishauser (30 January 1918--10 November
1970)",
fjournal = "Monatshefte f{\"u}r Mathematik",
journal-URL = "http://link.springer.com/journal/605",
language = "German",
}
@Book{Sneddon:1963:SFM,
author = "Ian Naismith Sneddon",
title = "{Spezielle Funktionen der mathematischen Physik und
Chemie. Mathematische Formelsammlung II}. ({German})
[Special {functions} of mathematical physics and
chemistry. {Mathematical} formula collection {II}]",
volume = "54",
publisher = pub-BIBLIO-INST,
address = pub-BIBLIO-INST:adr,
pages = "166",
year = "1963",
LCCN = "QA351 .S6415",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "B. I.-Hochschultaschenb{\"u}cher",
acknowledgement = ack-nhfb,
language = "German",
remark = "German translation of \cite{Sneddon:1961:SFM}.",
subject = "Functions; Mathematical physics",
}
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
title = "A circuit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}
@Article{Sweeney:1963:CEC,
author = "Dura W. Sweeney",
title = "On the Computation of {Euler}'s Constant",
journal = j-MATH-COMPUT,
volume = "17",
number = "82",
pages = "170--178",
month = apr,
year = "1963",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1963-0160308-X",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 3566 digits should be enough.",
}
@Article{Thacher:1963:ACEa,
author = "Henry C. {Thacher, Jr.}",
title = "{Algorithm 165}: {Complete} elliptic integrals",
journal = j-CACM,
volume = "6",
number = "4",
pages = "163--164",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Thacher:1963:CACa,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 55}: {Complete} elliptic
integral of the first kind",
journal = j-CACM,
volume = "6",
number = "4",
pages = "166--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Thacher:1963:CACb,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 149}: {Complete} elliptic
integral",
journal = j-CACM,
volume = "6",
number = "4",
pages = "166--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Book{Tocher:1963:AS,
author = "K. D. Tocher",
title = "The Art of Simulation",
publisher = "Van Nostrand",
address = "Princeton, NJ, USA",
pages = "viii + 184",
year = "1963",
LCCN = "TA177 .T6",
bibdate = "Sat Dec 16 17:47:12 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Simulation methods",
}
@Article{vandeRiet:1963:CAI,
author = "R. P. van de Riet",
title = "Certification of {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "6",
number = "4",
pages = "167--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Werner:1963:AFI,
author = "H. Werner and G. Raymann",
title = "An Approximation to the {Fermi} Integral {$ F_{1 /
2}(x) $}",
journal = j-MATH-COMPUT,
volume = "17",
number = "82",
pages = "193--194",
month = apr,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2003641",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors of $ 5 \times 10^{-4} $.",
}
@Article{Whittlesey:1963:IGF,
author = "John R. B. Whittlesey",
title = "Incomplete Gamma Functions for Evaluating {Erlang}
Process Probabilities",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "11--17",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InCollection{Abramowitz:1964:CWF,
author = "Milton Abramowitz",
title = "{Coulomb} Wave Functions",
crossref = "Abramowitz:1964:HMF",
pages = "537--554",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Abramowitz:1964:SFR,
author = "Milton Abramowitz",
title = "{Struve} Functions and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "495--502",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
title = "Proposed automatic calculating machine",
journal = j-IEEE-SPECTRUM,
volume = "1",
number = "8",
pages = "62--69",
month = aug,
year = "1964",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1964.6500770",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Tue Jan 14 11:14:17 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
abstract = "Here presented is the memorandum that 20 years ago
initiated a series of events whose revolutionary
implications are only beginning to manifest themselves
a description of the first large-scale general-purpose
automatic digital computer. Twenty years ago, on August
7, 1944, Mark I, the first large-scale general-purpose
automatic digital computer ever to be put in operation
was dedicated at Harvard University by James B. Conant,
then president of Harvard, and the late Thomas J.
Watson, founder of IBM.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
remark = "Pages 66--69 discuss computation of the elementary
functions with minimal intermediate storage: recipes
are given for integral and fractional power, log,
exponential, trigonometric, inverse trigonometric,
hyperbolic, and inverse hyperbolic. Mention is also
made of the probability integral, elliptic functions,
and Bessel functions, but the text says they will be
discussed later (meaning, in a future publication). The
methods involve recurrences and series summations, and
thus, can be regarded as precision independent.",
xxnote = "Previously unpublished memorandum written by Aiken and
dated by an unknown recipient as 4 November 1937.
Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
}
@InCollection{Antosiewicz:1964:BFF,
author = "H. A. Antosiewicz",
title = "{Bessel} Functions of Fractional Order",
crossref = "Abramowitz:1964:HMF",
pages = "435--478",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Blanch:1964:MF,
author = "Gertrude Blanch",
title = "{Mathieu} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "721--750",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "1897--1996",
citedby = "Fullerton:1980:BEM",
}
@Article{Bray:1964:CAGa,
author = "T. A. Bray",
title = "Certification of {Algorithm 225}: {Gamma} function
with controlled accuracy",
journal = j-CACM,
volume = "7",
number = "10",
pages = "586--586",
month = oct,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Gamma(x)$; special functions",
remark = "Fullerton: No corrections were necessary.",
}
@Article{Burgoyne:1964:GTF,
author = "F. D. Burgoyne",
title = "Generalized Trigonometric Functions (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "18",
number = "86",
pages = "314--316",
month = apr,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1964:DPS,
author = "William J. {Cody, Jr.}",
title = "Double-Precision Square Root for the {CDC-3600}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "715--718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:57 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC-1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has built-in
double-precision floating-point arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a double-precision subroutine for the
3600.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$sqrt(x)$; CDC 3600; elementary functions;
floating-point arithmetic",
}
@Article{Cowgill:1964:LEB,
author = "D. Cowgill",
title = "Logic Equations for a Built-In Square Root Method",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "156--157",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263791",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Curtiss:1964:EIB,
author = "C. F. Curtiss",
title = "Expansions of Integrals of {Bessel} Functions of Large
Order",
journal = j-J-MATH-PHYS,
volume = "5",
number = "4",
pages = "561--564",
month = apr,
year = "1964",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1704149",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 08:40:12 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v5/i4/p561_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "22 December 2004",
pagecount = "4",
}
@Article{Cyvin:1964:AGF,
author = "S. J. Cyvin and B. N. Cyvin",
title = "{Algorithm 225}: {Gamma} function with controlled
accuracy",
journal = j-CACM,
volume = "7",
number = "5",
pages = "295--295",
month = may,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:53 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Gamma(x)$; special functions",
remark = "Fullerton: 30-line Algol procedure based on
out-of-date method.",
}
@Article{Cyvin:1964:AND,
author = "S. J. Cyvin",
title = "{Algorithm 226}: {Normal} distribution function",
journal = j-CACM,
volume = "7",
number = "5",
pages = "295--295",
month = may,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/364099.364315",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:53 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
}
@InCollection{Davis:1964:GFR,
author = "Philip J. Davis",
title = "Gamma Function and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "253--294",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Eve:1964:EP,
author = "J. Eve",
title = "The evaluation of polynomials",
journal = j-NUM-MATH,
volume = "6",
number = "1",
pages = "17--21",
month = dec,
year = "1964",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386049",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "number of multiplications to evaluate a polynomial",
remark = "From the first two paragraphs: ``Ostrowski [5] has
shown that the $ 2 n $ operations required by this
algorithm [Horner's] are minimal for $ n \leq 4 $.
Motzkin [4] (see also Todd [8]) and Knuth [3] have
given methods whereby polynomials with $ 4 \leq n \leq
6 $ can be evaluated in $ [(1 / 2)(n + 3)] $
multiplications and not more than $ n + 1 $ additions.
Similar methods effecting a reduction in the number of
multiplications have been described by Pan [6] for $ n
\leq 12 $. Each of these methods is valid only for a
particular value of $n$.\par A general method due to
Pan [7] applicable to all polynomials with $ n \geq 5 $
results in an evaluation involving $ [(1 / 2) (n + 4)]
$ multiplications and $ n + 1 $ additions. Knuth has
also given a method applicable to all polynomials with
$ n \geq 3 $ in which $ n + 1 $ additions are required
while the number of multiplications varies between $
[(1 / 2) (n + 3)] $ and approximately $ (3 / 4)n $.''",
}
@TechReport{Fisherkeller:1964:TCE,
author = "M. A. Fisherkeller and W. J. {Cody, Jr.}",
title = "Tables of the Complete Elliptic Integrals $ {K} $, $
{K}' $, $ {E} $, and $ {E}' $",
type = "Technical Memo",
number = "ANL AMD 71",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "14",
year = "1964",
bibdate = "Thu Nov 17 10:44:21 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See review by John W. Wrench in Mathematics of
Computation, {\bf 19}(89--92), 342, 1965.",
acknowledgement = ack-nhfb,
}
@Article{Gargantini:1964:RCA,
author = "I. Gargantini and T. Pomentale",
title = "Rational {Chebyshev} approximations to the {Bessel}
function integrals {$ K i_s(x) $}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "727--730",
month = dec,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "31\#863",
bibdate = "Fri Nov 25 18:19:57 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The second Remes algorithm is used to approximate the
integrals $ K i_s $ by rational functions. The related
coefficients for the approximations of $ K i_1, K i_2,
K i_3 $ are given for different precisions.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Bessel functions; Kis(x); special functions",
remark = "Fullerton: Approximations for repeated integrals $
\operatorname {Ki}_s(x) $ of $ K(x) $ for $ s = 1, 2, 3
$ are given for accuracies down to $ 10^{-5} $ for $ s
= 1 $ and to $ 10^{-7} $ for $ s = 2, 3 $.",
}
@Article{Gautschi:1964:AAB,
author = "W. Gautschi",
title = "{ACM Algorithm 236}: {Bessel} Functions of the First
Kind [{S17}]",
journal = j-CACM,
volume = "7",
number = "8",
pages = "479--480",
month = aug,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355586.355587",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:55 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See remark \cite{Skovgaard:1975:RBF}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$J_n(x)$; Bessel functions of the first kind; special
functions",
}
@Article{Gautschi:1964:AGF,
author = "Walter Gautschi",
title = "{Algorithm 221}: {Gamma} functions",
journal = j-CACM,
volume = "7",
number = "3",
pages = "143--143",
month = mar,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:52 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Gamma(x)$; special functions",
}
@Article{Gautschi:1964:AIB,
author = "Walter Gautschi",
title = "{Algorithm 222}: {Incomplete} beta functions ratios",
journal = j-CACM,
volume = "7",
number = "3",
pages = "143--143",
month = mar,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:52 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "beta functions; special functions",
remark = "Fullerton: 200-line Algol procedure.",
}
@Article{Gautschi:1964:CAI,
author = "Walter Gautschi",
title = "Certification of {Algorithm 222}: {Incomplete} beta
function ratios",
journal = j-CACM,
volume = "7",
number = "4",
pages = "244--244",
month = apr,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:53 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "beta functions; special functions",
remark = "Fullerton: A typographical error is noted.",
}
@InCollection{Gautschi:1964:EFF,
author = "Walter Gautschi",
title = "Error Function and {Fresnel} Integrals",
crossref = "Abramowitz:1964:HMF",
pages = "295--330",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Gautschi:1964:EIR,
author = "Walter Gautschi and William F. Cahill",
title = "Exponential Integral and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "227--252",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Gray:1964:CAF,
author = "Malcolm Gray",
title = "Certification of {Algorithm 213}: {Fresnel}
integrals",
journal = j-CACM,
volume = "7",
number = "11",
pages = "661--661",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gray:1963:AFI,Gray:1963:RAE}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: Several corrections are given.",
}
@InCollection{Haynsworth:1964:BEP,
author = "Emilie V. Haynsworth and Karl Goldberg",
title = "{Bernoulli} and {Euler} Polynomials, {Riemann Zeta}
Function",
crossref = "Abramowitz:1964:HMF",
pages = "803--820",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Hochstrasser:1964:OP,
author = "Urs W. Hochstrasser",
title = "Orthogonal Polynomials",
crossref = "Abramowitz:1964:HMF",
pages = "771--802",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Hummer:1964:EDF,
author = "David G. Hummer",
title = "Expansions of {Dawson}'s Function in a Series of
{Chebyshev} Polynomials (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "18",
number = "86",
pages = "317--319",
month = apr,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Almost l5-digit approximations.",
}
@Article{Lanczos:1964:PAG,
author = "Cornelius Lanczos",
title = "A Precision Approximation of the Gamma Function",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "1",
number = "1",
pages = "86--96",
month = "????",
year = "1964",
DOI = "https://doi.org/10.1137/0701008",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
ISSN-L = "0887-459X",
MRclass = "33.15",
MRnumber = "0176115 (31 \#390)",
MRreviewer = "S. C. van Veen",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2949767",
ZMnumber = "Zbl 0136.05201",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics: Series B, Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
}
@Article{Lotsch:1964:AFI,
author = "Helmut Lotsch and Malcolm Gray",
title = "{Algorithm 244}: {Fresnel} Integrals [{S20}]",
journal = j-CACM,
volume = "7",
number = "11",
pages = "660--661",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This procedure computes the Fresnel sine and cosine
integrals $ C(w) = \int_0^\infty \cos [(\pi / 2)t^2] \,
d t $ and $ S(w) = \int_0^w \sin [(\pi / 2)t^2] \, d t
$. It is a modification of Algorithm 213 (Comm. ACM, 6
(Oct. 1963), 617) such that the accuracy, expressed by
\textit{eps}, is improved. eps can arbitrarily be
chosen up to $ \textit {eps} = 10^{-6} $ for a computer
with sufficient word length as, for example, the
Burroughs B5000 which has 11--12 significant digits.
Referring to the formulas of Algorithm 213: if $ |w| <
\sqrt {(26.20 / \pi)} $ the series expansions $ C(w) $
and $ S(w) $ are terminated when the absolute value of
the relative change in two successive terms is $ \leq
\textit {eps} $. If $ |w| \geq \sqrt {(26.20 / \pi)} $
the series $ Q(x) $ and $ P(x) $ are terminated when
the absolute value of the terms is $ \leq \textit {eps}
/ 2 $. However, this truncation point is not
necessarily valid for the range $ \sqrt {(26.20 / \pi)}
\leq |w| < \sqrt {(28.50 / \pi)} $ when $ \textit {eps}
= 10^{-6} $, since the asymptotic series must be
terminated before arriving at the minimum. In this
range the ignored terms of the series expansions are $
< 3 \times 10^6 $, and for larger arguments $ < 10^{-6}
$. This accuracy may be improved if desired: the
switch-over point from the regular to the asymptotic
series expansions has to be displaced to larger
arguments.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); Fresnel integrals; S(x); special functions",
remark = "Fullerton: 100-line Algol procedure.",
}
@InCollection{Lowan:1964:SWF,
author = "Arnold N. Lowan",
title = "Spheroidal Wave Functions",
crossref = "Abramowitz:1964:HMF",
pages = "751--770",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Luke:1964:IBF,
author = "Yudell L. Luke",
title = "Integrals of {Bessel} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "479--494",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Book{Meinardus:1964:AFI,
author = "Gunter Meinardus",
title = "{Approximation von Funktionen und ihre numerische
Behandlung}. ({German}) [{Approximation} of functions
and their numerical treatment]",
volume = "4",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 180",
year = "1964",
DOI = "https://doi.org/10.1007/978-3-642-85646-4",
ISBN = "3-540-03219-3, 3-642-85646-2, 3-642-85647-0 (print)",
ISBN-13 = "978-3-540-03219-9, 978-3-642-85646-4,
978-3-642-85647-1 (print)",
LCCN = "QA320 .M4",
bibdate = "Thu Oct 19 17:00:27 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Springer tracts in natural philosophy",
abstract = "[numerous OCR errors to be corrected] Erst in den
letzten Jahren hat sich derjenige Tell der
Approximations theorie, der sich auf numerische
Fragestellungen anwenden l{\"a}{\ss}t, starker
entwickelt. Das Prinzip der in einem gewissen Sinne
besten Ann{\"a}herung von Funktionen gewann
insbesondere durch die Verwendung elektronischer
Rechenmaschinen an Bedeutung. Einige der theoretischen
Grundlagen, die zur Behandlung der auftretenden
Probleme herange zogen werden mussen, finden sich
verstreut in wenigen Buchern. Der weitaus gro{\ss}te
Teil der theoretischen und praktischen Untersuchungen
ist jedoch nur in den Originalarbeiten nachzulesen.
Hieraus ergab sich die Zielsetzung des vorliegenden
Buches: Es sollte eine Zusammen stellung der
wesentlichen Ergebnisse der Approximationstheorie
gegeben werden, die einerseits ein rasches Eindringen
in die modernen Entwicklungen dieses Gebietes
ermoglicht und andererseits eine gewisse
Vollst{\"a}ndigkeit auf dem Problemkreis der
Tschebyscheff-Approximationen bietet, womit keineswegs
gemeint ist, da{\ss} eine vollst{\"a}ndige Literatur
{\"u}bersicht angestrebt wurde. Die Auswahl erfolgte
stets nach dem immer noch subjektiven Gesichtspunkt der
Bedeutung f{\"u}r die Anwendungen. Dies gilt z. B. auch
f{\"u}r die asymptotischen Untersuchungen des {\S} 3,
denn ich bin der Meinung, da{\ss} man sich auch
beinumerischen Approximationen {\"u}ber die, wenigstens
asymptotisch zu erwartende Genauigkeit Gedanken machen
sollte. Fast ausschlie{\ss}lich habe ich mich auf die
Theorie der gleich m{\"a}{\ss}igen Approximation
beschr{\"a}nkt, da diese die weitaus gro{\ss}te
praktische Bedeutung besitzt. Das erste Kapitel
behandelt lineare Approximationen. Der {\S} 3
enth{\"a}lt wohl den heute k{\"u}rzesten Zugang zur
linearen Theorie.",
acknowledgement = ack-nhfb,
author-dates = "1926--",
language = "German",
subject = "Aproximaciones",
tableofcontents = "I Lineare Approximationen \\
I.1. Das allgemeine lineare Approximationsproblem \\
I.2. Dichte Systeme \\
I.3. Allgemeine Theorie linearer
Tschebyscheff-Approximationen \\
I.4. Spezielle Tschebyscheff-Approximationen \\
I.5. Absch{\"a}tzungen der Gr{\"o}{\ss}enordnung des
Fehlers bei trigonometrischer und bei polynomialer
Approximation \\
I.6. Polynomapproximationen \\
I.7. Numerische Verfahren bei linearen
Tschebyscheff-Approximationen \\
II Nicht-lineare Approximationen \\
II.8. Allgemeine Theorie nicht-linearer
Tschebyscheff-Approximationen \\
II.9. Rationale Approximationen \\
II.10. Exponentialapproximationen",
}
@InCollection{Miller:1964:PCF,
author = "J. C. P. Miller",
title = "Parabolic Cylinder Functions",
crossref = "Abramowitz:1964:HMF",
pages = "685--720",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Milne-Thomson:1964:EI,
author = "L. M. Milne-Thomson",
title = "Elliptic Integrals",
crossref = "Abramowitz:1964:HMF",
pages = "587--626",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Milne-Thomson:1964:JEF,
author = "L. M. Milne-Thomson",
title = "{Jacobian} Elliptic Functions and Theta Functions",
crossref = "Abramowitz:1964:HMF",
pages = "567--586",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Morelock:1964:AAE,
author = "J. C. Morelock",
title = "{ACM} Algorithm 229: Elementary Functions by Continued
Fractions",
journal = j-CACM,
volume = "7",
number = "5",
pages = "296",
month = may,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:32:21 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@InCollection{Oberhettinger:1964:HF,
author = "Frtiz Oberhettinger",
title = "Hypergeometric Functions",
crossref = "Abramowitz:1964:HMF",
pages = "555--566",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Olver:1964:BFI,
author = "F. W. J. Olver",
title = "{Bessel} Functions of Integer Order",
crossref = "Abramowitz:1964:HMF",
pages = "355--434",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Schmidt:1964:AEC,
author = "Paul W. Schmidt",
title = "Asymptotic Expansion of Certain Integrals Containing
the {Bessel} Function {$ J_0 (x) $}",
journal = j-J-MATH-PHYS,
volume = "5",
number = "8",
pages = "1183--1184",
month = aug,
year = "1964",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1704223",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 08:40:15 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v5/i8/p1183_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "22 December 2004",
pagecount = "2",
}
@Article{Simauti:1964:AFS,
author = "Takakazu Simauti",
title = "Approximation formulas for some elementary functions",
journal = "Comment. Math. Univ. St. Paul.",
volume = "12",
pages = "23--35",
year = "1964",
CODEN = "COMAAC",
ISSN = "0010-258X",
MRclass = "65.25",
MRnumber = "28 \#5552",
MRreviewer = "John Todd",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Slater:1964:CHF,
author = "Lucy Joan Slater",
title = "Confluent Hvpergeometric Functions",
crossref = "Abramowitz:1964:HMF",
pages = "503--536",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Slepian:1964:PSW,
author = "David Slepian",
title = "Prolate Spheroidal Wave Functions, {Fourier} Analysis
and Uncertainty --- {IV}: Extensions to Many
Dimensions; Generalized Prolate Spheroidal Functions",
journal = j-BELL-SYST-TECH-J,
volume = "43",
number = "6",
pages = "3009--3057",
month = nov,
year = "1964",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.28",
MRnumber = "0181766 (31 \#5993)",
MRreviewer = "J. Meixner",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1964/BSTJ.1964.4306.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol43/bstj43-6-3009.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@InCollection{Southard:1964:WER,
author = "Thomas H. Southard",
title = "{Weierstrass} Elliptic and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "627--684",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Stegun:1964:LF,
author = "Irene A. Stegun",
title = "{Legendre} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "331--354",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Stegun:1964:MF,
author = "Irene A. Stegun",
title = "Miscellaneous Functions",
crossref = "Abramowitz:1964:HMF",
pages = "997--1010",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Clausen's integral; Clebsch--Gordan coefficients;
Debye function; Dilogarithm (Spence's integral);
Einstein function; Planck function; Sievert and related
integrals",
remark = "Fullerton: Debye, Planck and Einstein functions.
Sievert and related integrals. Dilogarithm (Spence's
integral). Clausen's integral. Clebsch--Gordan
coefficients.",
}
@Article{Wengert:1964:SAD,
author = "R. E. Wengert",
title = "A simple automatic derivative evaluation program",
journal = j-CACM,
volume = "7",
number = "8",
pages = "463--464",
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A procedure for automatic evaluation of total and
partial derivatives of arbitrary algebraic functions is
presented. The numerical values of derivatives are
computed without developing analytic expressions for
the derivatives. The function is decomposed into a
sequence of elementary expressions A library is
provided for differentiating of elementary functions.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "computer program.; differentiation arithmetic; point
algorithm",
referred = "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a];
[Kala83b]; [Laws88a]; [Laws91a]; [Neid87a]; [Neid89a];
[Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a];
[Wilk64a].",
}
@InCollection{Zelen:1964:PF,
author = "Marvin Zelen and Norman C. Severo",
title = "Probability Functions",
crossref = "Abramowitz:1964:HMF",
pages = "925--996",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Zucker:1964:ETF,
author = "Ruth Zucker",
title = "Elementary Transcendental Functions. {Logarithmic},
Exponential, Circular and Hyperbolic Functions",
crossref = "Abramowitz:1964:HMF",
pages = "65--226",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Bingulac:1965:ACG,
author = "S. P. Bingulac and E. A. Humo",
title = "Analog Computer Generation of {Bessel} Functions of
Arbitrary Order",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "886--889",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264084",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038609",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Braess:1965:MIG,
author = "Dietrich Braess",
title = "{Monotone Iterationsfolgen bei Gleichungssystemen mit
fehlerhaften Koeffizienten und
Iterationsbeschleunigung}. ({German}) [{Monotone}
Iteration Sequences for Equation Systems with
Coefficients Having Errors, and Iteration
Acceleration]",
journal = j-NUM-MATH,
volume = "7",
number = "1",
pages = "32--41",
month = feb,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration",
language = "German",
}
@Article{Bulirsch:1965:NCEa,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions",
journal = j-NUM-MATH,
volume = "7",
number = "1",
pages = "78--90",
month = feb,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Handbook Series Special functions",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bulirsch:1965:NCEb,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions. {II}",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "353--354",
month = aug,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Christiansen:1965:APE,
author = "S. Christiansen",
title = "{Algol} programming: Error Integral with Complex
Argument",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "4",
pages = "287--293",
month = dec,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01937509",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=4&spage=287",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: A 75-line Algol procedure with maximum
absolute error about $ 2 \times 10^{-6} $ is given for
$ w(z) = e^{-z^2} \erfc ( - i z) $.",
}
@Article{Cochran:1965:ZHF,
author = "J. A. Cochran",
title = "The zeros of {Hankel} functions as functions of their
order",
journal = j-NUM-MATH,
volume = "7",
number = "3",
pages = "238--250",
month = jun,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 10:06:00 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Cody:1965:CAC,
author = "W. J. {Cody, Jr.}",
title = "{Chebyshev} Approximations for the Complete Elliptic
Integrals {$K$} and {$E$}",
journal = j-MATH-COMPUT,
volume = "19",
number = "89--92",
pages = "105--112",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.05",
MRnumber = "30\#1601",
bibdate = "Fri Oct 23 11:10:16 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Cody:1966:CCA}.",
URL = "http://www.jstor.org/stable/2004103",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 4 \times 10^{-18}
$.",
}
@Article{Cody:1965:CPE,
author = "W. J. {Cody, Jr.}",
title = "{Chebyshev} Polynomial Expansions of Complete Elliptic
Integrals",
journal = j-MATH-COMPUT,
volume = "19",
number = "89--92",
pages = "249--259",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "31\#2820",
bibdate = "Fri Oct 23 11:10:33 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2003350",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 25-digit approximations.",
}
@Article{Combet:1965:CBT,
author = "M. Combet and H. {Van Zonneveld} and L. Verbeek",
title = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "863--867",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dahlquist:1965:CAP,
author = "Germund Dahlquist and Sven-{\AA}ke Gustafson and
K{\'a}roly Sikl{\'o}si",
title = "Convergence Acceleration from the Point of View of
Linear Programming",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "1",
pages = "1--16",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01975719",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=1",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "convergence acceleration",
}
@Article{Fettis:1965:CEI,
author = "Henry E. Fettis",
title = "Calculation of Elliptic Integrals of the Third Kind by
Means of {Gauss}' Transformation",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "97--104",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004102",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fields:1965:RAG,
author = "Jerry L. Fields",
title = "Rational Approximations to Generalized Hypergeometric
Functions",
journal = j-MATH-COMPUT,
volume = "19",
number = "92",
pages = "606--624",
month = oct,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Franke:1965:NEE,
author = "Charles H. Franke",
title = "Numerical Evaluation of the Elliptic Integral of the
Third Kind (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "494--496",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fraser:1965:SMC,
author = "W. Fraser",
title = "A Survey of Methods for Computing Minimax and
Near-Minimax Polynomial Approximations for Functions of
a Single Independent Variable",
journal = j-J-ACM,
volume = "12",
number = "3",
pages = "295--314",
month = jul,
year = "1965",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321281.321282",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Methods are described for the derivation of minimax
and near-minimax polynomial approximations. For minimax
approximations techniques are considered for both
analytically defined functions and functions defined by
a table of values. For near-minimax approximations
methods of determining the coefficients of the
Fourier--Chebyshev expansion are first described. These
consist of the rearrangement of the coefficients of a
power polynomial, and also direct determination of the
coefficients from the integral which defines them, or
the differential equation which defines the function.
Finally there is given a convenient modification of an
interpolation scheme which finds coefficients of a
near-minimax approximation without requiring numerical
integration or the numerical solution of a system of
equations.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Gautschi:1965:ALF,
author = "W. Gautschi",
title = "{Algorithm 259}: {Legendre} Functions for Arguments
Larger than One [{S16}]",
journal = j-CACM,
volume = "8",
number = "8",
pages = "488--492",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Jansen:1977:RLF}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Legendre functions; special functions",
remark = "Fullerton: Long Algol procedures for the associated
Legendre functions of the first and second kinds: $
P_a^n(x) $ and $ Q_n^m $.",
}
@Article{Gautschi:1965:CAS,
author = "Walter Gautschi",
title = "Certification of {Algorithm 236} [{S17}]: {Bessel}
functions of the first kind",
journal = j-CACM,
volume = "8",
number = "2",
pages = "105--106",
month = feb,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:58 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$J_n(x)$; Bessel functions of the first kind; special
functions",
}
@Article{Gunn:1965:ASa,
author = "J. H. Gunn",
title = "{Algorithm 260}: {6-$J$} symbols",
journal = j-CACM,
volume = "8",
number = "8",
pages = "492--492",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Gunn:1965:ASb,
author = "J. H. Gunn",
title = "{Algorithm 261}: {9-$J$} symbols",
journal = j-CACM,
volume = "8",
number = "8",
pages = "492--493",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Gunn:1965:AZV,
author = "J. H. Gunn",
title = "{Algorithm 252} [{Z}]: {Vector} coupling or
{Clebsch--Gordan} coefficients",
journal = j-CACM,
volume = "8",
number = "4",
pages = "217--217",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:59 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Heatley:1965:ETT,
author = "A. H. Heatley",
title = "An Extension of the Table of the {Toronto} Function
(in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "118--123",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Some 5 and 7-digit values.",
}
@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kazangapov:1965:REF,
author = "A. N. Kazangapov",
title = "Representation of elementary function in the system of
residual classes. ({Russian})",
journal = "Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk",
volume = "3",
pages = "79--84",
year = "1965",
MRclass = "65.25",
MRnumber = "33 \#5090",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{King:1965:LED,
author = "R. King",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Book{Lebedev:1965:SFT,
author = "N. N. (Nikola{\u\i}i Nikolaevich) Lebedev",
title = "Special Functions and Their Applications",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 308",
year = "1965",
LCCN = "QA351 .L3613",
bibdate = "Sat Apr 1 14:42:46 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Revised English edition translated and edited by
Richard A. Silverman.",
series = "Selected Russian publications in the mathematical
sciences",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Mathematical physics",
}
@Book{Lyusternik:1965:HCE,
author = "L. A. Lyusternik and O. A. Chervonenkis and A. R.
Yanpol{\'s}kii",
title = "Handbook for Computing Elementary Functions",
volume = "76",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xiii + 251",
year = "1965",
LCCN = "QA221.L513",
MRclass = "65.25",
MRnumber = "32 \#584",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translated from the Russian by G. J. Tee. Translation
edited by K. L. Stewart.",
series = "International series of monographs on pure and applied
mathematics",
acknowledgement = ack-nhfb,
}
@Article{MacLaren:1965:APN,
author = "M. D. MacLaren",
title = "{Algorithm 272}: {Procedure} for the Normal
Distribution Functions [{S15}]",
journal = j-CACM,
volume = "8",
number = "12",
pages = "789--790",
month = dec,
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/365691.365957",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:03 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remarks \cite{Hill:1967:RAS,MacLaren:1968:RAP}.",
abstract = "The procedure gives $ \Phi (a) = \sqrt {1 / (2 \pi)}
\int_{- \infty }^a \exp ( - t^2 / 2) \, d t $ and $
\Phi *(a) = 2 (\Phi (|a|) - 0.5) = \sqrt {2 / \pi }
\int_0^{|a|} \exp ( - t^2 / 2) \, d t $.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
}
@Article{Maklovic:1965:IIC,
author = "S. T. Maklovi{\v{c}}",
title = "Investigation of integrals containing {Bessel} and
elementary functions. ({Russian})",
journal = "Ki{\v{s}}inev. Gos. Univ. U{\v{c}}en. Zap.",
volume = "82",
pages = "75--81",
year = "1965",
MRclass = "33.25",
MRnumber = "34 \#387",
MRreviewer = "H. A. Lauwerier",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Markman:1965:RZF,
author = "B. Markman",
title = "The {Riemann} Zeta Function",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "2",
pages = "138--141",
year = "1965",
bibdate = "Sat Oct 30 08:53:17 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: A 25-line Algol procedure for evaluating $
\zeta (s) $ for all $ s \neq 1 $ is given.",
}
@Article{Medhurst:1965:EI,
author = "R. G. Medhurst and J. H. Roberts",
title = "Evaluation of the Integral $ {I}_n(b) = \frac {2}{\pi
} \int^\infty_0 \bigg (\frac {\sin x}{x} \bigg)^n \cos
(b x) d x $",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "113--117",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Metze:1965:MSR,
author = "Gernot Metze",
title = "Minimal Square Rooting",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "181--185",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.263963",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Miller:1965:ASF,
author = "G. F. Miller",
title = "Algorithms for Special Functions {II}",
journal = j-NUM-MATH,
volume = "7",
pages = "194--196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
remark = "Fullerton: Corrections and simplifications of the $
\sin $, $ \cos $ and $ \tan $ routines given in paper
I. See Clenshaw (1963).",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Nemeth:1965:CEF,
author = "G. N{\'e}meth",
title = "{Chebyshev} expansions for {Fresnel} integrals",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "310--312",
month = aug,
year = "1965",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01436524",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 20:47:18 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
remark = "Fullerton: Two series of 12-digit coefficients are
given to cover the range $ 0 \leq x < \infty $.",
}
@Article{Rice:1965:CPR,
author = "John R. Rice",
title = "On the Conditioning of Polynomial and Rational Forms",
journal = j-NUM-MATH,
volume = "7",
number = "5",
pages = "426--435",
month = oct,
year = "1965",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01436257",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.99",
MRnumber = "MR0189283 (32 \#6710)",
MRreviewer = "James H. Wilkinson",
bibdate = "Sun Oct 16 17:22:04 GMT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "number of multiplications to evaluate a polynomial",
}
@Article{Slepian:1965:EAP,
author = "David Slepian and Estelle Sonnenblick",
title = "Eigenvalues associated with prolate spheroidal wave
functions of zero order",
journal = j-BELL-SYST-TECH-J,
volume = "44",
number = "8",
pages = "1745--1759",
month = oct,
year = "1965",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "65.25",
MRnumber = "0183103 (32 \#585)",
MRreviewer = "R. Nicolovius",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1965/BSTJ.1965.4408.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol44/bstj44-8-1745.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Slepian:1965:SAE,
author = "David Slepian",
title = "Some Asymptotic Expansions for Prolate Spheroidal Wave
Functions",
journal = "J. Math. and Physics {XLIV(2)}",
volume = "??",
number = "??",
pages = "99--140",
month = jun,
year = "1965",
bibdate = "Sat Oct 30 10:46:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=189661",
acknowledgement = ack-nhfb,
author-dates = "1923--2007",
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Several complicated expansions are derived
and presented.",
}
@Article{Swarztrauber:1965:LED,
author = "P. N. Swarztrauber",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Aug 31 14:02:19 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Thompson:1965:AEI,
author = "G. T. Thompson",
title = "The Asymptotic Expansion of the Integrals Psi and Chi
in Terms of {Tchebycheff} Polynomials (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "92",
pages = "661--663",
month = oct,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Doppler Broadening",
}
@Book{Clenshaw:1966:CSB,
author = "C. W. Clenshaw and Susan M. Picken",
title = "{Chebyshev} series for {Bessel} functions of
fractional order",
volume = "8",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "iii + 53",
year = "1966",
MRclass = "33.25",
MRnumber = "203095",
MRreviewer = "L. J. Slater",
bibdate = "Sun Nov 12 06:18:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "National Physical Laboratory. Mathematical tables",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
xxpages = "51",
xxpages = "iii + 54",
}
@Article{Cody:1966:CCA,
author = "W. J. {Cody, Jr.}",
title = "Corrigenda: ``{Chebyshev} Approximations for the
Complete Elliptic Integrals $ {K} $ and $ {E} $''",
journal = j-MATH-COMPUT,
volume = "20",
number = "93",
pages = "207--207",
month = jan,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri Oct 23 11:13:58 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Cody:1965:CAC}.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Doring:1966:CZC,
author = "Boro Doring",
title = "Complex Zeros of Cylinder Functions",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "215--222",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fike:1966:SAS,
author = "C. T. Fike",
title = "Starting Approximations for Square Root Calculation on
{IBM System\slash 360}",
journal = j-CACM,
volume = "9",
number = "4",
pages = "297--299",
month = apr,
year = "1966",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/365278.365556",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
abstract = "Several starting approximations for square root
calculation by Newton's method are presented in a form
to facilitate their use in IBM System/360 square root
routines. These approximations include several for the
range [1/16, 1], which is the interval of primary
interest on IBM System/360.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; IBM S/360",
}
@Article{Filippi:1966:BEE,
author = "S. Filippi",
title = "{Die Berechnung einiger elementarer transzendenter
Funktionen mit Hilfe des Richardson-Algorithmus}
\toenglish {The Computation of Some Elementary
Transcendental Functions by Means of the Richardson
Algorithm} \endtoenglish",
journal = j-COMPUTING,
volume = "1",
number = "2",
pages = "127--132",
month = jun,
year = "1966",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02342622",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Gautschi:1966:AD,
author = "Walter Gautschi",
title = "{Algorithm 282}: {Derivatives} of $ e^x / x $, $ \cos
(x) / x $, and $ \sin (x) / x $",
journal = j-CACM,
volume = "9",
number = "4",
pages = "272--272",
month = apr,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:05 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Gautschi:1970:RAD}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\cos(x)/x$; $\sin(x)/x$; $e^x/x$; elementary
functions",
}
@Article{Gautschi:1966:ARC,
author = "Walter Gautschi",
title = "{Algorithm 292}: {Regular} {Coulomb} Wave Functions",
journal = j-CACM,
volume = "9",
number = "11",
pages = "793--795",
month = nov,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:10 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
}
@Article{Glasser:1966:ESI,
author = "M. L. Glasser",
title = "Evaluation of Some Integrals Involving the $ \psi
$-Function (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "332--333",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gustafson:1966:CAM,
author = "Sven-{\AA}ke Gustafson",
title = "Convergence Acceleration by Means of Numerical
Quadrature",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "2",
pages = "117--128",
month = jun,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933103",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=2&spage=117",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "convergence acceleration",
}
@Article{Hart:1966:CAR,
author = "Roger G. Hart",
title = "A Close Approximation Related to the Error Function
(in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "600--602",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Hastings:1966:RCB,
author = "C. W. Hastings",
title = "{R66-78} Computation of the Base Two Logarithm of
Binary Number",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "6",
pages = "956--957",
month = dec,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264517",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038956",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Book{Jurimae:1966:KFT,
author = "E. J{\"u}rim{\"a}e",
title = "Kompleksmuutuja funktsioonide teooria. {I}:
Elementaarsed funktsioonid. ({Estonian}) [Theory of
functions of a complex variable. {I}: Elementary
functions]",
publisher = "Tartu Riiklik {\"U}likool",
address = "Tartu, Estonia",
pages = "131",
year = "1966",
MRclass = "30.00",
MRnumber = "40 \#5827a",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Kogbetliantz:1966:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of Elementary Functions",
crossref = "Ralston:1960:MMD",
pages = "7--35",
year = "1966",
bibdate = "Sat Dec 09 14:09:27 1995",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@TechReport{Kuki:1966:CAE,
author = "H. Kuki",
title = "Comments on the {ANL} Evaluation of the {OS\slash 360
FORTRAN} Math Function Library",
type = "????",
number = "SSD 169, C4773",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "47--53",
year = "1966",
bibdate = "Wed Feb 14 19:13:50 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Larssen:1966:CAC,
author = "Gerhard Meidell Larssen",
title = "Certification of {Algorithm 56}: {Complete} elliptic
integral of the second kind",
journal = j-CACM,
volume = "9",
number = "1",
pages = "12--12",
month = jan,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:04 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Mechel:1966:CMB,
author = "Fr. Mechel",
title = "Calculation of the Modified {Bessel} Functions of the
Second Kind with Complex Argument",
journal = j-MATH-COMPUT,
volume = "20",
number = "95",
pages = "407--412",
month = jul,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Nellis:1966:REE,
author = "W. J. Nellis and B. C. Carlson",
title = "Reduction and Evaluation of Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "223--231",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Pike:1966:ALG,
author = "M. C. Pike and I. D. Hill",
title = "{Algorithm 291}: {Logarithm} of Gamma Function",
journal = j-CACM,
volume = "9",
number = "9",
pages = "684--684",
month = sep,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:09 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\log(\Gamma(x))$; special functions",
remark = "Fullerton: Short Algol procedure valid only for $ x >
0 $. Accurate to 10 digits.",
}
@TechReport{Price:1966:NAR,
author = "James F. Price",
title = "Numerical Analysis and Related Literature for
Scientific Computer Users",
type = "Mathematical Note",
number = "456 (D1-82-0517)",
institution = "Mathematics Research Laboratory, Boeing Scientific
Research Laboratories",
address = "Seattle, WA, USA",
edition = "Second",
pages = "ix + 191",
month = mar,
year = "1966",
bibdate = "Mon Jun 18 06:55:22 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.dtic.mil/dtic/tr/fulltext/u2/632244.pdf",
abstract = "The Second Edition of this annotated bibliography
lists the contents of over 150 books in English on
numerical analysis and related literature. It is meant
for the general scientific computer user and not for
the research numerical analyst; the descriptions and
suggestions are given with this in mind. It is expected
that the most useful section will be the 27-page index
which tells in which books various topics may be found.
There is also a section describing how to look up
further information on such topics which may be found
in the literature.",
acknowledgement = ack-nhfb,
tableofcontents = "Introduction / iv \\
I. Numerical Procedures in Books / 1 \\
II. How to Find What You Want / 157 \\
A. Bibliographies, lists of books, abstracting journals
/ 157 \\
B. Looking for Tables of Various Functions / 161 \\
C. Keeping Up with Some of the New Literature / 163 \\
III. Subject Index / 165",
}
@Book{Slater:1966:GHF,
author = "Lucy Joan Slater",
title = "Generalized Hypergeometric Functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiii + 273",
year = "1966",
LCCN = "QA351 .S565",
bibdate = "Sat Oct 30 21:01:55 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Takenaga:1966:EIG,
author = "Roy Takenaga",
title = "On the Evaluation of the Incomplete Gamma Function (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "606--610",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Thompson:1966:ESI,
author = "Rory Thompson",
title = "Evaluation of $ {I}_n(b) = 2 \pi^{-1} \int^\infty_0
\big (\frac {sin x}{x} \big)^n \cos (b x) d x $ and of
Similar Integrals (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "330--332",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Tolke:1966:PFT,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 2. Theta-Funktionen und
spezielle Weierstrasssche Funktionen}. ({German})
[{Practical} functional theory. 2. {Theta} functions
and special {Weierstrass} functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vii + 248",
year = "1966",
ISBN = "",
ISBN-13 = "",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Tricomi:1966:RUS,
author = "F. G. Tricomi",
title = "Lectures on the use of special functions by
calculations with electronic computers",
type = "Lecture Series",
number = "47",
institution = "The Institute for Fluid Dynamics and Applied
Mathematics, University of Maryland, College Park",
address = "College Park, MD, USA",
year = "1966",
bibdate = "Tue Mar 14 18:48:58 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Watson:1966:TTB,
author = "G. N. Watson",
title = "A Treatise on the Theory of {Bessel} Functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "vi + 804",
year = "1966",
ISBN = "0-521-09382-1",
ISBN-13 = "978-0-521-09382-8",
LCCN = "QA 408 W33t 1966",
bibdate = "Fri Nov 24 13:53:35 MST 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/matched-field-proc.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
alias = "Watson 66a",
sthbib = "M2 Wat 82 55",
}
@Article{Wood:1966:DBI,
author = "Van E. Wood and R. P. Kenan and M. L. Glasser",
title = "{Doppler} Broadening Integrals (in {Technical Notes
and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "610--611",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Anonymous:1967:CAP,
author = "Anonymous",
title = "Convergence acceleration from the point of view of
linear programming",
journal = j-BIT,
volume = "7",
number = "3",
pages = "256--256",
month = sep,
year = "1967",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939269",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:10 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=3&spage=256",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "convergence acceleration",
}
@Article{Bond:1967:AAF,
author = "Gillian Bond and M. L. V. Pitteway",
title = "{Algorithm 301}: {Airy} Function",
journal = j-CACM,
volume = "10",
number = "5",
pages = "291--292",
month = may,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Airy functions; special functions",
remark = "Fullerton: 100-line Algol program for $ \operatorname
{Ai} $, $ \operatorname {Bi} $. and their
derivatives.",
}
@Article{Cody:1967:CAN,
author = "W. J. Cody and K. E. Hillstrom",
title = "{Chebyshev} Approximations for the Natural Logarithm
of the Gamma Function",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "198--203",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 10^{-17} $.",
}
@Article{Cody:1967:CRC,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "Corrigendum: ``{Rational Chebyshev approximations for
Fermi--Dirac integrals of orders $ - 1 / 2 $, $ 1 / 2
$, and $ 3 / 2 $''}",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "525--525",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Sep 26 19:36:03 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Cody:1967:RCA}.",
URL = "http://www.jstor.org/stable/2003289",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
xxmonth = "(none)",
}
@Article{Cody:1967:LEA,
author = "William J. {Cody, Jr.}",
title = "Letter to the {Editor}: Another Aspect of Economical
Polynomials",
journal = j-CACM,
volume = "10",
number = "9",
pages = "531--531",
month = sep,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363566.363577",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Nov 17 10:20:03 1994",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fike:1967:MEP}.",
abstract = "In his paper ``Methods of Evaluating Polynomial
Approximations in Function Evaluation Routines'' [Comm.
ACM 10, (March 1967)], C. T. Fike fails to discuss one
very important aspect of the ``economical'' methods for
polynomials. Since these evaluation methods involve a
decreased number of arithmetic operations over the
usual Horner's method (or at least replace a
multiplication by an addition) the implication is that
they are faster to execute. Dr. Fike points out that
these methods can be poorly conditioned for particular
polynomials, thus requiring extended precision or
fixed-point arithmetic to maintain accuracy and costing
more in time than Horner's method. But even if we
assume the methods are well conditioned, the need to
store away and retrieve intermediate results in some
machines with only one floating-point arithmetic
register can wipe out the time savings effected by a
reduction in the number of arithmetic operations. On
many of today's high-performance computers the time
required to store away and retrieve a result is about
the same as the time required for a floating-point
addition. It is no longer sufficient to estimate the
efficiency of a method by a count of arithmetic
operations alone.",
acknowledgement = ack-wjc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic",
}
@Article{Cody:1967:RCA,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "Rational {Chebyshev} approximations for {Fermi--Dirac}
integrals of orders $ - 1 / 2 $, $ 1 / 2 $, and $ 3 / 2
$",
journal = j-MATH-COMPUT,
volume = "21",
number = "97",
pages = "30--40",
month = jan,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Sep 26 19:23:19 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Cody:1967:CRC}.",
URL = "http://www.jstor.org/stable/2003468",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 10^{-9} $.",
}
@Article{DiDonato:1967:ECI,
author = "A. R. DiDonato and M. P. Jarnagin",
title = "The Efficient Calculation of the Incomplete
Beta-Function Ratio for Half-Integer Values of the
Parameters $ a, b $",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "652--662",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fair:1967:RAI,
author = "Wyman G. Fair and Yudell L. Luke",
title = "Rational Approximations to the Incomplete Elliptic
Integrals of the First and Second Kinds",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "418--422",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fettis:1967:MCI,
author = "Henry E. Fettis",
title = "More on the Calculation of the Integral $ {I}_n(b) =
\frac {2}{\pi } \int^\infty_0 \big (\frac {\sin x}{x}
\big)^n \cos b x \, d x $ (in {Technical Notes and
Short Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "727--730",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fike:1967:LER,
author = "C. T. Fike",
title = "Letter to the {Editor}: {A} rational approximation
optimal by {Moursund}'s criterion",
journal = j-CACM,
volume = "10",
number = "11",
pages = "683--684",
month = nov,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363790.363795",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:16 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "elementary function; square root",
remark = "Gives a starting value for $ \sqrt {x} $ ($x$ on $ [1
/ 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x +
0.84106293)$, with an error of $ 2^{-12.496}$.",
}
@Article{Fike:1967:MEP,
author = "C. T. Fike",
title = "Methods of Evaluating Polynomial Approximations in
Function Evaluation Routines",
journal = j-CACM,
volume = "10",
number = "3",
pages = "175--178",
month = mar,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363162.363200",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remark on efficiency \cite{Cody:1967:LEA}.",
abstract = "The method of nested multiplication is commonly used
in function evaluation routines to evaluate
approximation polynomials. New polynomial evaluation
methods have been developed in recent years which
require fewer multiplications than nested
multiplication and may therefore be preferable for use
in function evaluation routines. Although some of these
methods do not appear to be practically useful because
of rounding-error difficulties, several methods of
evaluating low-degree polynomials have been found to be
satisfactory. Three such methods are described and
illustrated.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
received = "August 1966 (revised December 1966)",
}
@Article{Friedland:1967:AAV,
author = "Paul Friedland",
title = "{Algorithm 312}: {Absolute} Value and Square Root of a
Complex Number",
journal = j-CACM,
volume = "10",
number = "10",
pages = "665--665",
month = oct,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363717.363780",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(z)$; $\sqrt(z)$; elementary functions",
}
@Article{Gautschi:1967:CAT,
author = "Walter Gautschi",
title = "Computational Aspects of Three-Term Recurrence
Relations",
journal = j-SIAM-REVIEW,
volume = "9",
number = "1",
pages = "24--82",
month = jan,
year = "1967",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1009002",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:42 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/9/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://link.aip.org/link/?SIR/9/24/1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "Bessel functions; continued fractions; Coulomb wave
functions; Fourier coefficients; incomplete beta
functions; incomplete gamma functions; Legendre
functions; Sturm--Liouville boundary value problems;
three-term recurrence relations",
onlinedate = "January 1967",
remark = "This paper is frequently cited in later work on
continued fractions, three-term recurrence relations,
and special functions.",
}
@Article{Goldstein:1967:CSB,
author = "Max Goldstein and C. W. Clenshaw and Susan M. Picken",
title = "{Chebyshev} Series for {Bessel} Functions of
Fractional Order",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "509--??",
month = jul,
year = "1967",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2003271",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sun Nov 12 09:25:35 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "TO DO: Why is this missing from journal bibliography
file, mathcomp1970.bib?",
}
@Article{Gunn:1967:ACW,
author = "J. H. Gunn",
title = "{Algorithm 300}: {Coulomb} Wave Functions",
journal = j-CACM,
volume = "10",
number = "4",
pages = "244--245",
month = apr,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Vos:1973:RAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: 150-line Algol procedure that is superseded
by other routines in the physics literature.",
}
@Article{Hill:1967:ACS,
author = "I. D. Hill and M. C. Pike",
title = "{Algorithm 299}: {Chi}-Squared Integral",
journal = j-CACM,
volume = "10",
number = "4",
pages = "243--244",
month = apr,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Hill:1985:RCS,elLozy:1976:RAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "chi-squared; probability functions",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Hill:1967:ANCa,
author = "I. D. Hill and S. A. Joyce",
title = "{Algorithm 304}: {Normal} Curve Integral",
journal = j-CACM,
volume = "10",
number = "6",
pages = "374--375",
month = jun,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363332.363411",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remarks \cite{Hill:1967:RAS,Bergson:1968:ACR}.",
abstract = "{\tt normal(x,upper)} calculates the curve, i.e., tail
area of the standardized normal curve, i.e., $ (1 /
\sqrt {2 \pi }) \int \exp ( - t^2 / 2) \, d t $. If
{\tt upper} is {\tt true}, the limits of integration
are $x$ and $ \infty $. If {\tt upper} is {\tt false},
the limits of integration are $ - \infty $ and $x$.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
remark = "Fullerton: 75-line Algol procedure that is superseded
by numerous $ \erf $ routines.",
}
@Article{Hill:1967:RAS,
author = "I. D. Hill and S. A. Joyce",
title = "Remarks on {Algorithm 123} [{S15}]: {Real} error
function, {{\tt ERF(x)}}; {Algorithm 180} [{S15}]:
{Error} Function --- Large $ {X} $; {Algorithm 181}
[{S15}]: {Complementary} Error Function --- Large $ {X}
$; {Algorithm 209} [{S15}]: {Gauss}; {Algorithm 226}
[{S15}]: {Normal} Distribution Function; {Algorithm
272} [{S15}]: {Procedure} for the Normal Distribution
Functions; {Algorithm 304} [{S15}]: {Normal} Curve
Integral",
journal = j-CACM,
volume = "10",
number = "6",
pages = "377--378",
month = jun,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363332.365433",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Cyvin:1964:AND,MacLaren:1965:APN,Hill:1967:ANCa}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\erf(x)$; $\erfc(x)$; probability functions; special
functions",
}
@Article{Kilpatrick:1967:CIP,
author = "J. E. Kilpatrick and Shigetoshi Katsura and Yuji
Inoue",
title = "Calculations of Integrals of Products of {Bessel}
Functions",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "407--412",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Knuth:1967:CTE,
author = "Donald E. Knuth and Thomas J. Buckholtz",
title = "Computation of Tangent, {Euler}, and {Bernoulli}
Numbers",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "663--688",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "36 #4787",
bibdate = "Fri Mar 22 18:03:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database; MathSciNet database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: The first 119. 120 and 250 tangent, Euler
and Bernoulli numbers, respectively.",
}
@Book{MacRobert:1967:SHE,
author = "Thomas Murray MacRobert and Ian Naismith Sneddon",
title = "Spherical harmonics; an elementary treatise on
harmonic functions, with applications",
volume = "98",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
edition = "Third",
pages = "xviii + 349",
year = "1967",
LCCN = "QA406 .M3 1967",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "International series of monographs in pure and applied
mathematics",
acknowledgement = ack-nhfb,
author-dates = "1884--1962",
subject = "Spherical harmonics",
}
@Book{Meinardus:1967:AFT,
author = "G{\"u}nter Meinardus",
title = "Approximation of functions: Theory and numerical
methods",
volume = "13",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 198",
year = "1967",
ISBN = "0-387-03985-6, 3-540-03985-6",
ISBN-13 = "978-0-387-03985-5, 978-3-540-03985-3",
ISSN = "0081-3877",
LCCN = "QA221 .M3813",
bibdate = "Thu Oct 19 17:07:54 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Springer Tracts in Natural Philosophy",
URL = "http://catalogue.bnf.fr/ark:/12148/cb37378349d",
acknowledgement = ack-nhfb,
author-dates = "(1926--2007)",
remark = "Translation by Larry L. Schumaker of
\cite{Meinardus:1964:AFI}.",
subject = "Approximation theory; Numerical analysis; Th{\'e}orie
de l'approximation; Analyse num{\'e}rique; Fonctions
(math{\'e}matiques); Approximation, Th{\'e}orie de l';
Analyse num{\'e}rique; Approximation theory; Numerical
analysis; Approximation; Funktion; Mathematik",
tableofcontents = "Part I. Linear Approximation \\
1. The General Linear Approximation Problem / 1 \\
1.1. Statement of the Problem. Existence Theorem / 1
\\
1.2. Strictly Convex Spaces. Hilbert Space / 2 \\
1.3. Maximal Linear Functionals / 4 \\
2. Dense Systems / 5 \\
2.1. A General Criterion of Banach / 5 \\
2.2. Approximation Theorems of Weierstrass and Muntz /
6 \\
2.3. Approximation Theorems in the Complex Plane / 10
\\
3. General Theory of Linear Tchebycheff Approximation /
13 \\
3.1. Fundamentals. The Theorem of Kolmogoroff / 13 \\
3.2. The Haar Uniqueness Theorem. Linear Functionals
and Alternants / 16 \\
3.3. Further Uniqueness Results / 24 \\
3.4. Invariants / 26 \\
3.5. Vector-valued Functions / 28 \\
4. Special Tchebycheff Approximations / 28 \\
4.1. Tchebycheff Systems / 28 \\
4.2. Tchebycheff Polynomials / 31 \\
4.3. The Function ?? / 33 \\
4.4. A Problem of Bernstein and Achieser / 36 \\
4.5 Zolotareff's Problem / 41 \\
5. Estimating the Magnitude of Error in Trigonometric
and Polynomial Approximation / 45 \\
5.1. Projection Operators. Linear Polynomial Operators
/ 45 \\
5.2. The Connection between Trigonometric and
Polynomial Approximation / 45 \\
5.3. The Fej{\'e}r Operator / 47 \\
5.4. The Korovkin Operators / 50 \\
5.5. The Theorems of D. Jackson / 52 \\
5.6. The Theorems of Bernstein and Zygmund / 57 \\
5.7. Supplements / 65 \\
6. Approximation by Polynomials and Related Functions /
72 \\
6.1. Foundations / 72 \\
6.2. Upper Bounds for En (??) / 77 \\
6.3. Lower Bounds for En (??) / 82 \\
6.4. Dependence of the Approximation on the Interval /
85 \\
6.5. Regular Haar Systems / 87 \\
6.6. Asymptotic Results / 90 \\
6.7. Results for tho Alternants / 101 \\
7. Numerical Methods for Linear Tchebycheff
Approximation / 105 \\
7.1. The Iterative Methods of Remez / 105 \\
7.2. Initial Approximations / 116 \\
7.3. Direct Methods / 122 \\
7.4. Discretization. Other Methods / 124 \\
Part II. Non-linear Approximation \\
8. General Theory of Non-linear Tchebycheff
Approximation / 131 \\
8.1. Survey of the Problem. A Generalization of the
Kolmogoroff Theorem / 131 \\
8.2. The Haar Uniqueness Theorem. Alternants / 141 \\
8.3. The Investigations of Rice / 148 \\
8.4. The Newton Iteration Method / 149 \\
8.5. H-Sets / 153 \\
9. Rational Approximation / 154 \\
9.1. Existence. Invariants. A Theorem of Walsh / 154
\\
9.2. Theorems on Alternants. Anomalies. Continuity.
Examples / 160 \\
9.3. Asymptotic Results. Small Intervals / 167 \\
9.4. Numerical Methods / 170 \\
10. Exponential Approximation / 176 \\
10.1. The Results of Rice / 176 \\
10.2. An Anomaly Theorem. Constructive Methods / 179
\\
11. Segment Approximation / 183 \\
11.1. Statement of the Problem. Hypotheses / 183 \\
11.2. The principle of Lawson / 184 \\
H.3. Equidegree Polynomial Approximation / 188 \\
Bibliography / 189 \\
Subject Index / 197",
}
@Article{Moody:1967:ADF,
author = "William T. Moody",
title = "Approximations for the Psi (Digamma) Function (in
Technical Notes and Short Notices)",
journal = j-MATH-COMPUT,
volume = "21",
number = "97",
pages = "112--112",
month = jan,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Moursund:1967:OSV,
author = "David G. Moursund",
title = "Optimal starting values for {Newton--Raphson}
calculation of $ \sqrt {x} $",
journal = j-CACM,
volume = "10",
number = "7",
pages = "430--432",
month = jul,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363427.363454",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "39\#2297",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
abstract = "The problem of obtaining starting values for the
Newton-Raphson calculation of $ \sqrt {x} $ on a
digital computer is considered. It is shown that the
conventionally used best uniform approximations to $
\sqrt {x} $ do not provide optimal starting values. The
problem of obtaining optimal starting values is stated,
and several basic results are proved. A table of
optimal polynomial starting values is given.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
remark = "Title of article has incorrect $ \sqrt (x^{1 / 2}) $:
the article discusses computation of {\tt sqrt(x)}.",
}
@Article{Olver:1967:BSS,
author = "F. W. J. Olver",
title = "Bounds for the Solutions of Second-Order Linear
Difference Equations [{Anger--Weber} and {Struve}
Functions]",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "71B",
number = "4",
pages = "161--166",
month = oct,
year = "1967",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 09:37:44 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Truncation error estimates of an earlier
published algorithm.",
}
@Article{Olver:1967:NSS,
author = "F. W. J. Olver",
title = "Numerical solution of second-order linear difference
equations",
journal = j-J-RES-NATL-BUR-STAND-B,
volume = "71B",
number = "2--3",
pages = "111--129",
month = apr,
year = "1967",
CODEN = "JNBBAU",
DOI = "https://doi.org/10.6028/jres.071B.018",
ISSN = "0022-4340",
MRclass = "65.70",
MRnumber = "221789",
MRreviewer = "G. N. Lance",
bibdate = "Sun Nov 5 09:03:34 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/jres/71B/jresv71Bn2-3p111_A1b.pdf",
abstract = "A new algorithm is given for computing the solution of
any second-order linear difference equation which is
applicable when simple recurrence procedures cannot be
used because of instability. Compared with the
well-known Miller algorithm the new method has the
advantages of (i) automatically determining the correct
number of recurrence steps. (ii) applying to
inhomogeneous difference equations, (iii) enabling more
powerful error analyses to be constructed.\par
The method is illustrated by numerical computations,
including error analyses of Anger--Weber, Struve, and
Bessel functions, and the solution of a differential
equation in Chebyshev series",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
fjournal = "Journal of Research of the National Bureau of
Standards. Section B. Mathematics and Mathematical
Physics",
journal-URL = "http://www.nist.gov/nvl/jrespastpapers.cfm",
keywords = "Chebyshev series; difference equations; error
analysis; Miller algorithm. recurrence methods; special
functions",
}
@Article{Pike:1967:RAI,
author = "M. C. Pike and I. D. Hill",
title = "Remark on {Algorithm 179}: {Incomplete} {Beta} ratio",
journal = j-CACM,
volume = "10",
number = "6",
pages = "375--376",
month = jun,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$B(z,w)$; beta function; special functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Article{Pitteway:1967:RAA,
author = "M. L. V. Pitteway",
title = "Remark on {Algorithm 301}: {Airy} function",
journal = j-CACM,
volume = "10",
number = "7",
pages = "453--453",
month = jul,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:14 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Airy functions; special functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Book{Sen:1967:TSF,
author = "Bibhutibhusan Sen",
title = "A treatise on special functions, for scientists and
engineers",
publisher = "Allied Publishers",
address = "Bombay, India",
pages = "164",
year = "1967",
LCCN = "QA351 .S45",
bibdate = "Fri Oct 29 21:30:38 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Spherical harmonics",
}
@Book{Tolke:1967:PFE,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 4. Elliptische
Integralgruppen und Jacobische elliptische Funktionen
im Komplexen}. ({German}) [{Practical} functional
theory. 4. {Elliptical} integral groups and {Jacobian}
elliptic functions in the complex plane]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 191",
year = "1967",
DOI = "https://doi.org/10.1007/978-3-662-36381-2",
ISBN = "3-662-36381-X, 3-662-35552-3 (print), 3-662-36381-X
(e-book)",
ISBN-13 = "978-3-662-36381-2, 978-3-662-35552-7 (print),
978-3-662-36381-2 (e-book)",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/978-3-662-36381-2",
acknowledgement = ack-nhfb,
language = "German",
}
@Book{Tolke:1967:PFJ,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 3. Jacobische elliptische
Funktionen, Legendresche elliptische Normalintegrale
und spezielle Weierstrasssche Zeta- und
Sigma-Funktionen}. ({German}) [{Practical} functional
theory. 3. {Jacobian} elliptic functions, Legendre
elliptical normal Integrals and special {Weierstrass}
zeta- and sigma functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 180",
year = "1967",
DOI = "https://doi.org/10.1007/978-3-662-36379-9",
ISBN = "3-642-50264-4, 3-662-36379-8, 3-662-35550-7 (print),
3-662-36379-8 (e-book)",
ISBN-13 = "978-3-642-50264-4, 978-3-662-36379-9,
978-3-662-35550-3 (print), 978-3-662-36379-9 (e-book)",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/978-3-662-36379-9",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "5 Jacobische elliptische Funktionen und
zugeh{\"o}rige logarithmische Ableitungen \\
108. Definitionen \\
109. Funktionalgleichungen \\
110. Periodenverhalten und Substitutionen \\
111. Funktionswerte an den Stellen $ 0, \pm
\frac{1}{2}, \pm \frac{ix}{2}, \pm \frac{1}{2}, \pm
\frac{ix}{2} $ bzw. $ 0, \pm K, \pm iK', \pm K \pm iK'
$ \\
112. Trigonometrische und hyperbolische
Reihenentwicklungen \\
113. Potenzreihen-Entwicklungen \\
114. Imagin{\"a}re Argumenttransformation, reziproke
Modultransformation und imagin{\"a}re
Modultransformation \\
115. Ableitungen \\
116. Gausssche und Landensche Transformation.
Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und
$\zeta \pm \frac{ix}{4} $ \\
117. Additionstheoreme. Transformationsgleichungen
f{\"u}r doppeltes und halbes Argument. Weitere
Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und
$\zeta \pm \frac{ix}{4}$ sowie f{\"u}r $\zeta \pm
\frac{1}{4} \pm \frac{ix}{4} $ \\
118. Die Logarithmen der logarithmischen Ableitungen
der Jacobischen elliptischen Funktionen \\
119. {\"U}berg{\"a}nge vom (?,?)-System auf das $(z,
k)$-System \\
120. Funktionsverlauf der Jacobischen elliptischen
Funktionen und der zugeh{\"o}rigen Ableitungen und
logarithmischen Ableitungen im Reellen. Ausartungen \\
121. Differentialgleichungen erster und zweiter Ordnung
\\
122. Die Integrale der Jacobischen elliptischen
Funktionen \\
123. Die Integrale der logarithmischen Ableitungen der
Jacobischen elliptischen Funktionen \\
6 Umkehrfunktionen der Jacobischen elliptischen
Funktionen und elliptische Normalintegrale erster
Gattung. Elliptische Amplitudenfunktion sowie
Legendresche $F$- und $E$-Funktion. Elliptische
Normalintegrale zweiter Gattung. Jacobische Zeta- und
Heumansche Lambda-Funktion \\
124. Die 18 Umkehrfunktionen der Jacobischen
elliptischen Funktionen und ihrer logarithmischen
Ableitungen. (Elliptische Normalintegrale erster
Gattung.) Additionstheoreme der Umkehrfunktionen \\
125. Elliptische Normalintegrale erster Gattung in
hyperbolischer Form \\
126. Potenzreihen-Entwicklungen der Umkehrfunktionen
\\
127. Die elliptische Amplitudenfunktion $? = \am(z, k)$
und ihre Umkehrfunktion $z = F(?, k)$. Die vier
trigonometrischen Legendreschen Normalintegrale erster
Gattung \\
128. Darstellung der 18 Umkehrfunktionen und der
elliptischen Normalintegrale erster Gattung durch die
Funktion F. Die vier hyperbolischen Legendreschen
Normalintegrale erster Gattung und die Funktion $F$
f{\"u}r imagin{\"a}res Argument \\
129. Die Legendresche $E$-Funktion f{\"u}r reelles und
imagin{\"a}res Argument \\
130. Die 18 Integrale der Quadrate der Jacobischen
elliptischen Funktionen und ihrer logarithmischen
Ableitungen, die 12 durch Umformung der letzteren
entstehenden hyperbolischen Integrale, die 24
Normalintegrale zweiter Gattung und die acht
trigonometrischen und hyperbolischen Legendreschen
Normalintegrale zweiter Gattung \\
131. Die 46 Normalintegrale erster und zweiter Gattung
mit linearen trigonometrischen und hyperbolischen
Funktionen \\
132. Jacobische Zeta-Funktion und Heumansche
Lambda-Funktion \\
7 Normalintegrale dritter Gattung. Legendresche
$\Pi$-Funktion. Zur{\"u}ckf{\"u}hrung des allgemeinen
elliptischen Integrals auf Normalintegrale erster,
zweiter und dritter Gattung \\
133. Die 96 Normalintegrale dritter Gattung in
Jacobischer Form \\
134. Die acht zu den logarithmischen Ableitungen der
Jacobischen elliptischen Funktionen geh{\"o}rigen
Normalintegrale dritter Gattung \\
135. 48 Quotientenintegrale und 48 spezielle
Normalintegrale dritter Gattung in der Jacobischen Form
\\
136. Algebraische Form der elliptischen Normalintegrale
dritter Gattung \\
137. Darstellung der vollst{\"a}ndigen Normalintegrale
dritter Gattung durch Jacobische Zeta- und Heumansche
Lambda-Funktionen \\
138. Die $\Pi$-Funktion und die Integrale dritter
Gattung in trigonometrischer Form \\
139. Die 48 speziellen Normalintegrale dritter Gattung
in algebraischer Form \\
140. Weitere sechs spezielle Normalintegrale dritter
Gattung \\
141. Zur{\"u}ckf{\"u}hrung des allgemeinen elliptischen
Integrals in der Legendreschen Form auf Normalintegrale
erster, zweiter und dritter Gattung \\
8 Spezielle Weierstra{\ss}sche Zeta-Funktionen \\
142. Definitions- und Funktionalgleichungen \\
143. Substitutionen \\
144. Relatives Periodenverhalten. Spezielle
Funktionswerte. Funktionsverlauf \\
145. Lineare Beziehungen zu den logarithmischen
Ableitungen der Jacobischen elliptischen Funktionen und
deren Ableitungen \\
146. Integrale der $\Pi$-Funktionen als Weierstrasssche
Zeta-Funktionen und Ableitungen der Zeta-Funktionen \\
147. Differentialtransformationen f{\"u}r doppelte und
halbe Parameter \\
148. Gausssche und Landensche Transformation \\
149. Additionstheoreme und Transformationsgleichungen
f{\"u}r doppeltes und halbes Argument \\
150. Trigonometrische, hyperbolische und
Potenzreihen-Entwicklungen \\
151. Homogenit{\"a}tstransformation der Funktionen",
}
@Article{Verma:1967:NSG,
author = "Arun Verma",
title = "A Note on the Summation of the Generalised
Hypergeometric Functions (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "232--236",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wigner:1967:BRW,
author = "Eugene P. Wigner",
title = "Book Review: {Wilhelm Magnus, Fritz Oberhettinger, and
R. P. Soni, \booktitle{Formulas and Theorems for the
Special Functions of Mathematical Physics}}",
journal = j-PHYS-TODAY,
volume = "20",
number = "12",
pages = "81--81",
month = dec,
year = "1967",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.3034082",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Sat Jul 28 07:53:52 MDT 2012",
bibsource = "http://www.physicstoday.org/search;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.aip.org/link/phtoad/v20/i12/p81/s1",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
}
@Article{Wood:1967:CEI,
author = "Van E. Wood",
title = "{Chebyshev} Expansions for Integrals of the Error
Function (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "494--496",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 7-digit approximations for $ i^n \erfc (x),
n = 1, 2 $.",
}
@Article{Yarbrough:1967:PCC,
author = "Lynn Yarbrough",
title = "Precision calculations of $e$ and $ \pi $ constants",
journal = j-CACM,
volume = "10",
number = "9",
pages = "537--537",
month = sep,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363566.363578",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; number base conversion",
remark = "Gives decimal, octal, and hexadecimal values of $e$
and $ \pi $ to 100 digits, and notes ``The difficulty
arises because assemblers and compilers are hardly ever
designed to convert decimal constants to a precision of
more than a dozen or so digits. Thus, if calculations
to greater precision are to be done, constants usually
must be input in octal or other binary-derived
representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Anonymous:1968:ISA,
author = "Anonymous",
title = "Index by Subject to Algorithms, 1960--1968",
journal = j-CACM,
volume = "11",
number = "12",
pages = "827--830",
month = dec,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 09:29:34 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Book{Arsenin:1968:BES,
author = "V. Ja. (Vasilii Jakovlevich) Arsenin",
title = "Basic equations and special functions of mathematical
physics",
publisher = "Iliffe",
address = "London, UK",
pages = "7 + 361",
year = "1968",
ISBN = "0-592-05035-1",
ISBN-13 = "978-0-592-05035-5",
LCCN = "QC20 .A693",
bibdate = "Sat Oct 30 18:25:22 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Translation by S. Chomet, Kings College, London of
Matematicheska{\"e}i{\`\i}a fizika.",
acknowledgement = ack-nhfb,
subject = "Mathematical physics",
}
@Article{Ascari:1968:LRG,
author = "A. Ascari and P. G. Novario",
title = "L'algoritmo {$ Q D $} di {Rutishauser} e la
generazione di funzioni speciali nel calcolo
automatico. ({Italian}) [{The} {$ Q D $} algorithm of
{Rutishauser} and the generation of special functions
in automatic calculation]",
journal = j-CALCOLO,
volume = "5",
number = "1",
pages = "162--173",
month = "????",
year = "1968",
CODEN = "CALOBK",
DOI = "https://doi.org/10.1007/BF02576063",
ISSN = "0008-0624 (print), 1126-5434 (electronic)",
ISSN-L = "0008-0624",
bibdate = "Mon Aug 24 21:37:24 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/BF02576063",
acknowledgement = ack-nhfb,
fjournal = "Calcolo: a quarterly on numerical analysis and theory
of computation",
journal-URL = "http://link.springer.com/journal/10092",
language = "Italian",
subject-dates = "Heinz Rutishauser (30 January 1918--10 November
1970)",
}
@Book{Bell:1968:SFS,
author = "W. W. (William Wallace) Bell",
title = "Special functions for scientists and engineers",
publisher = "Van Nostrand",
address = "London, UK",
pages = "xiv + 247",
year = "1968",
LCCN = "QA351 .B4",
bibdate = "Fri Oct 29 21:30:38 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Gamma, Beta, Legendre, Bessel, and
Hypergeometric functions as well as orthogonal
polynomials. Reprinted in \cite{Bell:2004:SFS}.",
subject = "Functions, Special",
}
@Article{Bergson:1968:ACR,
author = "A. Bergson",
title = "Certification of and remark on {Algorithm 304}
[{S15}]: {Normal} curve integral",
journal = j-CACM,
volume = "11",
number = "4",
pages = "271--271",
month = apr,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362991.363048",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:19 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Hill:1967:ANCa,Hill:1967:RAS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
remark = "Fullerton: 50-line Algol Program that is superceded by
numerous {\tt erf} routines.",
}
@Article{Bingulac:1968:RAA,
author = "S. P. Bingulac",
title = "{R68-38} Accurate Analog Computer Generation of
{Bessel} Functions for Large Ranges",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "8",
pages = "819--819",
month = aug,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229133",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687462",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chiarella:1968:EIR,
author = "C. Chiarella and A. Reichel",
title = "On the Evaluation of Integrals Related to the Error
Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "137--143",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1968:RCAa,
author = "W. J. Cody and H. C. {Thacher, Jr.}",
title = "Rational {Chebyshev} approximations for the
exponential integral {$ E_1 (x) $}",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "641--649",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "38\#6745",
bibdate = "Wed Jan 17 08:57:34 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 10^{-21} $.",
}
@Article{Dorrer:1968:ADS,
author = "Egon Dorrer",
title = "{Algorithm 322}: {$F$}-Distribution [{S14}]",
journal = j-CACM,
volume = "11",
number = "2",
pages = "116--117",
month = feb,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:18 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: 50-line Algol Program.",
}
@Book{Fike:1968:CEM,
author = "C. T. Fike",
title = "Computer Evaluation of Mathematical Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 227",
year = "1968",
LCCN = "QA297 .F5",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Fleckner:1968:MCF,
author = "Oscar L. Fleckner",
title = "A Method for the Computation of the {Fresnel}
Integrals and Related Functions",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "635--640",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Fox:1968:CPN,
author = "L. Fox and I. B. Parker",
title = "{Chebyshev} Polynomials in Numerical Analysis",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "ix + 205",
year = "1968",
ISBN = "0-19-859614-6",
ISBN-13 = "978-0-19-859614-1",
LCCN = "QA297 .F65",
MRclass = "65.10",
MRnumber = "228149",
MRreviewer = "G. N. Lance",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
note = "Reprinted in 1972 with corrections, but same ISBN.",
series = "Oxford mathematical handbooks",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
mynote = "JRUL: 517",
series-editor = "John Crank and C. C. Ritchie",
subject = "Chebyshev polynomials; Numerical analysis",
tableofcontents = "TO DO: find this!",
xxauthor = "L. (Leslie) Fox and I. B. (Ian Bax) Parker",
}
@Article{Galant:1968:HAG,
author = "D. C. Galant and P. F. Byrd",
title = "High Accuracy Gamma Function Values for Some Rational
Arguments (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "104",
pages = "885--887",
month = oct,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Hart:1968:CAa,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-88275-642-7",
ISBN-13 = "978-0-88275-642-4",
LCCN = "QA 297 C64 1978",
bibdate = "Tue Dec 14 22:55:11 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Reprinted 1978 with corrections.",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
2: General Methods of Computing Functions / 10 \\
3: Least Maximum Approximations / 42 \\
4: The Choice and Application of Approximations / 58
\\
5: Description and Use of the Tables / 82 \\
6: Function Notes / 89 \\
7: Tables of Coefficients / 155 \\
Appendix A: Conversion Algorithms / 307 \\
Appendix B: Bibliography of Approximations / 313 \\
Appendix C: Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
tableofcontents = "1: The Design of a Function Subroutine / 1 \\
1.1 Introduction / 1 \\
1.2 General Considerations in Writing a Function
Subroutine / 2 \\
1.3 Relation of the Function Subroutine to the Computer
System / 3 \\
1.4 The Three Main Types of Function Subroutine / 4 \\
1.5 Special Programming Techniques / 7 \\
1.6 Subroutine Errors / 7 \\
1.7 Final Steps / 9 \\
2: General Methods of Computing Functions / 10 \\
2.1 Introduction / 10 \\
2.2 Application of Infinite Expansions / 11 \\
2.3 Recurrence and Difference Relations / 23 \\
2.4 Iterative Techniques / 27 \\
2.5 Integral Representations / 28 \\
2.6 Differential Equations / 29 \\
2.7 Tabular Data / 32 \\
2.8 Convergence Acceleration / 33 \\
3: Least Maximum Approximations / 42 \\
3.1 Introduction / 42 \\
3.2 Properties of Least Maximum Approximations / 43 \\
3.3 Nearly Least Maximum Approximations / 46 \\
3.4 Rational Approximation / 51 \\
3.5 Segmented Approximation / 54 \\
3.6 Computation of the Tables / 55 \\
4: The Choice and Application of Approximations / 58
\\
4.1 Introduction / 5 8 \\
4.2 Domain Considerations / 58 \\
4.3 Machine Considerations / 62 \\
4.4 Conditioning of Approximations / 65 \\
4.5 Polynomial Forms / 67 \\
4.6 Rational Forms / 73 \\
4.7 Transformation Algorithms / 78 \\
5: Description and Use of the Tables / 82 \\
5.1 Introduction / 22 \\
5.2 Function Notes / 82 \\
5.3 Accuracy of the Coefficients / 83 \\
5.4 How to Use the Tables / 86 \\
5.5 Preparation of the Tables / 88 \\
6: Function Notes / 89 \\
6.1 Square Root, Cube Root / 89 \\
6.2 Exponential and Hyperbolic Functions / 96 \\
6.3 The Logarithm Function / 105 \\
6.4 Trigonometric Functions / 112 \\
6.5 The Inverse Trigonometric Functions / 120 \\
6.6 The Gamma Function and Its Logarithm / 130 \\
6.7 The Error Function / 136 \\
6.8 Bessel Functions / 141 \\
6.9 Complete Elliptic Integrals / 150 \\
7: Tables of Coefficients / 155 \\
Appendix A Conversion Algorithms / 307 \\
Appendix B Bibliography of Approximations / 313 \\
Appendix C Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
}
@Book{Hart:1968:CAb,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-471-35630-1",
ISBN-13 = "978-0-471-35630-1",
LCCN = "QA297 .C64",
bibdate = "Sat Jan 14 14:53:06 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "The SIAM series in applied mathematics",
acknowledgement = ack-nhfb,
}
@Article{Kolbig:1968:ADS,
author = "K. S. K{\"o}lbig",
title = "{Algorithm 327}: {Dilogarithm} [{S22}]",
journal = j-CACM,
volume = "11",
number = "4",
pages = "270--271",
month = apr,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362991.363043",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:19 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$d(x) = \int_0^x (\ln|1-y|/y)\,dy$; dilogarithm;
special functions",
}
@Article{Luke:1968:AEI,
author = "Yudell L. Luke",
title = "Approximations for Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "627--634",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{MacLaren:1968:RAP,
author = "M. D. MacLaren",
title = "Remark on {Algorithm 272}: {Procedure} for the normal
distribution functions",
journal = j-CACM,
volume = "11",
number = "7",
pages = "498--498",
month = jul,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363397.363553",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:20 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{MacLaren:1965:APN}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
}
@Article{Mavromatis:1968:IFP,
author = "H. A. Mavromatis and K. Schilcher",
title = "Inverse Functions of the Products of Two {Bessel}
Functions and Applications to Potential Scattering",
journal = j-J-MATH-PHYS,
volume = "9",
number = "10",
pages = "1627--1632",
month = oct,
year = "1968",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1664492",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 11:55:17 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v9/i10/p1627_s1",
acknowledgement = ack-nhfb,
classification = "A0380 (General theory of scattering)",
corpsource = "Dept. Physics, American Univ. Beirut, Lebanon",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "functions; mathematics; scattering",
onlinedate = "28 October 2003",
pagecount = "6",
}
@Article{Mechel:1968:IRT,
author = "Fr. Mechel",
title = "Improvement in Recurrence Techniques for the
Computation of {Bessel} Functions of Integral Order (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "202--205",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Miller:1968:LTS,
author = "Willard Miller",
title = "{Lie} theory and special functions",
volume = "43",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 338",
year = "1968",
ISBN = "0-12-497450-3",
ISBN-13 = "978-0-12-497450-0",
LCCN = "QA387 .M55 1968eb",
bibdate = "Sat Oct 30 19:07:04 MDT 2010",
bibsource = "catalog.library.cornell.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in science and engineering",
acknowledgement = ack-nhfb,
remark = "Reprinted 1979 with same ISBN.",
subject = "Lie groups; Functions, Special",
}
@Article{Nagashima:1968:EFN,
author = "Takashi Nagashima",
title = "On elementary functions of natural numbers",
journal = "Hitotsubashi J. Arts Sci.",
volume = "9",
pages = "50--58",
year = "1968",
ISSN = "0073-2788",
MRclass = "02.72",
MRnumber = "MR0232678 (38 \#1001)",
MRreviewer = "R. L. Goodstein",
bibdate = "Mon Oct 24 11:33:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Hitotsubashi Journal of Arts \& Sciences",
}
@Article{Ng:1968:DSS,
author = "Edward W. Ng",
title = "On the direct summation of series involving higher
transcendental functions",
journal = j-J-COMPUT-PHYS,
volume = "3",
number = "2",
pages = "334--338",
month = oct,
year = "1968",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(68)90029-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 08:28:02 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999168900296",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{OBrien:1968:CAC,
author = "William M. O'Brien and Joan Wood",
title = "Certification of {Algorithm 299} [{S15}]:
{Chi-squared} integral",
journal = j-CACM,
volume = "11",
number = "4",
pages = "271--271",
month = apr,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:19 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "chi-squared; probability functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Article{Osborn:1968:IBF,
author = "David Osborn and Richard Madey",
title = "The Incomplete Beta Function and its Ratio to the
Complete Beta Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "159--162",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Richardson:1968:SUP,
author = "Daniel Richardson",
title = "Some Undecidable Problems Involving Elementary
Functions of a Real Variable",
journal = j-J-SYMBOLIC-LOGIC,
volume = "33",
number = "4",
pages = "514--520",
month = dec,
year = "1968",
CODEN = "JSYLA6",
ISSN = "0022-4812 (print), 1943-5886 (electronic)",
ISSN-L = "0022-4812",
MRclass = "02.75",
MRnumber = "39 #1330",
bibdate = "Mon May 19 13:04:20 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Logic",
journal-URL = "http://projecteuclid.org/euclid.jsl;
http://www.jstor.org/journal/jsymboliclogic",
}
@Article{Schmidt:1968:AEK,
author = "Jochen W. Schmidt",
title = "{Asymptotische Einschlie{\ss}ung bei
konvergenzbeschleunigenden Verfahren. II}. ({German})
[{Asymptotic enclosure with convergence acceleration
method. II}]",
journal = j-NUM-MATH,
volume = "11",
number = "1",
pages = "53--56",
month = jan,
year = "1968",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration",
language = "German",
}
@Article{Strecok:1968:CIE,
author = "Anthony J. Strecok",
title = "On the Calculation of the Inverse of the Error
Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "144--158",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004772",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 18-digit approximations.",
}
@Book{Talman:1968:SFG,
author = "James D. Talman",
title = "Special Functions: a Group Theoretic Approach Based on
Lectures by {Eugene P. Wigner}",
publisher = pub-BENJAMIN,
address = pub-BENJAMIN:adr,
pages = "xii + 260",
year = "1968",
LCCN = "????",
bibdate = "Sat Oct 30 16:57:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "With an introduction by Eugene P. Wigner.",
series = "The mathematical physics monograph series",
acknowledgement = ack-nhfb,
keywords = "group theory; mathematical function; special
functions",
}
@Book{Tolke:1968:PFA,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 5. Allgemeine
Weierstrasssche Funktionen und Ableitungen nach dem
Parameter: Integrale der Theta-Funktionen und
Bilinear-Entwicklungen}. ({German}) [{Practical}
functional theory. 5. {General} information on
{Weierstrass} functions and derivatives according to
the parameters: integrals of theta functions and
bilinear developments]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 158",
year = "1968",
ISBN = "3-662-11121-7, 3-662-11120-9",
ISBN-13 = "978-3-662-11121-5, 978-3-662-11120-8",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "12 Allgemeine Weierstra{\ss}sche Funktionen.
Doppelreihen-Entwicklungen \\
13 Die Ableitungen nach dem Parameter und dem Modul \\
14 Integrale von Theta-Funktionen (D-Funktionen) \\
15 Mehrdimensionale Theta- und D-Funktionen \\
16 Theta- und D-Funktionen mit imagin{\"a}ren
Parametern \\
17 Greensche Funktionen und Bilinear-Entwicklungen",
xxISBN = "3-662-11031-8",
xxISBN-13 = "978-3-662-11031-7",
}
@Article{Tooper:1968:SCP,
author = "Robert F. Tooper and John Mark",
title = "Simplified Calculation of {$ \operatorname {Ei}(x) $}
for Positive Arguments, and a Short Table of $
\operatorname {Shi}(x) $ (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "102",
pages = "448--449",
month = apr,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "exponential integral ($\operatorname{Ei}(x)$);
hyperbolic sine integral ($\operatorname{Shi}(x)$)",
}
@Article{Wilcox:1968:ZTN,
author = "Peter H. Wilcox",
title = "The Zeros of $ {P}^1_\nu (\cos \theta) $ and $ \frac
{\partial }{\partial \theta } {P}^1_\mu (\cos \theta) $
(in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "205--208",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004783",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: $ P_\nu^1 $ are Legendre functions.",
}
@Article{Wimp:1968:RFH,
author = "Jet Wimp",
title = "Recursion Formulae of Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "22",
number = "102",
pages = "363--373",
month = apr,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Witte:1968:AAJ,
author = "B. F. W. Witte",
title = "{ACM Algorithm 332}: {Jacobi} Polynomials",
journal = j-CACM,
volume = "11",
number = "6",
pages = "436--437",
month = jun,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:33:08 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Skovgaard:1975:RAJ}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Wrench:1968:CTS,
author = "John W. {Wrench, Jr.}",
title = "Concerning Two Series for the Gamma Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "617--626",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRnumber = "MR 0237078 (38:5371)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Aharoni:1969:C,
author = "Amikam Aharoni",
title = "Computation of {$ K_p(x) $}",
journal = j-J-COMPUT-PHYS,
volume = "4",
number = "2",
pages = "270--271",
month = aug,
year = "1969",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(69)90072-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 08:28:03 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999169900722",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Boersma:1969:ECW,
author = "J. Boersma",
title = "Expansions for {Coulomb} Wave Functions",
journal = j-MATH-COMPUT,
volume = "23",
number = "105",
pages = "51--59",
month = jan,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Buchholz:1969:CHF,
author = "Herbert Buchholz",
title = "The confluent hypergeometric function with special
emphasis on its applications",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xviii + 238",
year = "1969",
LCCN = "QA351 .B813",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Translation by H. Lichtblau and K. Wetzel to English
from German ``Die konfluente hypergeometrische
Funktion.''",
series = "Springer tracts in natural philosophy",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Bulirsch:1969:EBT,
author = "R. Bulirsch",
title = "An extension of the {Bartky}-transformation to
incomplete elliptic integrals of the third kind",
journal = j-NUM-MATH,
volume = "13",
number = "3",
pages = "266--284",
month = jul,
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bulirsch:1969:NCE,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions. {III}",
journal = j-NUM-MATH,
volume = "13",
number = "4",
pages = "305--315",
month = aug,
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Carlson:1969:CBE,
author = "B. C. Carlson",
title = "A connection between elementary functions and higher
transcendental functions",
journal = j-SIAM-J-APPL-MATH,
volume = "17",
pages = "116--148",
year = "1969",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
MRclass = "33.20 (30.00)",
MRnumber = "40 \#408",
MRreviewer = "S. K. Bose",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
}
@InProceedings{Clark:1969:SCE,
author = "N. W. Clark and W. J. Cody",
title = "Self-contained exponentiation",
crossref = "AFIPS:1969:ACPb",
pages = "701--706",
year = "1969",
bibdate = "Wed Sep 07 10:49:33 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Clemm:1969:ACV,
author = "Donald S. Clemm",
title = "{Algorithm 352}: {Characteristic} Values and
Associated Solutions of {Mathieu}'s Differential
Equation [{S22}]",
journal = j-CACM,
volume = "12",
number = "7",
pages = "399--407",
month = jul,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:27 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4170 (Differential equations); C7300 (Natural
sciences computing)",
corpsource = "Wright-Patterson Air Force Base, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "differential equations; function evaluation;
subroutines",
remark = "Fullerton: Long set of FORTRAN routines to evaluate
Mathieu functions as well as several Bessel
functions.",
}
@Article{Cobb:1969:CAS,
author = "S. M. Cobb",
title = "Certification of {Algorithm 47} [{S16}]: {Associated}
{Legendre} functions of the first kind for real or
imaginary arguments",
journal = j-CACM,
volume = "12",
number = "11",
pages = "635--636",
month = nov,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:28 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "associated Legendre functions of the first kind;
special functions",
remark = "Fullerton: Numerous additional corrections and changes
to an Algol procedure.",
}
@Article{Cody:1969:CAE,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "{Chebyshev} Approximations for the Exponential
Integral {$ \hbox {Ei}(x) $}",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "289--303",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "39\#3680",
bibdate = "Wed Jan 17 08:57:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1969:CRA,
author = "W. J. Cody and G. Meinardus and R. S. Varga",
title = "{Chebyshev} rational approximations to $ e^{-x} $ on $
[0, \infty) $ and applications to heat conduction
problems",
journal = j-J-APPROX-THEORY,
volume = "2",
number = "??",
pages = "50--65",
month = "??",
year = "1969",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "65.67 (41.00)",
MRnumber = "40\#999",
bibdate = "Wed Jan 17 08:57:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
}
@Article{Cody:1969:RCA,
author = "W. J. Cody",
title = "Rational {Chebyshev} Approximations for the Error
Function",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "631--637",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Farkas:1969:CAS,
author = "I. Farkas",
title = "Certification of {Algorithm 165} [{S21}]: {Complete}
elliptic integrals",
journal = j-CACM,
volume = "12",
number = "1",
pages = "38--38",
month = jan,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Gautschi:1969:ACE,
author = "Walter Gautschi",
title = "{Algorithm 363}: {Complex} Error Function [{S15}]",
journal = j-CACM,
volume = "12",
number = "11",
pages = "635--635",
month = nov,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:28 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Kolbig:1972:CAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\erf(z)$; special functions",
remark = "Fullerton: 50-line Algol procedure with accuracy to 10
decimal places.",
}
@Article{Gautschi:1969:RAS,
author = "Walter Gautschi",
title = "Remark on {Algorithm 292} [{S22}]: {Regular} {Coulomb}
wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "280--280",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: The first of many remarks.",
}
@Article{Herman:1969:NHE,
author = "G. T. Herman",
title = "A new hierarchy of elementary functions",
journal = j-PROC-AM-MATH-SOC,
volume = "20",
pages = "557--562",
year = "1969",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "02.77",
MRnumber = "40 \#4110",
MRreviewer = "G. E. Sacks",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Holzwarth:1969:VBB,
author = "A. Holzwarth",
title = "{Ein Verfahren zur Bestimmung bester
Tscheb\-y\-scheff-Ap\-prox\-i\-ma\-tion\-en der
Quadratwurzelfunktion}. ({German}) {A Method for
Determination of Best Chebyshev Approximations to the
Square Root Function}",
journal = j-COMPUTING,
volume = "4",
number = "2",
pages = "168--177",
month = jun,
year = "1969",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "T{\"u}bingen, West Germany",
classification = "C4130",
description = "Chebyshev approximation; numerical analysis",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{King:1969:LEN,
author = "Richard F. King and David L. Phillips",
title = "The Logarithmic Error and {Newton}'s Method for the
Square Root",
journal = j-CACM,
volume = "12",
number = "2",
pages = "87--88",
month = feb,
year = "1969",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362848.362861",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2333",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The problem of obtaining optimal starting values for
the calculation of the square root using Newton's
method is considered. It has been pointed out elsewhere
that if relative error is used as the measure of
goodness of fit, optimal results are not obtained when
the initial approximation is a best fit. It is shown
here that if, instead, the so-called logarithmic error
is used, then a best initial fit is optimal for both
types of error. Moreover, use of the logarithmic error
appears to simplify the problem of determining the
optimal initial approximation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Argonne Nat. Lab., Argonne, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; function evaluation;
iterative methods",
}
@Article{Kolbig:1969:CASa,
author = "K. S. K{\"o}lbig",
title = "Certification of {Algorithm 292} [{S22}]: {Regular}
{Coulomb} wave functions and of remark on {Algorithm
292} [{S22}]: {Regular} {Coulomb} wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "278--279",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: Tests of an Algol procedure.",
}
@Article{Kolbig:1969:CASb,
author = "K. S. K{\"o}lbig",
title = "Certification of {Algorithm 300} [{S22}]: {Coulomb}
wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "279--280",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: The first of many remarks.",
}
@Article{Kolbig:1969:RAS,
author = "K. S. K{\"o}lbig",
title = "Remark on {Algorithm 300} [{S22}]: {Coulomb} wave
functions",
journal = j-CACM,
volume = "12",
number = "12",
pages = "692--692",
month = dec,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: One of many remarks.",
}
@Article{Lardner:1969:RBB,
author = "Thomas J. Lardner",
title = "Relations Between {${}_0 F_3 $} and {Bessel}
Functions",
journal = j-SIAM-REVIEW,
volume = "11",
number = "1",
pages = "69--72",
month = "????",
year = "1969",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1011007",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:04 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/11/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1969",
}
@Article{Lewis:1969:FII,
author = "Richard L. Lewis",
title = "On Finite Integrals Involving Trigonometric, {Bessel},
and {Legendre} Functions",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "259--273",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Luke:1969:SFTa,
author = "Yudell L. Luke",
title = "The Special Functions and Their Approximations",
volume = "I",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xx + 349",
year = "1969",
ISBN = "0-12-459901-X",
ISBN-13 = "978-0-12-459901-7",
LCCN = "QA351 .L94 1969",
bibdate = "Wed Dec 15 17:55:35 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in Science and Engineering, Volume 53-I,
Editor: Richard Bellman",
acknowledgement = ack-nhfb,
}
@Book{Luke:1969:SFTb,
author = "Yudell L. Luke",
title = "The Special Functions and Their Approximations",
volume = "II",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xx + 485",
year = "1969",
ISBN = "0-12-459902-8",
ISBN-13 = "978-0-12-459902-4",
LCCN = "QA351 .L797",
bibdate = "Wed Dec 15 17:55:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Mathematics in Science and Engineering, Volume 53-II,
Editor: Richard Bellman",
URL = "http://www.sciencedirect.com/science/book/9780124599024",
acknowledgement = ack-nhfb,
tableofcontents = "Dedication / v \\
Preface / vii--ix \\
Contents of Volume I / xv \\
Introduction / xvii--xx \\
IX: Expansions of Generalized Hypergeometric Functions
in Series of Functions of the Same Kind / 1--65 \\
X: The $\tau$-Method / 66--91 \\
XI: Polynomial and Rational Approximations to
Generalized Hypergeometric Functions / 92--132 \\
XII: Recursion Formulas for Polynomials and Functions
which Occur in Infinite Series and Rational
Approximations to Generalized Hypergeometric Functions
/ 133--166 \\
XIII: Polynomial and Rational Approximations for $E(z)
= _2F_1(1, \sigma; \rho + 1; 1/z)$ / 167--185 \\
XIV: Polynomial and Rational Approximations for the
Incomplete Gamma Function / 186--213 \\
XV: Trapezoidal Rule Integration Formulas / 214--226
\\
XVI: Applications / 227--281 \\
XVII: Tables of Coefficients / 282--452 \\
Bibliography / 453--461 \\
Notation Index / 463--467 \\
Subject Index to Volumes I and II / 468--485",
}
@TechReport{Moses:1969:ICS,
author = "Joel Moses",
title = "The integration of a class of special functions with
the {Risch} algorithm",
type = "{AI} Memo (180)",
number = "MAC-M-421",
institution = "Artificial Intelligence Laboratory, Massachusetts
Institute of Technology",
address = "Cambridge, MA, USA",
pages = "13 + 1",
year = "1969",
LCCN = "Q334 M533 no. 180",
bibdate = "Sat Oct 30 18:37:28 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ng:1969:CPE,
author = "Edward W. Ng and C. J. Devine and R. F. Tooper",
title = "{Chebyshev} Polynomial Expansion of {Bose--Einstein}
Functions of Orders $1$ to $ 10$",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "639--643",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: $ B_p(\eta) = \frac {1}{\Gamma (p - 1)}
\int_0^\infty \frac {x^p}{e^{x - \eta } - 1} \, d t $.
Relative errors down to $ 3 \times 10^{-19} $.",
}
@Article{Reichel:1969:IPV,
author = "Alex Reichel",
title = "The Integral of the $n$ th Power of the {Voigt}
Function",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "645--649",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: The function $ \chi_n(t) = \int_{- \infty
}^\infty \{ U_0 (x, t) \}^n \, d x $, where $ U_0 (x,
t) = \frac {1}{\sqrt {4 \pi t}} \frac {\exp [ - (x -
y)^2 / 4 t]}{1 + y^2} \, d y $ is considered.",
}
@Article{Robertson:1969:CNC,
author = "G. H. Robertson",
title = "Computation of the Noncentral Chi-Square
Distribution",
journal = j-BELL-SYST-TECH-J,
volume = "48",
number = "1",
pages = "201--207",
month = jan,
year = "1969",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1969/BSTJ.1969.4801.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol48/bstj48-1-201.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Sollfrey:1969:IFP,
author = "William Sollfrey",
title = "Inverse Functions of the Products of Two {Bessel}
Functions",
journal = j-J-MATH-PHYS,
volume = "10",
number = "8",
pages = "1429--1430",
month = aug,
year = "1969",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1664985",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 11:55:26 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v10/i8/p1429_s1",
acknowledgement = ack-nhfb,
classification = "A0200 (Mathematical methods in physics)",
corpsource = "RAND Corp., Santa Monica, CA, USA",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "functions",
onlinedate = "4 November 2003",
pagecount = "2",
}
@Article{TadeudeMedeiros:1969:APF,
author = "Adilson {Tadeu de Medeiros} and Georges Schwachheim",
title = "{Algorithm 349}: {Polygamma} Functions with Arbitrary
Precision [{S14}]",
journal = j-CACM,
volume = "12",
number = "4",
pages = "213--214",
month = apr,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:25 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Lewis:1975:CPF}.",
abstract = "This procedure assigns to polygam the value of the
polygamma function of order n for any real argument
$z$. For $ n = 0$, we have the psi or digamma function,
for $ n = 1$ the trigamma function, for $ n = 2$ the
tetragamma function, and so on.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7300 (Natural sciences computing)",
corpsource = "Centro Brasileiro de Pesquisas Fisicas, Rio de
Janeiro, Brazil",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "digamma function; mathematics; polygamma function; psi
function; special functions; subroutines; tetragamma
function; trigamma function",
remark = "Fullerton: 150-line Algol procedure.",
}
@InProceedings{Tesler:1969:AEF,
author = "G. S. Tesler",
booktitle = "Mathematical provisioning of electronic digital
computers and effective organization of the computing
process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2",
title = "The approximation of elementary functions by means of
polynomials of degree zero and one. ({Russian})",
publisher = "Akad. Nauk Ukrain. SSR",
address = "Kiev, USSR",
pages = "75--88",
year = "1969",
MRclass = "65D15",
MRnumber = "45 \#4600",
MRreviewer = "I. Selihova",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Book{Tolke:1969:PFT,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet
der Theta-Funktionen und der elliptischen Funtionen}.
({German}) [{Practical} functional theory. 6. {Tables}
from the field of theta functions and elliptic
functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "lxxxii + 449 (vol. 1)",
year = "1969",
ISBN = "",
ISBN-13 = "",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Two volumes",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Turner:1969:DSC,
author = "L. R. Turner",
title = "Difficulty in {$ \sin $ \slash$ \cos $} Routine",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "13--13",
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Feb 15 15:23:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{VandeVel:1969:SEM,
author = "H. {Van de Vel}",
title = "On the Series Expansion Method for Computing
Incomplete Elliptic Integrals of the First and Second
Kinds",
journal = j-MATH-COMPUT,
volume = "23",
number = "105",
pages = "61--69",
month = jan,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Zaker:1969:CCE,
author = "T. A. Zaker",
title = "Calculation of the complementary error function of
complex argument",
journal = j-J-COMPUT-PHYS,
volume = "4",
number = "3",
pages = "427--430",
month = oct,
year = "1969",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(69)90011-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Thu Dec 04 16:20:39 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Bray:1970:CAR,
author = "T. Bray",
title = "Certification of {Algorithm 22, Ricatti--Bessel
Functions of First and Second Kind}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "448--448",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Oct 29 21:49:15 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: An error in an Algol procedure is
reported.",
}
@Article{Carlitz:1970:SRF,
author = "L. Carlitz",
title = "Some Reduction Formulas for Generalized Hypergeometric
Functions",
journal = j-SIAM-J-MATH-ANA,
volume = "1",
number = "2",
pages = "243--245",
month = may,
year = "1970",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sun Nov 28 19:21:58 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Carlson:1970:HSS,
author = "B. C. Carlson",
title = "Hidden Symmetries of Special Functions",
journal = j-SIAM-REVIEW,
volume = "12",
number = "3",
pages = "332--345",
month = jul,
year = "1970",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1012078",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:20 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/12/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://www.jstor.org/stable/2028552",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1970",
}
@Article{Chen:1970:CGI,
author = "Reuven Chen",
title = "On the Computation of the Generalized Integral in Glow
Curve Theory",
journal = j-J-COMPUT-PHYS,
volume = "6",
number = "2",
pages = "314--316",
month = oct,
year = "1970",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(70)90027-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Fri Oct 29 22:09:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Cochran:1970:NTF,
author = "James Alan Cochran and Judith N. Hoffspiegel",
title = "Numerical Techniques for Finding $ \nu $-Zeros of
{Hankel} Functions",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "413--422",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1970:CAC,
author = "W. J. Cody and K. E. Hillstrom",
title = "{Chebyshev} Approximations for the {Coulomb} Phase
Shift",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "671--677",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "42\#8661",
bibdate = "Wed Jan 17 08:57:04 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 4 \times 10^{-19}
$.",
}
@Article{Cody:1970:CAD,
author = "W. J. Cody and Kathleen A. Paciorek and Henry C.
{Thacher, Jr.}",
title = "{Chebyshev} approximations for {Dawson}'s integral",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "171--178",
month = jan,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.20",
MRnumber = "41\#2883",
bibdate = "Wed Jan 17 08:57:30 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1970:RAC,
author = "W. J. Cody and Kathleen A. Paciorek",
title = "Remark on {Algorithm} 292 [{S22}]: Regular {Coulomb}
Wave Functions",
journal = j-CACM,
volume = "13",
number = "9",
pages = "573",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Nov 16 23:58:51 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: More modifications to an Algol procedure.",
}
@Article{Darlington:1970:AAA,
author = "Sidney Darlington",
title = "Analytical Approximations to Approximations in the
{Chebyshev} Sense",
journal = j-BELL-SYST-TECH-J,
volume = "49",
number = "1",
pages = "1--32",
month = jan,
year = "1970",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4901.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-1-1.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@TechReport{DeLugish:1970:CAA,
author = "Bruce Gene DeLugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Functions in a Binary Computer",
number = "399",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, Illinois",
pages = "191",
year = "1970",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gautschi:1970:RAD,
author = "Walter Gautschi and Bruce J. Klein",
title = "Remark on {Algorithm 282, Derivatives of $ e^x / x $,
$ \cos (x) / x $, and $ \sin (x) / x $}",
journal = j-CACM,
volume = "13",
number = "1",
pages = "53--54",
month = jan,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 07:27:17 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gautschi:1966:AD}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Corrections are given for several Algol
procedures.",
}
@Article{Gautschi:1970:RCC,
author = "Walter Gautschi and Bruce J. Klein",
title = "Recursive computation of certain derivatives --- a
study of error propagation",
journal = j-CACM,
volume = "13",
number = "1",
pages = "7--9",
month = jan,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65Q05",
MRnumber = "46 1115",
MRreviewer = "D. F. Mayers",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A brief study is made of the propagation of errors in
linear first-order difference equations. The recursive
computation of successive derivatives of $ (e^x) / x $
and $ (\cos x) / x $ is considered as an
illustration.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4110 (Error analysis in numerical methods)",
corpsource = "Purdue Univ., Lafayette, IN, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "difference equations; error analysis; error
propagation; recursive computation; successive
derivatives",
remark = "Fullerton: Recursive calculation of derivatives of $
e^x / x $ and $ \cos (x) / x $ is considered.",
}
@Article{Hill:1970:AASa,
author = "G. W. Hill",
title = "{ACM Algorithm 395}: {Student}'s $t$-Distribution",
journal = j-CACM,
volume = "13",
number = "10",
pages = "617--619",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "statistics; subroutines",
remark = "Fullerton: Description of a 50-line Algol procedure.",
}
@Article{Hill:1970:AASb,
author = "G. W. Hill",
title = "{ACM Algorithm 396}: {Student}'s $t$-Quantiles",
journal = j-CACM,
volume = "13",
number = "10",
pages = "619--620",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also
\cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "function evaluation; statistics; subroutines",
remark = "Fullerton: Description of a 50-line Algol procedure.",
}
@Article{Holmgren:1970:RAN,
author = "Bo Holmgren",
title = "Remark on {Algorithm 304, Normal Curve Integral}",
journal = j-CACM,
volume = "13",
number = "10",
pages = "624--624",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 08:18:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Jones:1970:GHF,
author = "Alan L. Jones",
title = "The generalized hypergeometric function",
journal = j-SIGPLAN,
volume = "5",
number = "3",
pages = "26--27",
month = mar,
year = "1970",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 25 06:40:57 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Kolbig:1970:CZI,
author = "K. S. Kolbig",
title = "Complex Zeros of an Incomplete {Riemann} Zeta Function
and of the Incomplete Gamma Function",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "679--696",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lehman:1970:DZR,
author = "R. S. Lehman",
title = "On the distribution of zeros of the {Riemann}
zeta-function",
journal = j-PROC-LONDON-MATH-SOC-1,
volume = "3",
number = "20",
pages = "303--320",
month = "????",
year = "1970",
ISSN = "0024-6115 (print), 1460-244X (electronic)",
ISSN-L = "0024-6115",
MRnumber = "MR0258768 (41:3414)",
bibdate = "Mon Oct 24 12:42:07 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "This paper corrects several errors in
\cite{Turing:1953:SCR}. See also
\cite{Trudgian:2011:ITM}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the London Mathematical Society. First
Series",
journal-URL = "http://plms.oxfordjournals.org/content/by/year",
}
@TechReport{Lugish:1970:CAA,
author = "B. G. de Lugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Function in a Binary Computer",
type = "Report",
number = "399",
institution = "Department of Computer Science, University of
Illinois",
pages = "????",
month = jun,
year = "1970",
bibdate = "Fri Sep 02 22:49:20 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Luke:1970:FAE,
author = "Yudell L. Luke",
title = "Further Approximations for Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "191--198",
month = jan,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Minton:1970:GHF,
author = "Barry M. Minton",
title = "Generalized Hypergeometric Function of Unit Argument",
journal = j-J-MATH-PHYS,
volume = "11",
number = "4",
pages = "1375--1376",
month = apr,
year = "1970",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1665270",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 16:39:25 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v11/i4/p1375_s1",
acknowledgement = ack-nhfb,
classification = "A0200 (Mathematical methods in physics)",
corpsource = "Univ. Calgary, Alta., Canada",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "functions",
onlinedate = "28 October 2003",
pagecount = "2",
}
@Article{Ng:1970:CAE,
author = "E. N. Ng",
title = "Certification of {Algorithm 385, Exponential Integral
$ \operatorname {Ei}(x) $}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "448--449",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 09:18:14 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Comments on a FORTRAN routine.",
}
@Article{Ng:1970:CDF,
author = "E. W. Ng and C. J. Devine",
title = "On the Computation of {Debye} Functions of Integer
Orders",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "405--407",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Debye functions are incomplete Riemann zeta
functions. $ \overbar {D}_p(x) = \frac {1}{\Gamma (p -
1)} \int_0^x \frac {t^p}{e^t - 1} \, d t $ and the
complementary integral are calculated to 20 digits.",
}
@Article{Ninomiya:1970:BRS,
author = "Ichizo Ninomiya",
title = "Best Rational Starting Approximations and Improved
{Newton} Iteration for the Square Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "391--404",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Nagoya Univ., Chikua ku, Japan",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computing procedure; function approximation; iterative
methods; Newton iteration; rational approximation;
square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Paciorek:1970:AEI,
author = "K. A. Paciorek",
title = "{Algorithm 385}: {Exponential} Integral {$
\operatorname {Ei}(x) $}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "446--447",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Redish:1970:RAE,Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation);
C7300 (Natural sciences computing)",
corpsource = "Argonne Nat. Lab., IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "integration; subroutines",
remark = "Fullerton: A 100-line FORTRAN routine for both $
\operatorname {E1}(x) $ and $ \operatorname {Ei}(x)
$.",
}
@Article{Raff:1970:CGF,
author = "Morton S. Raff",
title = "On Calculating the Gamma Function of Non-Integral
Arguments",
journal = j-AMER-STAT,
volume = "24",
number = "2",
pages = "22--24",
month = apr,
year = "1970",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 10:52:18 MST 2012",
bibsource = "http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326364;
https://www.math.utah.edu/pub/tex/bib/amstat1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2681926",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Redish:1970:RAE,
author = "K. A. Redish",
title = "Remark on {Algorithm 385, Exponential Integral $
\operatorname {Ei}(x) $}",
journal = j-CACM,
volume = "13",
number = "12",
pages = "750--750",
month = dec,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 09:56:59 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Paciorek:1970:AEI}",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Minor corrections to a FORTRAN routine.",
}
@TechReport{Rothmaier:1970:BQN,
author = "B. Rothmaier",
title = "{Die Berechnung der Quadratwurzel nebst Schranken auf
Dualmaschinen} \toenglish {The Computation of the
Square Root together with [Interval] Bounds on Binary
Machines} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/17",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rothmaier:1970:DSB,
author = "B. Rothmaier",
title = "{Dokumentation der Standardfunktionen des
Betriebssystems Hydra X8} \toenglish {Documentation} of
the Elementary Functions of the Operating System {Hydra
X8} \endtoenglish",
type = "Interner {Bericht}",
number = "Nr. 70/8",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1970",
bibdate = "Fri Jun 11 12:37:53 1999",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Smith:1970:ASH,
author = "Robert R. Smith and Dennis McCall",
title = "{Algorithm 392}: {Systems} of Hyperbolic {P.D.E.}",
journal = j-CACM,
volume = "13",
number = "9",
pages = "567--570",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
classcodes = "C4170 (Differential equations); C7310 (Mathematics
computing)",
corpsource = "US Naval Electronics Lab. Center, San Diego, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "boundary-value problems; partial differential
equations",
}
@Book{Spain:1970:FMP,
author = "Barry Spain and M. G. (Michael Gambier) Smith",
title = "Functions of Mathematical Physics",
publisher = pub-VAN-NOSTRAND-REINHOLD,
address = pub-VAN-NOSTRAND-REINHOLD:adr,
pages = "xi + 208",
year = "1970",
ISBN = "0-442-07871-4, 0-442-07876-5 (hardcover)",
ISBN-13 = "978-0-442-07871-3, 978-0-442-07876-8 (hardcover)",
LCCN = "QA351 .S69",
bibdate = "Tue Dec 5 10:54:45 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "The New university mathematics series",
URL = "http://books.google.com/books?id=kYgZAQAAIAAJ",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Mathematical physics; Fonctions
sp{\'e}ciales; Physique math{\'e}matique; Functions,
Special; Mathematical physics; Functions, Special;
Fonctions",
tableofcontents = "1: Series solution of second-order linear
homogeneous equations \\
2: Contour integral solutions of an ordinary linear
differential equation \\
3: Oscillation Theorems and Sturm--Liouville Theory \\
4: Asymptotics \\
5: The Gamma function \\
6: The Hypergeometric Equation \\
7: The confluent hypergeometric function \\
8: The Legendre Functions \\
9: Bessel Functions \\
10: Laguerre Polynomials \\
11: Hermite Polynomials \\
Appendix 1: The Laplace and Helmholtz Equations \\
Appendix 2: The Schr{\"o}dinger Equation \\
References \\
Index",
}
@Article{Squire:1970:RAI,
author = "William Squire",
title = "A Rational Approximation to an Integral Appearing in
Glow Curve Theory",
journal = j-J-COMPUT-PHYS,
volume = "6",
number = "1",
pages = "152--253",
month = aug,
year = "1970",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(70)90016-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 10:57:00 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Srivastava:1970:CRI,
author = "H. M. Srivastava",
title = "Certain Results Involving Generalized Hypergeometric
Functions",
journal = j-SIAM-J-MATH-ANA,
volume = "1",
number = "1",
pages = "75--81",
month = feb,
year = "1970",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sun Nov 28 19:21:56 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Stegun:1970:ACM,
author = "I. A. Stegun and R. Zucker",
title = "Automatic Computing Methods for Special Functions.
Part 1. {Error}, Probability, and Related Functions",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "74B",
number = "3",
pages = "211--224",
month = jul,
year = "1970",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:58:39 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Adjustable double precision FORTRAN
routines for $ \erf $ and $ \erfc $.",
}
@Book{Tolke:1970:PFT,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet
der Theta-Funktionen und der elliptischen Funtionen}.
({German}) [{Practical} functional theory. 6. {Tables}
from the field of theta functions and elliptic
functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "452--1047 (vol. 2)",
year = "1970",
ISBN = "3-662-13079-3 (print), 3-662-13078-5",
ISBN-13 = "978-3-662-13079-7 (print), 978-3-662-13078-0",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Two volumes",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "Sechsstellige Tafel III der Theta-Funktionen und
ihrer logarithmischen Ableitungen, der Jacobischen
elliptischen Funktionen und ihrer logarithmischen
Ableitungen sowie der Weierstrassschen $z$, $?$, und
$?$-Funktionen einschlie{\ss}lich einiger
Parameterfunktionen f{\"u}r $? = z/2K$ als Argument und
bzw. $1/?$ als Parameter $2$ H{\"a}lfte,
Parameterbereich $1 ? 1 / ? 0$ \\
Neunstellige Tafel IV der Legendreschen Normalintegrale
erster und zweiter Gattung sowie der Jacobischen
Zeta-Funktion und der abgewandelten Heumanschen
Lambda-Funktion \\
Sechsstellige Tafel V der $D$-Funktionen erster bis
vierter Ordnung f{\"u}r die Charakteristiken 1 bis 4
\\
Sechsstellige Tafel VI der Legendreschen
Normalintegrale erster und zweiter Gattung sowie der
Funktion \\
\ldots{}",
}
@Article{Wilson:1970:OSA,
author = "M. Wayne Wilson",
title = "Optimal Starting Approximations for Generating Square
Root for Slow or No Divide",
journal = j-CACM,
volume = "13",
number = "9",
pages = "559--560",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2338",
MRreviewer = "J. E. {Dennis, Jr.}",
bibdate = "Tue Apr 08 20:38:30 1997",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "On computing machines with slow or no division, it is
preferable to use an iterative scheme for the square
root different from the classical Heron scheme. The
problem of optimal initial approximants is considered,
and some optimal polynomial initial approximations are
tabulated.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, Houston, TX, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "CACMA; digital arithmetic; ele; iterative methods;
mathematics; numerical methods; optimisation",
}
@Article{Winograd:1970:NMN,
author = "Shmuel Winograd",
title = "On the number of multiplications necessary to compute
certain functions",
journal = j-COMM-PURE-APPL-MATH,
volume = "23",
number = "2",
pages = "165--179",
month = mar,
year = "1970",
CODEN = "CPAMAT, CPMAMV",
DOI = "https://doi.org/10.1002/cpa.3160230204",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
bibdate = "Sat Oct 21 12:05:50 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "Comm. Pure Appl. Math.",
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
keywords = "number of multiplications to evaluate a polynomial",
remark = "From the second paragraph: ``Motzkin [3] introduced
the notion of preconditioning of the coefficients.
Motzkin showed that if, in the course of computing $
P_n(x) = \sum_{i = 0}^n a_i x^i $, operations which
depend only the $ a_i $ are not counted, then only
about $ n / 2 $ multiplications are necessary to
evaluate $ P_n(x) $. The obvious application of this
result is when the same polynomial $ P_n(x) $ has to be
evaluated at many different points.''.",
}
@TechReport{Yohe:1970:RBC,
author = "J. M. Yohe",
title = "Rigorous Bounds on Computed Approximations to Square
Roots and Cube Roots",
type = "MRC Technical Summary",
number = "1088",
institution = "University of Wisconsin, Madison",
year = "1970",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-jr,
}
@Article{Yong:1970:GBA,
author = "Lam Lay Yong",
title = "The Geometrical Basis of the {Ancient Chinese}
Square-Root Method",
journal = j-ISIS,
volume = "61",
number = "1",
pages = "92--102",
month = "Spring",
year = "1970",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:28:39 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302287;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
URL = "http://www.jstor.org/stable/229151",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Zill:1970:SEI,
author = "D. G. Zill and B. C. Carlson",
title = "Symmetric Elliptic Integrals of the Third Kind",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "199--214",
month = jan,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bohan:1971:ADC,
author = "K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov",
title = "The analytic definition of certain elementary
functions. ({Russian}) Questions of modern mathematics
and methods of teaching it at institutions of higher
learning",
journal = "Leningrad. Gos. Ped. Inst. U{\v{c}}en. Zap.",
volume = "404",
pages = "59--78",
year = "1971",
MRclass = "26A09",
MRnumber = "55 \#10612",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Book{Byrd:1971:HEI,
author = "Paul F. Byrd and Morris D. Friedman",
title = "Handbook of Elliptic Integrals for Engineers and
Scientists",
volume = "67",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xvi + 358",
year = "1971",
DOI = "https://doi.org/10.1007/978-3-642-65138-0",
ISBN = "0-387-05318-2 (New York)",
ISBN-13 = "978-0-387-05318-9 (New York)",
LCCN = "QA343 .B95 1971",
bibdate = "Mon Oct 15 16:40:14 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
series = "Die Grundlehren der mathematischen Wissenschaften in
Einzeldarstellungen",
acknowledgement = ack-nhfb,
subject = "Elliptic functions",
tableofcontents = "Introduction / 1--7 \\
Definitions and Fundamental Relations / 8--41 \\
Reduction of Algebraic Integrands to Jacobian Elliptic
Functions / 42--161 \\
Reduction of Trigonometric Integrands to Jacobian
Elliptic Functions / 162--181 \\
Reduction of Hyperbolic Integrands to Jacobian Elliptic
Functions / 182--190 \\
Table of Integrals of Jacobian Elliptic Functions /
191--222 \\
Elliptic Integrals of the Third Kind / 223--239 \\
Miscellaneous Elliptic Integrals Involving
Trigonometric and Hyperbolic Integrands / 240--248 \\
Elliptic Integrals Resulting from Laplace
Transformations / 249--251 \\
Hyperelliptic Integrals / 252--271 \\
Integrals of the Elliptic Integrals / 272--281 \\
Derivatives / 282--287 \\
Miscellaneous Integrals and Formulas / 288--297 \\
Expansions in Series / 298--307 \\
Appendix / 308 \\
Bibliography / 351 \\
Supplemental Bibliography / 353 \\
Index / 355",
}
@Misc{Chen:1971:BAU,
author = "Tien Chi Chen",
title = "Binary arithmetic unit implementing a multiplicative
iteration for the exponential, logarithm, quotient and
square root functions",
howpublished = "United States Patent 3,631,230",
day = "28",
month = dec,
year = "1971",
bibdate = "Tue Jan 08 21:54:11 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/3631230.html",
abstract = "Apparatus and a method is described for efficiently
achieving arithmetic evaluations for functions such as
exponential, logarithm, quotient, and square root with
a minimum use of multiplications or divisions.
Basically, use is made of the fact that $ x(1 \pm
2^{-m}) $ can be evaluated by a shift followed by an
add. A pair of numbers $ (x_k, y_k) $ can represent a
function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
y_n) = y_n $ for logarithm, quotient and square root.
Then, multiplication by shifting is applied to $ x_k $
with suitable adjustments on $ y_k $, until $ x_k $ is
close to unity, at which time $ y_k $ represents the
desired answer. The exponential is computed by
essentially reversing the logarithm procedure. A
termination algorithm further improves accuracy. The
apparatus involves two registers for $ x_k $ and $ y_k
$, a local memory, an adder and a shift register.",
acknowledgement = ack-nhfb,
}
@Article{Choong:1971:RA,
author = "K. Y. Choong and D. E. Daykin and C. R. Rathbone",
title = "Rational Approximations to $ \pi $",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "387--392",
month = apr,
year = "1971",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1971-0300981-0",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
database",
note = "See errata \cite{Shanks:1976:TER}.",
URL = "http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0300981-0",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1971:CAR,
author = "W. J. Cody and K. E. Hillstrom and Henry C. {Thatcher,
Jr.}",
title = "{Chebyshev} approximations for the {Riemann} zeta
function",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "537--547",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20",
MRnumber = "47 2785",
bibdate = "Wed Jan 17 08:57:00 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 20-digit approximations for either $ \zeta
(s) $ or $ \zeta (s) - 1 $.",
}
@InCollection{Cody:1971:SEF,
author = "W. J. Cody",
title = "Software for the Elementary Functions",
crossref = "Rice:1971:MS",
pages = "171--186",
year = "1971",
bibdate = "Thu Sep 15 18:56:47 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Glasser:1971:CFE,
author = "M. L. Glasser and V. E. Wood",
title = "A Closed Form Evaluation of the Elliptic Integral",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "535--536",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Glasser:1971:EII,
author = "M. L. Glasser",
title = "An Elliptic Integral Identity",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "533--534",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Herman:1971:EDH,
author = "G. T. Herman",
title = "The equivalence of different hierarchies of elementary
functions",
journal = "Z. Math. Logik Grundlagen Math.",
volume = "17",
pages = "219--224",
year = "1971",
MRclass = "02.77 (68.00)",
MRnumber = "44 \#6494",
MRreviewer = "D. A. Clarke",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Hochstadt:1971:FMP,
author = "Harry Hochstadt",
title = "The Functions of Mathematical Physics",
volume = "XXIII",
publisher = pub-WI,
address = pub-WI:adr,
pages = "xi + 322",
year = "1971",
ISBN = "0-471-40170-6 (hardcover)",
ISBN-13 = "978-0-471-40170-4 (hardcover)",
LCCN = "QA351 .H68",
bibdate = "Tue Dec 5 10:48:41 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Pure and applied mathematics: a series of texts and
monographs",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Fonctions sp{\'e}ciales; Fonctions
(math{\'e}matiques)",
tableofcontents = "1: Orthogonal Polynomials \\
1 Linear Spaces / 1 \\
2 Orthogonal Polynomials / 6 \\
3 The Recurrence Formula / 8 \\
4 The Christoffel--Darboux Formula / 9 \\
5 The Weierstrass Approximation Theorem / 11 \\
6 The Zeros of the Orthogonal Polynomials / 14 \\
7 Approximation Theory / 16 \\
8 More about the Zeros of the Orthonormal Polynomials /
23 \\
9 The completeness of the Orthonormal Polynomials in
the Space of Square-Integrable Functions / 27 \\
10 Generalizations and an Application to Conformal
Mappings / 32 \\
\\
2: The Classical Orthogonal Polynomials 1 Rodrigues'
Formula and the Classical Orthogonal Polynomials / 39
\\
2 The Differential Equations Satisfied by the Classical
Orthogonal Polynomials / 43 \\
3 On the Zeros of the Jacobi Polynomials / 45 \\
4 An Alternative Approach to the Tchebicheff
Polynomials / 46 \\
5 An Application of the Hermite Polynomials to Quantum
Mechanics / 49 \\
6 The Completeness of the Hermite and Laguerre
Polynomials / 53 \\
7 Generating Functions / 57 \\
\\
3: The Gamma Function 1 Definitions and Basic
Properties / 61 \\
2 Analytic Continuation and Integral Representations /
65 \\
3 Asymptotic Expansions / 69 \\
4 Beta Functions / 75 \\
5 The Logarithmic Derivative of the Gamma Function / 77
\\
6 Mellin--Barnes Integrals / 78 \\
7 Mellin Transforms / 80 \\
8 Applications to Algebraic Equations / 81 \\
\\
4: Hypergeometric Functions 1 Review of Linear
Differential Equations with Regular Singular Points /
88 \\
2 The Hypergeometric Differential Equation / 90 \\
3 The Hypergeometric Function / 93 \\
4 A General Method for Finding Integral Representations
/ 100 \\
5 Integral Representations for the Hypergeometric
Function / 105 \\
6 The Twenty-four Solutions of the Hypergeometric /
Equation / 106 \\
7 The Schwarz--Christoffel Transformation / 112 \\
8 Mappings of Curvilinear Triangles / 119 \\
9 Group Theoretic Discussion of the Case $ \pi(\alpha_1
+ \alpha_2 + \alpha_3) > \pi$ / 130 \\
10 Nonlinear Transformations of Hypergeometric
Functions / 132 \\
\\
5: The Legendre Functions 1 Laplace's Differential
Equation / 138 \\
2 Maxwell's Theory of Poles / 140 \\
3 Relationship to the Hypergeometric Functions / 141
\\
4 Expansion Formulas / 147 \\
5 The Addition Theorem / 149 \\
6 Green's Functions / 153 \\
7 The Complete Solution of Legendre's Differential
Equation / 156 \\
8 Asymptotic Formulas / 161 \\
\\
6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous
Polynomials / 168 \\
2 Orthogonality of Spherical Harmonics / 171 \\
3 Legendre Polynomials / 175 \\
4 Applications to Boundary Value Problems / 183 \\
\\
7: Confluent Hypergeometric Functions 1 Relationship to
the Hypergeometric Functions / 189 \\
2 Applications of These Functions in Mathematical
Physics / 191 \\
3 Integral Representations / 195 \\
4 Asymptotic Representations / 198 \\
\\
8: Bessel Functions 1 Basic Definitions / 200 \\
2 Integral Representations / 203 \\
3 Relationship to the Legendre Functions / 205 \\
4 The Generating Function of the Bessel Function / 207
\\
5 More Integral Representations / 210 \\
6 Addition Theorems / 216 \\
7 The Complete Solution of Bessel's Equation / 223 \\
8 Asymptotic Expansions for Large Argument / 225 \\
9 Airy Functions / 230 \\
10 Asymptotic Expansions for Large Indices and Large
Arguments / 235 \\
11 Some Applications of Bessel Functions in Physical
Optics / 241 \\
12 The Zeros of Bessel Functions / 249 \\
13 Fourier--Bessel Expansions / 257 \\
14 Applications in Mathematical Physics / 266 \\
15 Discontinuous Integrals / 269 \\
\\
9: Hill's Equation 1 Mathieu's Equation / 281 \\
2 Hill's Equation / 282 \\
3 The Discriminant / 287 \\
4 Expansion Theorems / 299 \\
5 Inverse Problems / 305 \\
6 Hill's Equations with Even Coefficients / 309 \\
7 Mathieu's Equation Revisited / 310 \\
8 Energy Bands in Crystals / 313 \\
Appendix / 314 \\
\\
Bibliography / 318 \\
\\
Index / 321",
}
@Article{Honey:1971:CCD,
author = "D. W. Honey",
title = "Correspondence: Calculation of a double-length square
root from a double length number using single precision
techniques",
journal = j-COMP-J,
volume = "14",
number = "4",
pages = "443--443",
month = nov,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:58 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Kuki:1971:FEP,
author = "H. Kuki and J. Ascoly",
title = "{FORTRAN} extended-precision library",
journal = j-IBM-SYS-J,
volume = "10",
number = "1",
pages = "39--61",
year = "1971",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:51:32 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
acknowledgement = ack-nj,
fjournal = "IBM Systems Journal",
xxmonth = "(none)",
}
@InCollection{Kuki:1971:MFS,
author = "H. Kuki",
title = "Mathematical Function Subprograms for Basic System
Libraries{}\emdash Objectives, Constraints, and
Trade-Off",
crossref = "Rice:1971:MS",
pages = "187--199",
year = "1971",
bibdate = "Fri Sep 16 16:27:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Lehmer:1971:CCM,
author = "D. H. Lehmer",
title = "On the compounding of certain means",
journal = j-J-MATH-ANAL-APPL,
volume = "36",
number = "1",
pages = "183--200",
month = oct,
year = "1971",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247x(71)90029-1",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
bibdate = "Tue Mar 14 18:52:11 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "arithmetic--geometric mean (AGM) iteration; complete
elliptic integrals of the first and second kinds.
Landen s transformation",
}
@Article{Liron:1971:ISR,
author = "N. Liron",
title = "Infinite Sums of Roots for a Class of Transcendental
Equations and {Bessel} Functions of Order One-Half",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "769--781",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lucas:1971:AAC,
author = "C. W. {Lucas, Jr.} and C. W. Terrill",
title = "{ACM Algorithm 404}: Complex Gamma Function [{S14}]",
journal = j-CACM,
volume = "14",
number = "1",
pages = "48--49",
month = jan,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:00:03 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#LucasT71;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "Coll. William and Mary, Williamsburg, VA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; CGAMMA; complex gamma function evaluation;
formula; function evaluation; poles of gamma function;
recursion formula; reflection; Stirling's asymptotic
series; subroutine in ALGOL; subroutines",
oldlabel = "LucasT71",
remark = "Fullerton: Fortran routine with machine-dependent
constants.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/LucasT71",
}
@Article{Luke:1971:MTBa,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "323--330",
month = apr,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Luke:1971:MTBb,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions, {II}",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "789--795",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Majithia:1971:CAN,
author = "J. C. Majithia and R. Kitai",
title = "A Cellular Array for the Nonrestoring Extraction of
Square Roots",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1617--1618",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223191",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Matta:1971:UCE,
author = "F. Matta and A. Reichel",
title = "Uniform Computation of the Error Function and Other
Related Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "339--344",
month = apr,
year = "1971",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1971-0295538-4",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
URL = "http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0295538-4",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@PhdThesis{Rothmaier:1971:BEF,
author = "B. Rothmaier",
title = "{Die Berechnung der elementaren Funktionen mit
beliebiger Genauigkeit} \toenglish {The Computation of
Elementary Functions with Arbitrary Accuracy}
\endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1971",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Sarkar:1971:EPP,
author = "B. P. Sarkar and E. V. Krishnamurthy",
title = "Economic Pseudodivision Processes for Obtaining Square
Root, Logarithm, and Arctan",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1589--1593",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223178",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 01 10:32:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Scarton:1971:DPF,
author = "Henry A. Scarton",
title = "Double precision {FORTRAN} subroutines to compute both
ordinary and modified {Bessel} functions of the first
kind and of integer order with arbitrary complex
argument: {$ J_n(x + j y) $} and {$ I_n(x + j y) $}",
journal = j-J-COMPUT-PHYS,
volume = "8",
number = "2",
pages = "295--299",
month = oct,
year = "1971",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(71)90010-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:04 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999171900106",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Shenton:1971:CFP,
author = "L. R. Shenton and K. O. Bowman",
title = "Continued Fractions for the Psi Function and its
Derivatives",
journal = j-SIAM-J-APPL-MATH,
volume = "20",
number = "4",
pages = "547--554",
month = jun,
year = "1971",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2099856",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
}
@Article{Shipman:1971:HSE,
author = "L. L. Shipman and R. E. Christoffersen",
title = "High Speed Evaluation of {$ F_0 (x) $}",
journal = j-COMP-PHYS-COMM,
volume = "2",
number = "4",
pages = "201--206",
month = may # "\slash " # jun,
year = "1971",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(71)90053-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:40:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465571900531",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "Fullerton: $ F_0 (x) = \int_0^1 \exp ( - x u^2) \, d u
$, which is simply related to $ \erf $ for $ x > 0 $
and to Dawson's function for $ x < 0 $.",
}
@Article{Spellucci:1971:DPA,
author = "P. Spellucci",
title = "Double precision approximations to the elementary
functions using {Jacobi-fractions}",
journal = j-NUM-MATH,
volume = "18",
pages = "127--143",
year = "1971/1972",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D20",
MRnumber = "45 \#7938",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Spira:1971:CGF,
author = "Robert Spira",
title = "Calculation of the Gamma Function by {Stirling}'s
Formula",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "317--322",
month = apr,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Sundblad:1971:AFT,
author = "Y. Sundblad",
title = "The {Ackermann} Function. {A} Theoretical,
Computational, and Formula Manipulative Study",
journal = j-BIT,
volume = "11",
number = "1",
pages = "107--119",
month = mar,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01935330",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:11 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=1&spage=107",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: Ackermann's function is a recursively
defined function of importance to computer science
theorists.",
}
@InProceedings{Walther:1971:UAE,
author = "J. S. Walther",
title = "A unified algorithm for elementary functions",
crossref = "AFIPS:1971:ACP",
volume = "38",
pages = "379--385",
year = "1971",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Wills:1971:URR,
author = "John G. Wills",
title = "On the use of recursion relations in the numerical
evaluation of spherical {Bessel} functions and
{Coulomb} functions",
journal = j-J-COMPUT-PHYS,
volume = "8",
number = "1",
pages = "162--166",
month = aug,
year = "1971",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(71)90043-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:04 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199917190043X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Wong:1971:SEI,
author = "R. Wong and E. Rosenbloom",
title = "Series Expansions of $ {W}_{k, m}(z) $ Involving
Parabolic Cylinder Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "783--787",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bardin:1972:CFE,
author = "C. Bardin and Y. Dandeu and L. Gauthier and J.
Guillermin. T. Lena. J.-M. Pernet and H. H. Wolter and
T. Tamura",
title = "{Coulomb} Functions in Entire $ (\eta, \rho) $ Plane",
journal = j-COMP-PHYS-COMM,
volume = "3",
number = "2",
pages = "73--87",
month = mar,
year = "1972",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(72)90057-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:09:33 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Book{Bark:1972:MTF,
author = "L. S. Bark",
title = "{{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh
funktsi{\u\i}}} ($ \operatorname {sin} x $, $
\operatorname {cos} x $, $ e^x $ {\cyr i} $ e^{-x} $).
({Russian}) [Multiplace tables of the elementary
functions ($ \operatorname {sin} \ x $, $ \operatorname
{cos} \ x $, $ e^x $ and $ e^{-x} $ )]",
publisher = "Vy{\v{c}}isl. Centr Akad. Nauk SSSR",
address = "Moscow, USSR",
edition = "Second, unrevised",
pages = "134",
year = "1972",
MRclass = "65A05",
MRnumber = "50 \#6100",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Tables processed and text translated from the English
by L. S. Bark. Library of Mathematical Tables, No. 9.
1972",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Carlson:1972:ACL,
author = "B. C. Carlson",
title = "An algorithm for computing logarithms and
arctangents",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "543--549",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Iowa State Univ., Ames, IA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "acceleration; arctangents; auxiliary; Borchardt's
algorithm; convergence; fast; function approximation;
functions; inverse circular functions; inverse
hyperbolic; iterative algorithm; logarithms; numerical
methods; rational operations; recurrence relation;
square roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Chen:1972:ACE,
author = "Tien Chi Chen",
title = "Automatic Computation of Exponentials, Logarithms,
Ratios and Square Roots",
journal = j-IBM-JRD,
volume = "16",
number = "4",
pages = "380--388",
month = jul,
year = "1972",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65D20",
MRnumber = "49 \#1738",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.research.ibm.com/journal/rd/164/chen.pdf",
abstract = "It is shown how a relatively simple device can
evaluate exponentials, logarithms, ratios and square
roots for fraction arguments, employing only shifts,
adds, high-speed table lookups, and bit counting. The
scheme is based on the cotransformation of a number
pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
invariant; when $x$ is driven towards a known value $
x_w $, $y$ is driven towards the result. For an $N$-bit
fraction about $ N / 4 $ iterations are required, each
involving two or three adds; then a termination
algorithm, based on an add and an abbreviated multiply,
completes the process, for a total cost of about one
conventional multiply time. Convergence, errors and
simulation using APL are discussed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, San Jose, CA, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "adds; APL; bit counting; convergence;
cotransformation; digital arithmetic; errors;
exponentials; high speed table; iteration; logarithms;
lookups; ratios; shifts; simulation; square roots;
termination algorithm",
reviewer = "F. Gotze",
treatment = "P Practical",
}
@TechReport{Ercegovac:1972:RES,
author = "Milos D. Ercegovac",
title = "Radix 16 Evaluation of Some Elementary Functions",
number = "540",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, Illinois",
pages = "30",
year = "1972",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Frisch:1972:RAR,
author = "Michael J. Frisch",
title = "Remark on ``{Algorithms 352, 385, 392}: Remarks on
Characteristic Values and Associated Solutions of
{Mathieu}'s Differential Equation, Exponential
Integral, and Systems of Hyperbolic {P.D.E.}''",
journal = j-CACM,
volume = "15",
number = "12",
pages = "1074--??",
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:42:24 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Frisch72;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Clemm:1969:ACV,Paciorek:1970:AEI,Smith:1970:ASH}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Frisch72",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Frisch72",
}
@Article{Fullerton:1972:MIG,
author = "W. Fullerton",
title = "{ACM Algorithm 435}: Modified Incomplete Gamma
Function",
journal = j-CACM,
volume = "15",
number = "11",
pages = "993--995",
month = nov,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:47:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Schoene:1978:RMI}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Fortran subprogram for evaluating $ e^{x_1}
\int_{x_1}^{x_2} |y|^{a - 1} e^{-y} \, d y $ for $a$
roughly between $1$ and $2$.",
}
@Article{Hunter:1972:NEC,
author = "D. B. Hunter and T. Regan",
title = "A note on the evaluation of the complementary error
function",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "539--541",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation)",
corpsource = "Univ. Bradford, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "complementary error function; complex variable;
evaluation; integration; method of Matta and Reichel;
modification; numerical; stability",
treatment = "T Theoretical or Mathematical",
}
@Article{Kim:1972:AEH,
author = "Shoon K. Kim",
title = "The Asymptotic Expansion of a Hypergeometric Function
$_2 {F}_2 (1, \alpha; \rho_1, \rho_2; z)$",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "963--963",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kolbig:1972:CAC,
author = "K. S. K{\"o}lbig",
title = "Certification of ``{Algorithm 363}: {Complex} error
function''",
journal = j-CACM,
volume = "15",
number = "6",
pages = "465--466",
month = jun,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:55:38 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kolbig72;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gautschi:1969:ACE}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "CERN, Geneva, Switzerland",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\erf(z)$; complex error function; function
evaluation; special functions; subroutines; Voigt
function",
oldlabel = "Kolbig72",
remark = "Fullerton: Corrections and tests of an Algol
procedure.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kolbig72",
}
@Article{Kolbig:1972:PCL,
author = "K. S. K{\"o}lbig",
title = "Programs for Computing the Logarithm of the Gamma
Function, and the Digamma Function, for Complex
Argument",
journal = j-COMP-PHYS-COMM,
volume = "4",
number = "2",
pages = "221--226",
month = nov,
year = "1972",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(72)90012-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 08:33:42 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Kolbig:1972:RCC,
author = "K. S. K{\"o}lbig",
title = "Remarks on the Computation of {Coulomb}
Wavefunctions",
journal = j-COMP-PHYS-COMM,
volume = "4",
number = "2",
pages = "214--220",
month = nov,
year = "1972",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(72)90011-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 08:35:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Kolbig:1972:ZIG,
author = "K. S. Kolbig",
title = "On the Zeros of the Incomplete Gamma Function",
journal = j-MATH-COMPUT,
volume = "26",
number = "119",
pages = "751--755",
month = jul,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "CERN, Geneva, Switzerland",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic formulae; complex w plane; function
approximation; incomplete gamma function; poles and
zeros; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Kuki:1972:AAC,
author = "Hirondo Kuki",
title = "{ACM Algorithm 421}: Complex Gamma Function with Error
Control [{S14}]",
journal = j-CACM,
volume = "15",
number = "4",
pages = "271--272",
month = apr,
year = "1972",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/361284.361296",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "47 1249",
MRreviewer = "L. Fox",
bibdate = "Mon Jan 22 06:56:30 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; complex; complex gamma function; complex
loggamma; error control; FORTRAN; function; function
approximation; loggamma function; programme;
subroutines",
oldlabel = "Kuki72a",
remark = "Fullerton: 100-line FORTRAN routine with double
complex accuracy to $ 10^{-14} $.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}
@Article{Kuki:1972:CGF,
author = "Hirondo Kuki",
title = "Complex Gamma Function with Error Control [{S14}]",
journal = j-CACM,
volume = "15",
number = "4",
pages = "262--267",
month = apr,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "47 1249",
MRreviewer = "L. Fox",
bibdate = "Mon Jan 22 06:56:30 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; complex; complex gamma function; complex
loggamma; error control; FORTRAN; function; function
approximation; loggamma function; programme;
subroutines",
oldlabel = "Kuki72a",
remark = "Fullerton: Description of a FORTRAN routine with some
math details.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}
@Book{Lebedev:1972:SFT,
author = "N. N. (Nikolai Nikolaevich) Lebedev",
title = "Special functions and their applications",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xii + 308",
year = "1972",
ISBN = "0-486-60624-4 (paperback)",
ISBN-13 = "978-0-486-60624-8 (paperback)",
LCCN = "QA351 .L3613 1972",
bibdate = "Sat Oct 30 16:25:05 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated to English and edited by Richard A.
Silverman.",
URL = "http://www.loc.gov/catdir/description/dover031/72086228.html",
acknowledgement = ack-nhfb,
remark = "Translation of Spe{\"e}t{\`\i}sial\S{}nye
funk{\"e}t{\`\i}sii i ikh prilozheni{\"e}i{\`\i}a.",
subject = "Functions, Special; Mathematical physics",
tableofcontents = "1 The Gamma Function \\
\\
1.1. Definition of the Gamma Function \\
1.2. Some Relations Satisfied by the Gamma Function \\
1.3. The Logarithmic Derivative of the Gamma Function
\\
1.4. Asymptotic Representation of the Gamma Function
for Large $|z|$ \\
1.5. Definite Integrals Related to the Gamma Function
\\
Problems \\
\\
2 The Probability Integral and Related Functions \\
\\
2.1. The Probability Integral and Its Basic Properties
\\
2.2. Asymptotic Representation of the Probability
Integral for Large $|z|$ \\
2.3. The Probability Integral of Imaginary Argument.
The Function $F(z)$ \\
2.4. The Probability Integral of Argument $\sqrt{i} x$.
The Fresnel Integrals, 21. \\
2.5. Application to Probability Theory \\
2.6. Application to the Theory of Heat Conduction.
Cooling of the Surface of a Heated Object \\
2.7. Application to the Theory of Vibrations.
Transverse Vibrations of an Infinite Rod under the
Action of a Suddenly Applied Concentrated Force \\
Problems \\
\\
3 The Exponential Integral and Related Functions \\
\\
3.1. The Exponential Integral and its Basic Properties
\\
3.2. Asymptotic Representation of the Exponential
Integral for Large $|z|$ \\
3.3. The Exponential Integral of Imaginary Argument.
The Sine and Cosine Integrals \\
3.4. The Logarithmic Integral \\
3.5. Application to Electromagnetic Theory, Radiation
of a Linear Half-Wave Oscillator Problems \\
\\
4 Orthogonal Polynomials \\
\\
4.1. Introductory Remarks \\
4.2. Definition and Generating Function of the Legendre
Polynomials \\
4.3. Recurrence Relations and Differential Equation for
the Legendre Polynomials \\
4.4. Integral Representations of the Legendre
Polynomials \\
4.5. Orthogonality of the Legendre Polynomials \\
4.6. Asymptotic Representation of the Legendre
Polynomials for Large $n$ \\
4.7. Expansion of Functions in Series of Legendre
Polynomials \\
4.8. Examples of Expansions in Series of Legendre
Polynomials \\
4.9. Definition and Generating Function of the Hermite
Polynomials \\
4.10. Recurrence Relations and Differential Equation
for the Hermite Polynomials \\
4.11. Integral Representations of the Hermite
Polynomials \\
4.12. Integral Equations Satisfied by the Hermite
Polynomials \\
4.13. Orthogonality of the Hermite Polynomials \\
4.14. Asymptotic Representation of the Hermite
Polynomials for Large n \\
4.15. Expansion of Functions in Series of Hermite
Polynomials \\
4.16. Examples of Expansions in Series of Hermite
Polynomials \\
4.17. Definition and Generating Function of the
Laguerre Polynomials \\
4.18. Recurrence Relations and Differential Equation
for the Laguerre Polynomials \\
4.19. An Integral Representation of the Laguerre
Polynomials. Relation between the Laguerre and Hermite
Polynomials \\
4.20. An Integral Equation Satisfied by the Laguerre
Polynomials \\
4.21. Orthogonality of the Laguerre Polynomials \\
4.22. Asymptotic Representation of the Laguerre
Polynomials for Large $n$ \\
4.23. Expansion of Functions in Series of Laguerre
Polynomials \\
4.24. Examples of Expansions in Series of Laguerre
Polynomials \\
4.25. Application to the Theory of Propagation of
Electromagnetic Waves. Reflection from the End of a
Long Transmission Line Terminated by a Lumped
Inductance \\
Problems \\
\\
5 Cylinder Functions: Theory \\
\\
5.1. Introductory Remarks \\
5.2. Bessel Functions of Nonnegative Integral Order \\
5.3. Bessel Functions of Arbitrary Order \\
5.4. General Cylinder Functions. Bessel Functions of
the Second Kind \\
5.5. Series Expansion of the Function $Y_n(z)$ \\
5.6. Bessel Functions of the Third Kind \\
5.7. Bessel Functions of Imaginary Argument \\
5.8. Cylinder Functions of Half-Integral Order \\
5.9. Wronskians of Pairs of Solutions of Bessel s
Equation \\
5.10. Integral Representations of the Cylinder
Functions \\
5.11. Asymptotic Representations of the Cylinder
Functions for Large $|z|$ \\
5.12. Addition Theorems for the Cylinder Functions,
124.Zeros of the Cylinder Functions \\
5.13. Expansions in Series and Integrals Involving
Cylinder Functions \\
5.14. Definite Integrals Involving Cylinder Functions
\\
5.15. Cylinder Functions of Nonnegative Argument and
Order \\
5.16. Airy Functions \\
Problems \\
\\
6 Cylinder Functions: Applications \\
\\
6.1. Introductory Remarks \\
6.2. Separation of Variables in Cylindrical Coordinates
\\
6.3. The Boundary Value Problems of Potential Theory.
The Dirichlet Problem for a Cylinder \\
6.4. The Dirichlet Problem for a Domain Bounded by Two
Parallel Planes \\
6.5. The Dirichlet Problem for a Wedge \\
6.6. The Field of a Point Charge near the Edge of a
Conducting Sheet \\
6.7. Cooling of a Heated Cylinder \\
6.8. Diffraction by a Cylinder \\
Problems \\
\\
7 Spherical Harmonics: Theory \\
\\
7.1. Introductory Remarks \\
7.2. The Hypergeometric Equation and Its Series
Solution \\
7.3. Legendre Functions \\
7.4. Integral Representations of the Legendre Functions
\\
7.5. Some Relations Satisfied by the Legendre Functions
\\
7.6. Series Representations of the Legendre Functions
\\
7.7. Wronskians of Pairs of Solutions of Legend-re s
Equation \\
7.8. Recurrence Relations for the Legendre Functions
\\
7.9. Legendre Functions of Nonnegative Integral Degree
and Their Relation to Legendre Polynomials \\
7.10. Legendre Functions of Half-Integral Degree \\
7.11. Asymptotic Representations of the Legendre
Functions for Large $|v|$ \\
7.12. Associated Legendre Functions \\
Problems \\
\\
8 Spherical Harmonics: Applications \\
\\
8.1. Introductory Remarks \\
8.2. Solution of Laplace s Equation in Spherical
Coordinates \\
8.3. The Dirichlet Problem for a Sphere \\
8.4. The Field of a Point Charge Inside a Hollow
Conducting Sphere \\
8.5. The Dirichlet Problem for a Cone \\
8.6. Solution of Laplace s Equation in Spheroidal
Coordinates \\
8.7. The Dirichlet Problem for a Spheroid \\
8.8. The Gravitational Attraction of a Homogeneous
Solid Spheroid \\
8.9. The Dirichlet Problem for a Hyperboloid of
Revolution \\
8.10. Solution of Laplace s Equation in Toroidal
Coordinates \\
8.11. The Dirichlet Problem for a Torus \\
8.12. The Dirichlet Problem for a Domain Bounded by Two
Intersecting Spheres \\
8.13. Solution of Laplace s Equation in Bipolar
Coordinates \\
8.14. Solution of Helmholtz s Equation in Spherical
Coordinates \\
Problems \\
\\
9 Hypergeometric Functions \\
\\
9.1. The Hypergeometric Series and Its Analytic
Continuation \\
9.2. Elementary Properties of the Hypergeometric
Function \\
9.3. Evaluation of $F(\alpha, \beta; \gamma; z)$ for
$\Re(\gamma \alpha \beta) > 0$, 243. \\
9.4. $F(\alpha, \beta; \gamma; z)$ as a Function of its
Parameters \\
9.5. Linear Transformations of the Hypergeometric
Function \\
9.6. Quadratic Transformations of the Hypergeometric
Function \\
9.7. Formulas for Analytic Continuation of $F(\alpha,
\beta; \gamma; z)$ in Exceptional Cases \\
9.8. Representation of Various Functions in Terms of
the Hypergeometric Function \\
9.9. The Confluent Hypergeometric Function \\
9.10. The Differential Equation for the Confluent
Hypergeometric Function and Its Solution. The Confluent
Hypergeometric Function of the Second Kind \\
9.11. Integral Representations of the Confluent
Hypergeometric Functions \\
9.12. Asymptotic Representations of the Confluent
Hypergeometric Functions for Large $|z|$ \\
9.13. Representation of Various Functions in Terms of
the Confluent Hypergeometric Functions \\
9.14. Generalized Hypergeometric Functions \\
Problems \\
\\
10 Parabolic Cylinder Functions \\
\\
10.1. Separation of Variables in Laplace s Equation in
Parabolic Coordinates \\
10.2. Hermite Functions \\
10.3. Some Relations Satisfied by the Hermite Functions
\\
10.4. Recurrence Relations for the Hermite Functions
\\
10.5. Integral Representations of the Hermite Functions
\\
10.6. Asymptotic Representations of the Hermite
Functions for Large $|z|$ \\
10.7. The Dirichlet Problem for a Parabolic Cylinder
\\
10.8. Application to Quantum Mechanics \\
Problems \\
\\
Bibliography \\
\\
Index",
}
@Article{Ling:1972:EM,
author = "Chih-Bing Ling and Jung Lin",
title = "On Evaluation of Moments of $ {K}_\nu (t) / {I}_\nu
(t) $",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "529--537",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods)",
corpsource = "Virginia Politech. Inst., Blacksburg, VA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "evaluation; K/sub nu/(t)/I/sub; moments; nu/(t);
numerical methods; Watson's method",
treatment = "T Theoretical or Mathematical",
}
@Article{Linz:1972:MCB,
author = "Peter Linz",
title = "A Method for Computing {Bessel} Function Integrals",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "509--513",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation)",
corpsource = "Univ. California, Davis, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Abel; Bessel function integrals; Fourier integrals;
infinite integrals; integration; numerical computation;
transform",
treatment = "T Theoretical or Mathematical",
}
@Article{Luke:1972:MTB,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions. {III}",
journal = j-MATH-COMPUT,
volume = "26",
number = "117",
pages = "237--240",
month = jan,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods)",
corpsource = "Univ. Missouri, Kansas City, KS, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; miniaturized tables; numerical
methods",
treatment = "T Theoretical or Mathematical",
}
@Article{MacKinnon:1972:AEH,
author = "Robert F. MacKinnon",
title = "The asymptotic expansions of {Hankel} transforms and
related integrals",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "515--527",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0230 (Integral transforms); C1130 (Integral
transforms)",
corpsource = "Defence Res. Establ., Pacific, Victoria, BC, Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic expansions; Bessel; functions; Hankel
transforms; integrals; transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Majithia:1972:CAE,
author = "J. C. Majithia",
title = "Cellular Array for Extraction of Squares and Square
Roots of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1023--1024",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009084",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Manos:1972:CCA,
author = "Paul Manos and L. Richard Turner",
title = "Constrained {Chebyshev} approximations to some
elementary functions suitable for evaluation with
floating-point arithmetic",
type = "{NASA} Technical Note",
number = "TN D-6698",
institution = pub-NASA,
address = pub-NASA:adr,
pages = "iii + 68",
month = mar,
year = "1972",
bibdate = "Mon May 22 11:27:24 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
acknowledgement = ack-nhfb,
}
@Article{Marino:1972:NAA,
author = "D. Marino",
title = "New Algorithms for the Approximate Evaluation in
Hardware of Binary Logarithms and Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1416--1421",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223516",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 08:05:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Morita:1972:CAG,
author = "Tohru Morita and Tsuyoshi Horiguchi",
title = "Convergence of the arithmetic-geometric mean procedure
for the complex variables and the calculation of the
complete elliptic integrals with complex modulus",
journal = j-NUM-MATH,
volume = "20",
number = "5",
pages = "425--430",
month = oct,
year = "1972",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01402565",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Thu Jan 13 10:01:46 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=20&issue=5;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=20&issue=5&spage=425",
abstract = "The convergence of the arithmetic-geometric mean
procedure is checked for complex variables. The
procedure is shown to be useful for the evaluation of
the complete elliptic integrals of the first and second
kinds with complex modulus. It is suggested that the
procedure will be useful also for the numerical
calculation of the elliptic integrals and the Jacobian
elliptic functions with complex modulus in general.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Moses:1972:TGT,
author = "Joel Moses",
title = "Toward a General Theory of Special Functions",
journal = j-CACM,
volume = "15",
number = "7",
pages = "550--554",
month = jul,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "34-02 12H05",
MRnumber = "53 3384",
MRreviewer = "K. Okugawa",
bibdate = "Mon Jan 22 07:06:21 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Moses72;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/macsyma.bib",
note = "Twenty-fifth anniversary of the Association for
Computing Machinery.",
acknowledgement = ack-nhfb,
classcodes = "C1100 (Mathematical techniques)",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "general theory; mathematics; special functions",
oldlabel = "Moses72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Moses72",
}
@Article{Olver:1972:NBR,
author = "F. W. J. Olver and D. J. Sookne",
title = "Note on Backward Recurrence Algorithms",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "941--947",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290Z (Other numerical methods); C4190 (Other
numerical methods)",
corpsource = "Univ. Maryland, College Park, MD, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "backward recurrence algorithms; Bessel; Bessel
functions; difference equations; functions; recessive
solution; second order linear difference equation",
treatment = "T Theoretical or Mathematical",
}
@Article{Parnes:1972:CZM,
author = "R. Parnes",
title = "Complex zeros of the modified {Bessel} function {$
K_n(Z) $}",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "949--953",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "City Univ., New York, NY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "and zeros; Bessel functions; complex zeros;
interpolation; interpolation scheme; iterative;
iterative methods; modified Bessel function; poles",
treatment = "T Theoretical or Mathematical",
}
@Article{Rabin:1972:FEP,
author = "Michael O. Rabin and Shmuel Winograd",
title = "Fast evaluation of polynomials by rational
preparation",
journal = j-COMM-PURE-APPL-MATH,
volume = "25",
number = "4",
pages = "433--458",
month = jul,
year = "1972",
CODEN = "CPAMAT, CPMAMV",
DOI = "https://doi.org/10.1002/cpa.3160250405",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
bibdate = "Fri Oct 20 09:03:28 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "Comm. Pure Appl. Math.",
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
keywords = "number of multiplications to evaluate a polynomial",
}
@Article{Ramamoorthy:1972:SPI,
author = "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
title = "Some Properties of Iterative Square-Rooting Methods
Using High-Speed Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "837--847",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:45 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Samet:1972:CDL,
author = "P. A. Samet and D. W. Honey",
title = "Calculation of a Double-Length Square Root from
Double-Length Number using Single Precision
Techniques",
journal = j-COMP-J,
volume = "15",
number = "2",
pages = "116--116",
month = may,
year = "1972",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/15.2.116",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:49 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/15/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Coll., London, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; double length; precision
techniques; single; square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Strecok:1972:HPE,
author = "A. J. Strecok and J. A. Gregory",
title = "High Precision Evaluation of the Irregular {Coulomb}
Wave Functions",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "955--961 + s1--s10",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "A0365G (Solutions of wave equations: bound state in
quantum theory); B0290F (Interpolation and function
approximation); C4130 (Interpolation and function
approximation)",
corpsource = "Argonne Nat. Lab., IL, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "function approximation; high precision evaluation;
irregular Coulomb wave functions; numerical methods;
wave functions",
treatment = "T Theoretical or Mathematical",
}
@Article{Turunov:1972:EFD,
author = "M. Turunov",
title = "Elementary functions of a discrete real and complex
argument. ({Russian})",
journal = "Ta{\v{s}}kent. Gos. Univ. Nau{\v{c}}n. Trudy",
volume = "418 Voprosy Mat.",
pages = "263--271, 386",
year = "1972",
MRclass = "30A95",
MRnumber = "50 \#13556",
MRreviewer = "G. Berzsenyi",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Wimp:1972:CPE,
author = "Jet Wimp",
title = "Corrigendum: {{\booktitle{Polynomial expansions of
Bessel functions and some associated functions}} (Math.
Comp. {\bf 16} (1962), 446--458)}",
journal = j-MATH-COMPUT,
volume = "26",
number = "117",
pages = "309--309",
month = jan,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sat Dec 22 06:54:10 MST 2018",
bibsource = "http://www.ams.org/mcom/1972-26-117;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
note = "See \cite{Wimp:1962:PEB}.",
URL = "http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X;
http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X/S0025-5718-1972-0400659-X.pdf;
https://www.ams.org/mathscinet-getitem?mr=400659;
https://www.ams.org/mathscinet/search/authors.html?authorName=Wimp%2C%20Jet",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wynn:1972:CAM,
author = "Peter Wynn",
title = "Convergence Acceleration by a Method of
Intercalation",
journal = j-COMPUTING,
volume = "9",
number = "4",
pages = "267--273",
year = "1972",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "Louisiana State Univ., New Orleans, LA, USA",
classification = "B0290Z; C4190",
description = "convergence; series (mathematics)",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "convergence acceleration; method of intercalation;
series of real terms",
}
@Article{Amos:1973:BIC,
author = "D. E. Amos",
title = "Bounds on Iterated Coerror Functions and Their
Ratios",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "413--427",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Baker:1973:PAS,
author = "P. W. Baker",
title = "Predictive algorithms for some elementary functions in
radix $2$",
journal = j-ELECT-LETTERS,
volume = "9",
pages = "493--494",
year = "1973",
CODEN = "ELLEAK",
ISBN = "0013-5194",
ISBN-13 = "0013-5194",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
MRclass = "68A10",
MRnumber = "57 \#18203",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Besslich:1973:MDS,
author = "P. W. Besslich and S. Raman",
title = "Multiplication, Division and Square Root Extraction
Methods for Electronic Desk Calculators",
journal = "Journal of the Institution of Telecommunication
Engineers (India)",
volume = "19",
number = "4",
month = apr,
year = "1973",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Braithwaite:1973:ALP,
author = "W. J. Braithwaite",
title = "Associated {Legendre} Polynomials, Ordinary and
Modified Spherical Harmonics",
journal = j-COMP-PHYS-COMM,
volume = "5",
number = "5",
pages = "390--394",
month = may,
year = "1973",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(73)90065-9",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:45:41 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Cody:1973:CAP,
author = "W. J. Cody and Anthony J. Strecok and Henry C.
{Thacher, Jr.}",
title = "{Chebyshev} Approximations for the Psi Function",
journal = j-MATH-COMPUT,
volume = "27",
number = "121",
pages = "123--127",
month = jan,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65-06 (68-06)",
MRnumber = "50 6095",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Argonne Nat. Lab., IL, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Chebyshev approximation; Chebyshev approximations;
digamma function; psi function",
remark = "Fullerton: Relative errors down to $ 10^{-20} $",
treatment = "T Theoretical or Mathematical",
}
@Book{Dingle:1973:AET,
author = "Robert B. Dingle",
title = "Asymptotic expansions: their derivation and
interpretation",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 521",
year = "1973",
ISBN = "0-12-216550-0",
ISBN-13 = "978-0-12-216550-4",
LCCN = "QA295 .D45",
bibdate = "Sat Feb 18 14:52:17 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Asymptotic expansions; Power series",
}
@Article{Ercegovac:1973:REC,
author = "M. D. Ercegovac",
title = "Radix-16 Evaluation of Certain Elementary Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "561--566",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009107",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fettis:1973:CZE,
author = "Henry E. Fettis and James C. Caslin and Kenneth R.
Cramer",
title = "Complex zeros of the error function and of the
complementary error function",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "401--407",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Wright-Patterson Air Force Base, OH, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic formula; complementary error function;
complex zeros; error function; errors; first one
hundred zeros; function evaluation; poles and zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Fettis:1973:SPC,
author = "Henry E. Fettis and James C. Caslin and Kenneth R.
Cramer",
title = "Saddle Points of the Complementary Error Function",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "409--412",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Sandia Labs., Albuquerque, NM, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic; complementary error function; errors;
formula; function evaluation; poles and zeros; saddle
points",
treatment = "T Theoretical or Mathematical",
}
@Article{Fisher:1973:NEI,
author = "N. I. Fisher",
title = "A note on the evaluation of the incomplete gamma
function",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "2",
number = "4",
pages = "325--332",
year = "1973",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657308810058",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:10:34 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Gautschi:1973:AAE,
author = "Walter Gautschi",
title = "{ACM Algorithm 471}: Exponential Integrals [{S13}]",
journal = j-CACM,
volume = "16",
number = "12",
pages = "761--763",
month = dec,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:43:23 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Gautschi73;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation);
C7310 (Mathematics computing)",
corpsource = "Purdue Univ., Lafayette, IN, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "ALGOL; computation; continued fractions; exponential
integrals; integration; recurrence relations;
recursive; subroutine; subroutines",
oldlabel = "Gautschi73",
remark = "Fullerton: Algol-language routine for $ E_n(x) =
\int_1^\infty e^{-x t} t^n \, d t, x > 0 $.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gautschi73",
}
@TechReport{Hemker:1973:SDL,
author = "P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen}
and H. L. Oudshoorn and D. T. Winter",
title = "Single- and double-length computation of elementary
functions",
number = "NW 7",
institution = "Mathematical Centre",
address = "Amsterdam",
year = "1973",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1973:AAN,
author = "G. W. Hill and A. W. Davis",
title = "{ACM Algorithm 442}: Normal Deviate [{S14}]",
journal = j-CACM,
volume = "16",
number = "1",
pages = "51--52",
month = jan,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:49:54 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1973.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#HillD73;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
country = "USA",
descriptors = "RVG",
enum = "7393",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "ALGOL; normal deviate; normal distribution inverse;
probit; statistics; subroutines; Taylor series
approximation; transform",
oldlabel = "HillD73",
references = "0",
remark = "Fullerton: Short Algol-language procedure with
accuracy to 24 digits.",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/HillD73",
}
@Article{Hill:1973:AAS,
author = "G. W. Hill",
title = "{ACM Algorithm 465}: {Student}'s $t$ Frequency
[{S14}]",
journal = j-CACM,
volume = "16",
number = "11",
pages = "690--690",
month = nov,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:49:52 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Hill73a;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, SA, Australia",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "ALGOL; approximation; density function; series;
statistics; student's t statistic; subroutine;
subroutines",
oldlabel = "Hill73a",
remark = "Fullerton: Algol-language routine for $ f(t | n) =
\frac {\Gamma (n / 2 + 1 / 2)}{(\pi n)^{1 / 2} \Gamma
(n / 2)} (1 + t^2 / n)^{n / 2 + 1 / 2} $.",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Hill73a",
}
@Article{Hill:1973:SAA,
author = "I. D. Hill",
title = "Statistical Algorithms: {Algorithm AS 66}: The Normal
Integral",
journal = j-APPL-STAT,
volume = "22",
number = "3",
pages = "424--427",
month = sep,
year = "1973",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:20:49 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://lib.stat.cmu.edu/apstat/66",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@Article{Hwang:1973:RRS,
author = "W. G. Hwang and John Todd",
title = "A recurrence relation for the square root",
journal = j-J-APPROX-THEORY,
volume = "9",
pages = "299--306",
year = "1973",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(73)90075-0",
ISSN = "0021-9045,1096-0430",
ISSN-L = "0021-9045",
MRclass = "65H05",
MRnumber = "373270",
MRreviewer = "L. Fox",
bibdate = "Sat Oct 21 14:25:01 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0271.65032",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
received = "19 April 1971",
ZBmath = "3426800",
}
@Article{Laurenzi:1973:DWF,
author = "Bernard J. Laurenzi",
title = "Derivatives of {Whittaker} Functions $ {W}_{k, 1 / 2}
$ and $ {M}_{k, 1 / 2} $ with Respect to Order $ {K}
$",
journal = j-MATH-COMPUT,
volume = "27",
number = "121",
pages = "129--132",
month = jan,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Levin:1973:DNL,
author = "D. Levin",
title = "Development of non-linear transformations for
improving convergence of sequences",
journal = j-INT-J-COMPUT-MATH,
volume = "3",
number = "1--4",
pages = "371--388",
month = "????",
year = "1973",
CODEN = "IJCMAT",
DOI = "https://doi.org/10.1080/00207167308803075",
ISSN = "0020-7160",
ISSN-L = "0020-7160",
bibdate = "Thu Dec 01 10:27:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0274.65004",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Computer Mathematics",
journal-URL = "http://www.tandfonline.com/loi/gcom20",
keywords = "convergence acceleration",
}
@Article{Linz:1973:NCI,
author = "Peter Linz and T. E. Kropp",
title = "A note on the computation of integrals involving
products of trigonometric and {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "27",
number = "124",
pages = "871--872",
month = oct,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Univ. California, Davies, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; computation; integration; numerical;
numerical methods; products; trigonometric",
treatment = "T Theoretical or Mathematical",
}
@Article{Lozier:1973:BCP,
author = "D. W. Lozier and L. C. Maximon and W. L. Sadowski",
title = "A bit comparison program for algorithm testing",
journal = j-COMP-J,
volume = "16",
number = "2",
pages = "111--117",
month = may,
year = "1973",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:11 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif",
acknowledgement = ack-nhfb,
classcodes = "C6150G (Diagnostic, testing, debugging and evaluating
systems)",
corpsource = "Nat. Bur. Stand., Washington, DC, USA",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "accuracy; algorithm testing; bit comparison program;
computer algorithms; program debugging",
treatment = "P Practical",
}
@Article{McNolty:1973:SPD,
author = "Frank McNolty",
title = "Some probability density functions and their
characteristic functions",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "495--504",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0240 (Probability and statistics); C1140 (Probability
and statistics)",
corpsource = "Lockheed Palo Alto Res. Lab., CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel function; characteristic functions; functions;
hypergeometric function; probability; probability
density functions",
treatment = "T Theoretical or Mathematical",
}
@Article{Rice:1973:EEI,
author = "S. O. Rice",
title = "Efficient Evaluation of Integrals of Analytic
Functions by the Trapezoidal Rule",
journal = j-BELL-SYST-TECH-J,
volume = "52",
number = "5",
pages = "707--722",
month = may # "--" # jun,
year = "1973",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1973/BSTJ.1973.5205.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol52/bstj52-5-707.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Schmid:1973:BLVa,
author = "H. Schmid",
title = "{BCD} logic {V}: {BCD} square root",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "17",
pages = "62--69",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
keywords = "decimal fixed-point arithmetic",
}
@Article{Sookne:1973:BFC,
author = "D. J. Sookne",
title = "{Bessel} Functions {$I$} and {$J$} of Complex Argument
and Integer Order",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "77B",
number = "3--4",
pages = "111--114",
month = jul,
year = "1973",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:49:13 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: A program is described but not published.",
}
@Article{Sookne:1973:BFR,
author = "D. J. Sookne",
title = "{Bessel} Functions of Real Argument and Integer
Order",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "77A",
number = "3--4",
pages = "125--132",
month = jul,
year = "1973",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:51:18 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Sequences of $ I_n(x) $ and $ J_n(x) $ are
computed with a FORTRAN routine.",
}
@Article{Sookne:1973:CABa,
author = "D. J. Sookne",
title = "Certification of an Algorithm for {Bessel} Functions
of Real Argument",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "77B",
number = "3--4",
pages = "115--124",
month = jul,
year = "1973",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:55:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: An algorithm is shown to lose at most about
3 bits of precision.",
}
@Article{Sookne:1973:CABb,
author = "D. J. Sookne",
title = "Certification of an Algorithm for {Bessel} Functions
of Complex Argument",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "77B",
number = "3",
pages = "133--136",
month = jul,
year = "1973",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:53:39 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: The algorithm is shown to lose at most
about 3 bits of precision.",
}
@Article{Vos:1973:RAC,
author = "H. Vos",
title = "Remark on ``{Algorithm 300}: {Coulomb} Wave
Functions''",
journal = j-CACM,
volume = "16",
number = "5",
pages = "308--309",
month = may,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:27:34 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Vos73;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gunn:1967:ACW}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
corpsource = "Vrije Univ., Amsterdam, Netherlands",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; function evaluation;
mathematics; wave functions",
oldlabel = "Vos73",
remark = "Fullerton: Algol-language accuracy monitor for
Algorithm 300, which is generally accurate only to 3
digits.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Vos73",
}
@Article{Wong:1973:AEL,
author = "R. Wong",
title = "An Asymptotic Expansion of {$ W_{k, m}(z) $} with
Large Variable and Parameters",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "429--436",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wong:1973:UAE,
author = "R. Wong",
title = "On uniform asymptotic expansion of definite
integrals",
journal = j-J-APPROX-THEORY,
volume = "7",
number = "1",
pages = "76--86",
month = jan,
year = "1973",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(73)90055-5",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A60",
MRnumber = "0340910",
MRreviewer = "L. Berg",
bibdate = "Sat Feb 18 15:20:40 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021904573900555",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
keywords = "incomplete gamma functions",
}
@Article{Wrench:1973:ECT,
author = "John W. Wrench",
title = "Erratum: {Concerning Two Series for the Gamma
Function}",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "681--682",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Minor last-digit rounding errors are
reported.",
}
@Article{Wrigge:1973:EII,
author = "H. S. Wrigge",
title = "An Elliptic Integral Identity",
journal = j-MATH-COMPUT,
volume = "27",
number = "124",
pages = "839--840",
month = oct,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Yohe:1973:IBS,
author = "J. M. Yohe",
title = "Interval Bounds for Square Roots and Cube Roots",
journal = j-COMPUTING,
volume = "11",
number = "1",
pages = "51--57",
month = mar,
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-jr # " and " # ack-nhfb,
affiliation = "Univ. Wisconsin, Madison, WI, USA",
classification = "C5230",
description = "digital arithmetic; error analysis",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "binary computers; cube roots; error analysis; interval
bounds; machine representable number; optimal upward
directed rounding; smallest machine representable
interval; square roots",
}
@Article{Acton:1974:RRF,
author = "Forman S. Acton",
title = "Recurrence relations for the {Fresnel} integral $
\int_0^{\infty } \exp ( - c t) \, d t / \sqrt {t (1 +
t^2)} $ and similar integrals",
journal = j-CACM,
volume = "17",
number = "8",
pages = "480--481",
month = aug,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20 (33A70)",
MRnumber = "49 6554",
bibdate = "Mon Jan 22 06:20:27 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Acton74;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The class of functions defined by $ \int_0^\infty
[\exp ( - c X)d t / (1 + Y)(t^{1 / 2})^k] $ where $X$
and $Y$ are either $t$ or $ t^2 $ and $k$ is $ - 1 $,
$0$, or $1$ can be evaluated by recurrences for all but
small values of the parameter $c$. These recurrences,
given here, are more efficient than the usual
asymptotic series.",
acknowledgement = ack-nhfb,
classification = "921",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "exponential integral; Fresnel integral; mathematical
techniques; recurrence relations",
oldlabel = "Acton74",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Acton74",
}
@Article{Amos:1974:CMB,
author = "D. E. Amos",
title = "Computation of modified {Bessel} functions and their
ratios",
journal = j-MATH-COMPUT,
volume = "28",
number = "125",
pages = "239--251",
month = jan,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Sandia Labs., Albuquerque, NM, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; computation; low order Bessel
functions; modified Bessel functions; monotonicity;
properties; ratios; recursion; relation",
remark = "Fullerton: Ratios $ I_{\nu + 1}(x) / I_\nu (x) $ are
considered.",
treatment = "T Theoretical or Mathematical",
}
@Book{Anonymous:1974:TCH,
editor = "Anonymous",
title = "Tables of Complex Hyperbolic and Circular Functions",
volume = "23",
publisher = "Corona Pub. Co.",
address = "Tokyo, Japan",
pages = "621",
year = "1974",
LCCN = "QA55 .T172",
bibdate = "Sat Apr 1 14:49:41 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Advanced series of mathematical and engineering
tables",
acknowledgement = ack-nhfb,
remark = "Title and introduction also in Japanese: Fukuso
s{\aa}okyokusen kans{\aa}u hy{\aa}o.",
subject = "Mathematics; Tables; Exponential functions;
Trigonometrical functions",
}
@Article{Barlow:1974:CCF,
author = "R. H. Barlow",
title = "Convergent Continued Fraction Approximants to
Generalised Polylogarithms",
journal = j-BIT,
volume = "14",
number = "1",
pages = "112--116",
month = mar,
year = "1974",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933124",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:13 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=14&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=1&spage=112",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: Nielsen's generalization $ S_{n, p}(z) =
\frac {( - 1)^{n + p - 1}(n - 1)! p!} \int_0^1 \ln^{n -
1}(t) \ln^p(1 - z t) / t \, d t $ is evaluated in the
complex plane.",
}
@Article{Barnett:1974:CWF,
author = "A. R. Barnett and D. H. Feng and J. W. Steed and L. J.
B. Goldfarb",
title = "{Coulomb} wave functions for all real $ \eta $ and $
\rho $",
journal = j-COMP-PHYS-COMM,
volume = "8",
number = "5",
pages = "377--395",
month = dec,
year = "1974",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(74)90013-7",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Jul 14 09:47:42 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "This paper may contain the first presentation of
Steed's algorithm for computing continued fractions.",
}
@Article{Blair:1974:RCA,
author = "J. M. Blair",
title = "Rational {Chebyshev} approximations for the modified
{Bessel} functions {$ I_0 (x) $} and {$ I_1 (x) $}",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "581--583",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Atomic Energy Canada Ltd., Chalk River, Ont., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Chebyshev approximation; functions; modified Bessel;
nearly best rational approximations; rational Chebyshev
approximations; series (mathematics)",
remark = "Fullerton: With microfiche supplement. Relative errors
down to $ 10^{-23} $.",
treatment = "T Theoretical or Mathematical",
}
@Article{Bosten:1974:RAI,
author = "Nancy E. Bosten and E. L. Battiste",
title = "Remark on ``{Algorithm 179}: {Incomplete} Beta
Ratio''",
journal = j-CACM,
volume = "17",
number = "3",
pages = "156--157",
month = mar,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:27:36 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#BostenB74;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Ludwig:1963:AIB,Pike:1976:RIB}.",
acknowledgement = ack-nhfb,
bdate = "Mon Jan 22 06:27:36 MST 2001",
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C7310
(Mathematics computing)",
corpsource = "IMSL, Houston, TX, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Algorithm 179; computer aided analysis; function
approximation; incomplete beta ratio; subroutines",
oldlabel = "BostenB74",
remark = "Fullerton: FORTRAN routine with accuracy about $
10^{-6} $. See M. C. Pike (1976) for a Remark.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/BostenB74",
}
@Article{Brent:1974:AAG,
author = "Richard P. Brent",
title = "{ACM Algorithm 488}: a {Gaussian} pseudo-random number
generator [{G5}]",
journal = j-CACM,
volume = "17",
number = "12",
pages = "704--706",
month = dec,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:05 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Brent74;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7890 (Other special applications of computing)",
corpsource = "Australian Nat. Univ., Canberra, Australia",
country = "USA",
descriptors = "RVG",
enum = "7061",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "distribution; FORTRAN; Gaussian; generator; GRAND;
normal distribution; pseudo random numbers; random
number generation; random numbers; subroutines",
location = "SEL: Wi",
oldlabel = "Brent74",
references = "0",
remark = "Fullerton: A FORTRAN routine that returns normally
distributed numbers with zero mean and unit standard
deviation.",
revision = "16/01/94",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Brent74",
}
@Article{Burrell:1974:AAE,
author = "Keith H. Burrell",
title = "{ACM Algorithm 484}: Evaluation of the Modified
{Bessel} Functions {$ K_0 (z) $} and {$ K_1 (z) $} for
Complex Arguments [{S17}]",
journal = j-CACM,
volume = "17",
number = "9",
pages = "524--526",
month = sep,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:58 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Burrell74;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
corpsource = "California Inst. Technol., Pasadena, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; applications of computers; Bessel
functions; complex arguments; function evaluation;
Gauss-Hermite quadrature; Hankel functions; modified
Bessel functions; natural sciences; subroutines",
oldlabel = "Burrell74",
remark = "Fullerton: 10-digit accuracy FORTRAN program.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Burrell74",
}
@Article{Buschman:1974:FSR,
author = "R. G. Buschman",
title = "Finite sum representations for partial derivatives of
special functions with respect to parameters",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "817--824",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Univ. Wyoming, Laramie, WY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; differentiation; finite sum
representations; finite sums; functions; G function;
Gegenbauer functions; hypergeometric; Legendre; Mellin
transformation; partial derivatives; special functions;
Whittaker functions",
remark = "Fullerton: Whittaker and Bessel functions are
considered.",
treatment = "T Theoretical or Mathematical",
}
@Article{Carta:1974:HLR,
author = "David G. Carta",
title = "Help!!: {The} Lost Reference: ({A} Modified {Newton}
Method for Square Roots)",
journal = j-SIGNUM,
volume = "9",
number = "4",
pages = "9--9",
month = oct,
year = "1974",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1206085.1206086",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Jun 17 18:47:00 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
abstract = "Around 1970 I saw a journal article describing a
modified Newton iteration for square roots. It involved
changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
(x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
0.5 $, thereby increasing the asymptotic rate of
convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
1} = 0.25 e_n^2 $.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Fettis:1974:SAC,
author = "Henry E. Fettis",
title = "A stable algorithm for computing the inverse error
function in the `tail-end' region",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "585--587",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Wright-Patterson Air Force Base, OH, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "function evaluation; inverse error function; iterative
algorithm; stability; stable algorithm; tail end
region",
treatment = "T Theoretical or Mathematical",
}
@Article{Glasser:1974:SDI,
author = "M. L. Glasser",
title = "Some definite integrals of the product of two {Bessel}
functions of the second kind: (order zero)",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "613--615",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Battelle Memorial Inst., Columbus, OH, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; definite integrals; evaluate;
function evaluation; integral representation; order;
second kind; zero",
treatment = "T Theoretical or Mathematical",
}
@Article{Hitotumatu:1974:NMC,
author = "Sin Hitotumatu",
title = "A new method for the computation of square root,
exponential and logarithmic functions through
hyperbolic {CORDIC}",
journal = "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
l'Approximation",
volume = "3",
number = "2",
pages = "173--180",
year = "1974",
ISSN = "1010-3376 (print), 2457-8118 (electronic)",
ISSN-L = "1010-3376",
MRclass = "65D20",
MRnumber = "381249",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://ictp.acad.ro/jnaat/journal/article/view/1974-vol3-no2-art7",
acknowledgement = ack-nhfb,
ajournal = "Rev. Anal. Num{\'e}r. Th{\'e}orie Approximation",
fjournal = "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
l'Approximation",
journal-URL = "https://ictp.acad.ro/jnaat/journal",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Koppelaar:1974:CRA,
author = "Henk Koppelaar",
title = "Certification and Remark on ``{Algorithm 191}:
Hypergeometric''",
journal = j-CACM,
volume = "17",
number = "10",
pages = "589--590",
month = oct,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:55:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Kopelaar74;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Relph:1963:AH}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "Utrecht State Univ., Netherlands",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; hypergeometric; improvements; inefficiency;
natural sciences applications of computers;
subroutines",
oldlabel = "Kopelaar74",
remark = "Fullerton: Algol-language modifications for Algorithm
191, which does not appear to be accurate far from the
origin.",
treatment = "G General Review; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kopelaar74",
}
@Article{Kyriakopoulos:1974:GFH,
author = "E. Kyriakopoulos",
title = "Generating functions of the hypergeometric functions",
journal = j-J-MATH-PHYS,
volume = "15",
number = "6",
pages = "753--759",
month = jun,
year = "1974",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1666724",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 16:40:13 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v15/i6/p753_s1",
acknowledgement = ack-nhfb,
classification = "A0210 (Algebra, set theory, and graph theory); A0220
(Group theory); A0230 (Function theory, analysis)",
corpsource = "Nuclear Res. Center 'Democritos', Athens, Greece",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "functions; generating functions; hypergeometric
functions; Lie groups; Lie theory; multiplier
representation theory; Weisner's technique",
onlinedate = "4 November 2003",
pagecount = "7",
treatment = "T Theoretical or Mathematical",
}
@Article{Latham:1974:CPC,
author = "W. P. Latham and Rogers W. Redding",
title = "On the calculation of the parabolic cylinder
functions",
journal = j-J-COMPUT-PHYS,
volume = "16",
number = "1",
pages = "66--75",
month = sep,
year = "1974",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(74)90104-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:15 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999174901041",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{McCabe:1974:CFE,
author = "J. H. McCabe",
title = "A continued fraction expansion, with a truncation
error estimate, for {Dawson}'s integral",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "811--816",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
corpsource = "Univ. St. Andrews, Fife, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "continued fraction expansion; convergents; Dawson's
integral; error analysis; function approximation;
rational approximations; truncation error estimate",
treatment = "T Theoretical or Mathematical",
}
@Article{Nasell:1974:IMB,
author = "Ingemar Nasell",
title = "Inequalities for Modified {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "28",
number = "125",
pages = "253--256",
month = jan,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Bell Labs., Holmdel, NJ, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; inequalities; modified Bessel
functions; sharp versions",
treatment = "T Theoretical or Mathematical",
}
@Book{Olver:1974:ASF,
author = "F. W. J. Olver",
title = "Asymptotics and Special Functions",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvi + 572",
year = "1974",
ISBN = "0-12-525850-X",
ISBN-13 = "978-0-12-525850-0",
LCCN = "QA351 .O481 1974",
bibdate = "Wed Dec 15 10:40:06 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pisarskii:1974:QCD,
author = "A. V. Pisarski{\u\i} and A. F. Kurgaev and A. V.
Palagin",
title = "On the question of the convergence of the {``digit by
digit''} methods of computing the elementary
functions",
journal = "Kibernetika (Kiev)",
volume = "4",
pages = "147--149",
year = "1974",
CODEN = "KBRNA5",
ISSN = "0023-1274",
MRclass = "65D20",
MRnumber = "53 \#1915",
MRreviewer = "V. V. Ivanov",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pomeranz:1974:AAE,
author = "John Pomeranz",
title = "{ACM Algorithm 487}: Exact Cumulative Distribution of
the {Kolmogorov--Smirnov} Statistic for Small Samples",
journal = j-CACM,
volume = "17",
number = "12",
pages = "703--704",
month = dec,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:12:56 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Pomeranz74;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Pomeranz:1976:REC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "Purdue Univ., West Lafayette, IN, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; exact cumulative distribution; FORTRAN;
Kolmogorov Smirnov test; natural sciences applications
of computers; small samples; statistic; statistics;
subroutines",
oldlabel = "Pomeranz74",
remark = "Fullerton: FORTRAN routine accurate apparently to 5
digits.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Pomeranz74",
}
@Article{Shaw:1974:NME,
author = "Mary Shaw and J. F. Traub",
title = "On the Number of Multiplications for the Evaluation of
a Polynomial and Some of Its Derivatives",
journal = j-J-ACM,
volume = "21",
number = "1",
pages = "161--167",
month = jan,
year = "1974",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321796.321810",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "A family of new algorithms is given for evaluating the
first $m$ derivatives of a polynomial. In particular,
it is shown that all derivatives may be evaluated in $
3 n - 2 $ multiplications. The best previous result
required $ (1 / 2) n (n + 1) $ multiplications. Some
optimality results are presented.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
classification = "921",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "https://dl.acm.org/loi/jacm",
keywords = "mathematical techniques; number of multiplications to
evaluate a polynomial",
}
@Article{Sheorey:1974:CEW,
author = "V. B. Sheorey",
title = "{Chebyshev} Expansions for Wavefunctions",
journal = j-COMP-PHYS-COMM,
volume = "7",
number = "1",
pages = "1--12",
month = jan,
year = "1974",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(74)90053-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:36:29 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Stegun:1974:ACM,
author = "I. A. Stegun and R. Zucker",
title = "Automatic Computing Methods for Special Functions.
{Part II}. {The} Exponential Integral {$ E_n(x) $}",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "78B",
number = "4",
pages = "199--216",
month = oct,
year = "1974",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 11:00:40 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Adjustable double precision FORTRAN
routines for $ E_n(x) $ and $ e^x E_n(x) $.",
}
@Article{Wang:1974:UEZ,
author = "Paul S. Wang",
title = "The Undecidability of the Existence of Zeros of Real
Elementary Functions",
journal = j-J-ACM,
volume = "21",
number = "4",
pages = "586--589",
month = oct,
year = "1974",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "From Richardson's undecidability results, it is shown
that the predicate ``there exists a real number such
that G(r) equals 0'' is recursively undecidable for
G(x) in a class of functions which involves polynomials
and the sine function. The deduction follows that the
convergence of a class of improper integrals is
recursively undecidable.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
classification = "921",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
keywords = "mathematical techniques",
}
@Article{Wimp:1974:CTP,
author = "J. Wimp",
title = "On the computation of {Tricomi}'s {Psi} function",
journal = j-COMPUTING,
volume = "13",
number = "3--4",
pages = "195--203",
year = "1974",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:52 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nhfb,
affiliation = "Drexel Univ., Philadelphia, PA, USA",
citedby = "Fullerton:1980:BEM",
classification = "723; 921; B0290D; C4120",
description = "convergence of numerical methods; function
evaluation",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "computation; computer programming --- Subroutines;
confluent hypergeometric function; convergence;
mathematical techniques; recurrence relations;
Tricomi's",
remark = "Fullerton: Backward recursion methods are discussed.",
}
@Article{Baker:1975:MER,
author = "P. W. Baker",
title = "More efficient radix-$2$ algorithms for some
elementary functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "11",
pages = "1049--1054",
month = nov,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224132",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68A10",
MRnumber = "52 \#7193",
MRreviewer = "I. Kaufmann",
bibdate = "Tue Jul 12 07:57:58 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672725",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Baker:1975:PMA,
author = "P. W. Baker",
title = "Parallel Multiplicative Algorithms for Some Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "322--325",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224215",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672808",
abstract = "This correspondence presents generalized higher radix
algorithms for some elementary functions which use fast
parallel $m$-bit multipliers where $ \mathrm {radix} =
2^m $. These algorithms are extensions of those
iterative schemes which are based on multiplications by
$ (1 + 2^{-i}) $ and the use of prestored values of $
\ln (1 + 2^{-i}) $ and $ \tan^{-1}(2^{-i}) $. The
particular functions under consideration are $ y / x $,
$ y / x^{1 / 2} $, $ y \exp (x) $, $ y + \ln (x) $, $
\sin (x) $ and $ \cos (x) $ [and hence $ \tan (x) $ ].
The extended algorithms rely on multiplication by $ (1
+ \mathrm {dir}^{-k}) $ where $ \mathrm {dir} $, $ 0
\leq \mathrm {dir} $, is an $m$-bit integer. Using a
simple selection procedure for $ \mathrm {dir} $,
simulations show that $p$ (radix $r$ ) digits of a
function may be generated, on the average, in less than
$ p + 1 $ iterations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Boris:1975:NEO,
author = "Jay P. Boris and Elaine S. Oran",
title = "Numerical evaluation of oscillatory integrals such as
the modified {Bessel} function {$ K_{i \zeta }(x) $}",
journal = j-J-COMPUT-PHYS,
volume = "17",
number = "4",
pages = "425--433",
month = apr,
year = "1975",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(75)90045-5",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:17 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999175900455",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@TechReport{Brent:1975:FMP,
author = "R. P. Brent",
title = "Fast Multiple-precision Evaluation of Elementary
Functions",
type = "Technical Report",
number = "STAN-CS-75-515",
institution = inst-STAN-CS,
address = inst-STAN-CS:adr,
pages = "i + 22",
month = aug,
year = "1975",
bibdate = "Thu Jan 11 16:47:21 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://bitsavers.org/pdf/stanford/cs_techReports/STAN-CS-75_515_Brent_Fast_Multiple-Precision_Evaluation_Of_Elementary_Functions_Aug75.pdf",
abstract = "Let $ f(x) $ be one of the usual elementary functions
($ \exp $, $ \log $, $ \arctan $, $ \sin $, $ \cosh $,
etc.), and let $ M(n) $ be the number of
single-precision operations required to multiply n-bit
integers. We show that f(x) can be evaluated, with
relative error $ O(2^{-n}) $, in $ O(M(n) \log (n)) $
operations as $ n \to \infty $, for any floating-point
number $x$ (with an $n$-bit fraction) in a suitable
finite interval. From the Sch{\"o}nhage--Strassen bound
on $ M(n)$, it follows that an $n$-bit approximation to
$ f(x)$ may be evaluated in $ O(n \log^2 (n) \log \log
(n))$ operations. Special cases include the evaluation
of constants such as $ \pi $, $e$, and $ e^p i$. The
algorithms depend on the theory of elliptic integrals,
using the arithmetic--geometric mean iteration and
ascending Landen transformations.",
acknowledgement = ack-nhfb,
}
@TechReport{Brent:1975:MZM,
author = "R. P. (Richard P.) Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "26",
year = "1975",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "Iterative methods (Mathematics)",
searchkey = "ti:elementary n1 function",
}
@Article{Bujnowski:1975:EFC,
author = "G. Rudnicki Bujnowski",
title = "Explicit Formulas for {Clebsch--Gordan} Coefficients",
journal = j-COMP-PHYS-COMM,
volume = "10",
number = "4",
pages = "245--250",
month = oct,
year = "1975",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(75)90069-7",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:13:20 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465575900697",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "Fullerton: A PL/I-FORMAC procedure is discussed.",
}
@Article{Carta:1975:LOA,
author = "David G. Carta",
title = "Low-Order Approximations for the Normal Probability
Integral and the Error Function",
journal = j-MATH-COMPUT,
volume = "29",
number = "131",
pages = "856--862",
month = jul,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0260 (Optimisation techniques); B0290R (Integral
equations); C1180 (Optimisation techniques); C4180
(Integral equations)",
corpsource = "Jet Propulsion Lab., California Inst. of Technol.,
Pasadena, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "error function; fraction; integral equations; linear
minimax problems; linear programming; low; normal
probability integral; order approximations;
polynomials; rational",
treatment = "T Theoretical or Mathematical",
}
@Article{Cody:1975:FPS,
author = "W. J. Cody",
title = "The {FUNPACK} Package of Special Function
Subroutines",
journal = j-TOMS,
volume = "1",
number = "1",
pages = "13--25",
month = mar,
year = "1975",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355626.355631",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@PhdThesis{Epstein:1975:AET,
author = "Harvey Irwin Epstein",
title = "Algorithms for elementary transcendental function
arithmetic",
school = "University of Wisconsin",
address = "Madison, WI, USA",
pages = "409",
year = "1975",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
annote = "Typescript. Vita. Thesis (Ph. D.)--University of
Wisconsin--Madison, 1975.",
keywords = "Algorithms.; Functions -- Data processing.; Functions,
Transcendental.",
searchkey = "ti:elementary n1 function",
}
@PhdThesis{Ercegovac:1975:GMEa,
author = "Milo{\v{s}} Dragutin Ercegovac",
title = "A General Method for Evaluation of Functions and
Computations in a Digital Computer",
type = "{Ph.D.} Thesis",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana-Champaign, IL, USA",
pages = "viii + 109",
month = jul,
year = "1975",
bibdate = "Mon Feb 10 07:18:12 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/302756306",
acknowledgement = ack-nhfb,
advisor = "James E. Robertson",
}
@Article{Ferguson:1975:PFI,
author = "Helaman Rolfe Pratt Ferguson and Dale E. Nielsen and
Grant Cook",
title = "A partition formula for the integer coefficients of
the theta function nome",
journal = j-MATH-COMPUT,
volume = "29",
number = "131",
pages = "851--855",
month = jul,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290R (Integral equations); C4180 (Integral
equations)",
corpsource = "Dept. of Math., Brigham Young Univ., Provo, UT, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "coefficients; complete elliptic integrals; elliptic
function theory; elliptic integrals; incomplete;
integral equations; partition formula; theta function
nome integer",
remark = "Fullerton: Incomplete elliptic integrals can be
expressed as a series of theta functions.",
treatment = "T Theoretical or Mathematical",
}
@Article{Fornberg:1975:CZJ,
author = "B. Fornberg and K. S. Kolbig",
title = "Complex zeros of the {Jonquiere} or polylogarithm
function",
journal = j-MATH-COMPUT,
volume = "29",
number = "130",
pages = "582--599",
month = apr,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "CERN, Geneva, Switzerland",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic; behaviour; complex zero trajectories;
Jonquiere function; poles and zeros; polylogarithm
function; polynomials; Riemann zeta function",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Gargantini:1975:PSR,
author = "I. Gargantini",
editor = "K. Nickel",
booktitle = "Interval Mathematics",
title = "Parallel Square Root Iterations",
volume = "29",
publisher = pub-SV,
address = pub-SV:adr,
pages = "196--204",
year = "1975",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture Notes In Computer Science",
acknowledgement = ack-jr,
}
@InProceedings{Gautschi:1975:CMS,
author = "W. Gautschi",
title = "Computational Methods in Special Functions --- a
Survey",
crossref = "Askey:1975:TAS",
pages = "1--98",
year = "1975",
bibdate = "Sat Oct 30 07:42:41 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Extensive list of references.",
}
@Article{Ginsberg:1975:AAD,
author = "E. S. Ginsberg and Dorothy Zaborowski",
title = "{ACM Algorithm 490}: The Dilogarithm Function of a
Real Argument [{S22}]",
journal = j-CACM,
volume = "18",
number = "4",
pages = "200--202",
month = apr,
year = "1975",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/360715.360722",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:44:28 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#GinsbergZ75;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Morris:1976:RDF}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
corpsource = "Dept. of Phys., Univ. of Massachusetts, Boston, MA,
USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "dilogarithm function; electrodynamics; ferromagnets;
function evaluation; function subroutine; ideal;
library; network analysis; polymers; quantum; real
argument; subprograms; subroutines; thermodynamics",
oldlabel = "GinsbergZ75",
remark = "Fullerton: FORTRAN routine accurate to 15 digits for
evaluating $ \operatorname {Li}_2 (x) = - \int_0^\infty
\frac {\ln (1 z)z} \, d z $.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GinsbergZ75",
}
@Article{Headley:1975:DZG,
author = "V. B. Headley and V. K. Barwell",
title = "On the distribution of the zeros of generalized {Airy}
functions",
journal = j-MATH-COMPUT,
volume = "29",
number = "131",
pages = "863--877",
month = jul,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290P (Differential equations); C4170 (Differential
equations)",
corpsource = "Dept. of Math., Brock Univ., St. Catherines, Ont.,
Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; boundary rays; differential
equations; generalized Airy functions; nonreal zeros;
zeros distribution",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Hitotumatu:1975:SRU,
author = "Sin Hitotumatu",
title = "Some remarks on the unified treatment of elementary
functions by microprogramming",
crossref = "Miller:1975:TNA",
pages = "51--56 (vol. 2)",
year = "1975",
MRclass = "65D15",
MRnumber = "54 \#11733",
MRreviewer = "Luciano Biasini",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ikebe:1975:ZRC,
author = "Yasuhiko Ikebe",
title = "The Zeros of Regular {Coulomb} Wave Functions and of
Their Derivatives",
journal = j-MATH-COMPUT,
volume = "29",
number = "131",
pages = "878--887",
month = jul,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Centre Numerical Analysis, Univ. of Texas, Austin, TX,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel function; compact matrix; eigenvalues;
eigenvalues and eigenfunctions; function zeros
characterisation; matrix algebra; methods; numerical;
operators; regular Coulomb wave functions; wave
functions; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Kioustelidis:1975:PLA,
author = "J. B. Kioustelidis and J. K. Petrou",
title = "A Piecewise Linear Approximation of $ \log_2 x $ with
Equal Maximum Errors in All Intervals",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "9",
pages = "858--861",
month = sep,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224330",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672923",
abstract = "In this paper it is shown how to divide the interval $
[1, 2] $ into $n$ parts so that the uniform linear
approximation of $ \log_2 x $ in each subinterval has
the same maximum error. This error is, in the case $ n
= 4 $, smaller by a factor of $ 2.3 $ than the error of
the linear mean-square approximation given by Hall et
al. [1]. The final products of the mathematical
analysis are explicit formulas which allow the direct
determination of all parameters and the maximum error
for any desired number $n$ of subdivisions of $ [1, 2]
$.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "$\log_2(x)$; elementary function",
}
@Article{Lewis:1975:CPF,
author = "John Gregg Lewis",
title = "Certification of ``{Algorithm} 349: Polygamma
Functions with Arbitrary Precision''",
journal = j-TOMS,
volume = "1",
number = "4",
pages = "380--382",
month = dec,
year = "1975",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Jun 16 10:31:40 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{TadeudeMedeiros:1969:APF}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "polygamma functions; special functions",
}
@Book{Luke:1975:MFT,
author = "Yudell L. Luke",
title = "Mathematical Functions and Their Approximations",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 568",
year = "1975",
ISBN = "0-12-459950-8, 1-4832-6245-6 (e-book)",
ISBN-13 = "978-0-12-459950-5, 978-1-4832-6245-1 (e-book)",
LCCN = "QA55 .L96 1975",
bibdate = "Fri Jun 30 05:58:16 MDT 2023",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
URL = "https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5",
acknowledgement = ack-nhfb,
libnote = "Not in my library.",
remark = "An updated version of part of Handbook of mathematical
functions with formulas, graphs, and mathematical
tables, edited by M. Abramowitz and I.A. Stegun.
Includes indexes.",
subject = "Mathematics; Tables; Fonctions (Math{\'e}ematiques);
Math{\'e}ematiques; Calculus; Mathematical Analysis;
Mathematics; Approximation; Funktion; Mathematik;
Spezielle Funktion",
tableofcontents = "Preface / xv \\
\\
I. The Gamma Function and Related Functions \\
\\
1.1 Definitions and Elementary Properties / 1 \\
1.2 Power Series and Other Series Expansions / 1 \\
1.3 Asymptotic Expansions / 7 \\
1.4 Rational Approximations for y (z) / 13 \\
1.5 Inequalities / 17 \\
1.6 Bibliographic and Numerical Data / 20 \\
1.6.1 General References / 20 \\
1.6.2 Description of and References to Tables / 21 \\
1.6.3 Description of and References to Other
Approximations and Expansions / 22 \\
\\
II. The Binomial Function \\
\\
2.1 Power Series / 24 \\
2.2 Expansions in Series of Jacobi and Chebyshev
Polynomials / 24 \\
2.3 Expansions in Series of Bessel Functions / 26 \\
2.4 Pad{\'e} Approximations / 27 \\
24.1 $(1 + 1 / z)^{-c}$ / 27 \\
2.4.2 The Square Root / 28 \\
2.4.3 Pad{\'e} Coefficients / 30 \\
2.4.4 The Function $e^{-w}$ / 31 \\
2.5 Inequalities / 34 \\
\\
III. Elementary Functions \\
\\
3.1 Logarithmic Functions / 36 \\
3.1.1 Power Series / 36 \\
3.1.2 Expansion in Series of Chebyshev Polynomials / 38
\\
3.1.3 Pad{\'e} Approximations / 39 \\
3.1.4 Inequalities / 41 \\
3.2 Exponential Function / 42 \\
3.2.1 Series Expansions / 42 \\
3.2.2 Expansions in Series of Jacobi and Chebyshev
Polynomials and Bessel Functions / 42 \\
3.2.3 Pad{\'e} Approximations / 46 \\
3.2.4 Inequalities / 51 \\
3.3 Circular and Hyperbolic Functions / 52 \\
3.3.1 Power Series / 52 \\
3.3.2 Expansions in Series of Jacobi and Chebyshev
Polynomials and Bessel Functions / 52 \\
3.3.3 Rational and Pad{\'e} Approximations / 57 \\
3.3.4 Inequalities / 60 \\
3.4 Inverse Circular and Hyperbolic Functions / 61 \\
3.4.1 Power Series / 61 \\
3.4.2 Expansions in Series of Chebyshev Polynomials /
63 \\
3.4.3 Pad{\'e} Approximations / 68 \\
3.4.4 Inequalities / 72 \\
3.5 Bibliographic and Numerical Data / 74 \\
3.5.1 Description of and References to Tables / 74 \\
3.5.2 Description of and References to Other
Approximations and Expansions / 74 \\
\\
IV. Incomplete Gamma Functions \\
\\
4.1 Definitions and Series Expansions / 77 \\
4.2 Differential Equations and Difference Equations /
78 \\
4.3 Pad{\'e} Approximations / 79 \\
4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\
4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\
4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq
\pi$ / 84 \\
4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu,
z)$ / 89 \\
4.4 Inequalities / 95 \\
4.4.1 $H(\nu, z)$ / 95 \\
4.4.2 $\Gamma(\nu, z)$ / 96 \\
4.5 Notes on the Computation of the Incomplete Gamma
Function / 97 \\
4.6 Exponential Integrals / 103 \\
4.6.1 Relation to Incomplete Gamma Function and Other
Properties / 103 \\
4.6.2 Expansions in Series of Chebyshev Polynomials /
104 \\
4.6.3 Rational and Pad Approximations / 106 \\
4.7 Cosine and Sine Integrals / 115 \\
4.7.1 Relation to Exponential Integral and Other
Properties / 115 \\
4.7.2 Expansions in Series of Chebyshev Polynomials /
116 \\
4.8 Error Functions / 119 \\
4.8.1 Relation to Incomplete Gamma Function and Other
Properties / 119 \\
4.8.2 Expansions in Series of Chebyshev Polynomials and
Bessel Functions / 122 \\
4.8.3 Pad{\'e} Approximations / 124 \\
4.8.4 Trapezoidal Rule Approximations / 134 \\
4.8.5 Inequalities / 137 \\
4.9 Fresnel Integrals / 139 \\
4.9.1 Relation to Error Functions and Other Properties
/ 139 \\
4.9.2 Expansions in Series of Chebyshev Polynomials /
140 \\
4.10 Bibliographic and Numerical Data / 143 \\
4.10.1 References / 143 \\
4.10.2 Description of and References to Tables / 143
\\
4.10.3 Description of and References to Other
Approximations and Expansions / 149 \\
\\
V. The Generalized Hypergeometric Function $_pF_g$ and
the $G$-Function \\
\\
5.1 Introduction / 154 \\
5.2 The $_pF_q$ / 155 \\
5.2.1 Power Series / 155 \\
5.2.2 Derivatives and Contiguous Relations / 159 \\
5.2.3 Integral Representations and Integrals Involving
the $_pF_q$ / 160 \\
5.2.4 Evaluation for Special Values of the Variable and
Parameters / 163 \\
5.3 The $G$-Function / 170 \\
5.3.1 Definition and Relation to the $_pF_q$ / 170 \\
5.3.2 Elementary Properties / 176 \\
5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ /
178 \\
5.4 The Confluence Principle / 179 \\
5.5 Multiplication Theorems / 184 \\
5.6 Integrals Involving $G$-Functions / 186 \\
5.7 Differential Equations / 190 \\
5.7.1 The $_pF_q$ / 190 \\
5.7.2 The $G$-Function / 192 \\
5.8 Series of $G$-Functions / 194 \\
5.8.1 Introduction / 194 \\
5.8.2 Notation / 194 \\
5.8.3 Expansion Theorems / 197 \\
5.9 Asymptotic Expansions / 199 \\
5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\
5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\
5.9.3 $_pF_q(z)$ / 206 \\
5.10 Expansions in Series of Generalized Jacobi,
Generalized Laguerre and Chebyshev Polynomials / 213
\\
5.10.1 Expansions for $G$-Functions / 213 \\
5.10.2 Expansions for $_pF_q$ / 220 \\
5.11 Expansions in Series of Bessel Functions / 223 \\
5.12 Polynomial and Rational Approximations / 224 \\
5.13 Recurrence Formulas for Polynomials and Functions
Occurring in Approximations to Generalized
Hypergeometric Functions / 234 \\
5.13.1 Introduction / 234 \\
5.13.2 Recursion Formulas for Extended Jacobi and
Laguerre Functions / 235 \\
5.13.3 Recursion Formulas for the Numerator and
Denominator Polynomials in the Rational Approximations
for the Generalized Hypergeometric Function / 244 \\
5.13.4 Recursion Formula for Coefficients in the
Expansion of the $G$-Function in Series of Extended
Jacobi Polynomials / 247 \\
5.14 Inequalities / 252 \\
\\
VI. The Gaussian Hypergeometric Function $_2F_1$ \\
\\
6.1 Introduction / 257 \\
6.2 Elementary Properties / 257 \\
6.2.1 Derivatives / 257 \\
6.2.2 Contiguous Relations / 258 \\
6.2.3 Integral Representations / 259 \\
6.3 Differential Equations / 260 \\
6.4 Kummer Solutions and Transformation Formulae / 262
\\
6.5 Analytic Continuation / 263 \\
6.6 The Complete Solution and Wronskians / 265 \\
6.7 Quadratic Transformations / 270 \\
6.8 The $_2F_1$ for Special Values of the Argument /
271 \\
6.9 Expansion in Series of Chebyshev Polynomials / 274
\\
6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho
+ 1;-1/z)$ / 274 \\
6.11 Inequalities / 278 \\
6.12 Bibliographic and Numerical Data / 279 \\
6.12.1 References / 279 \\
6.12.2 Description of and References to Tables / 279
\\
\\
VII. The Confluent Hypergeometric Function \\
\\
7.1 Introduction / 284 \\
7.2 Integral Representations / 284 \\
7.3 Elementary Relations / 285 \\
7.3.1 Derivatives / 285 \\
7.3.2 Contiguous Relations / 285 \\
7.3.3 Products of Confluent Functions / 286 \\
7.4 Differential Equations / 287 \\
7.5 The Complete Solution and Wronskians / 288 \\
7.6 Asymptotic Expansions / 291 \\
7.7 Expansions in Series of Chebyshev Polynomials / 293
\\
7.8 Expansions in Series of Besse! Functions / 294 \\
7.9 Inequalities / 295 \\
7.10 Other Notations and Related Functions / 295 \\
7.11 Bibliographic and Numerical Data / 296 \\
7.11.1 References / 296 \\
7.11.2 Description of and References to Tables and
Other Approximations / 296 \\
\\
VIII. Identification of the $_pF_q$, and $G$-Functions
with the Special Functions \\
\\
8.1 Introduction / 298 \\
8.2 Named Special Functions Expressed as $_pF_q$'s /
298 \\
8.2.1 Elementary Functions / 298 \\
8.2.2 The Incomplete Gamma Function and Related
Functions / 298 \\
8.2.3 The Gaussian Hypergeometric Function / 298 \\
8.2.4 Legendre Functions / 299 \\
8.2.5 Orthogonal Polynomials / 299 \\
8.2.6 Complete Elliptic Integrals / 299 \\
8.2.7 Confluent Hypergeometric Functions, Whittaker
Functions and Bessel Functions / 300 \\
8.3 Named Functions Expressed in Terms of the
$G$-Function / 300 \\
8.4 The $G$-Function Expressed as a Named Function /
306 \\
\\
IX. Bessel Functions and Their Integrals \\
\\
9.1 Introduction / 311 \\
9.2 Definitions, Connecting Relations and Power Series
/ 311 \\
9.3 Difference--Differential Formulas / 313 \\
9.4 Products of Bessel Functions / 314 \\
9.5 Asymptotic Expansions for Large Variable / 315 \\
9.6 Integrals of Bessel Functions / 315 \\
9.7 Expansions in Series of Chebyshev Polynomials / 316
\\
9.8 Expansions in Series of Bessel Functions / 360 \\
9.9 Rational Approximations / 361 \\
9.9.1 Introduction / 361 \\
9.9.2 $I_\nu(z)$, $z$ Small / 361 \\
9.9.3 $K_\nu(z)$, $z$ Large / 366 \\
9.10 Computation of Bessel Functions by Use of
Recurrence Formulas / 380 \\
9.10.1 Introduction / 380 \\
9.10.2 Backward Recurrence Schemata for Generating
$I_\nu(z)$ / 380 \\
9.10.3 Closed Form Expressions / 382 \\
9.10.4 Expressions for $J_\nu(z)$ / 389 \\
9.10.5 Numerical Examples / 392 \\
9.11 Evaluation of Bessel Functions by Application of
Trapezoidal Type Integration Formulas / 395 \\
9.12 Inequalities / 399 \\
9.13 Bibliographic and Numerical Data / 403 \\
9.13.1 References / 403 \\
9.13.2 Description of and References to Tables / 404
\\
9.13.3 Description of and References to Other
Approximations and Expansions / 410 \\
\\
X. Lommel Functions, Struve Functions, and Associated
Bessel Functions \\
\\
10.1 Definitions, Connecting Relations and Power Series
/ 413 \\
10.2 Asymptotic Expansions / 415 \\
10.3 Expansions in Series of Chebyshev Polynomials and
Bessel Functions / 415 \\
10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$
and the Errors in These Approximations / 422 \\
10.5 Bibliographic and Numerical Data / 426 \\
10.5.1 References / 426 \\
10.5.2 Description of and References to Tables / 426
\\
\\
XI. Orthogonal Polynomials \\
\\
11.1 Introduction / 428 \\
11.2 Orthogonal Properties / 428 \\
11.3 Jacobi Polynomials / 436 \\
11.3.1 Expansion Formulae / 436 \\
11.3.2 Difference--Differential Formulae / 439 \\
11.3.3 Integrals / 439 \\
11.3.4 Expansion of $x^\rho$ in Series of Jacobi
Polynomials / 440 \\
11.3.5 Convergence Theorems for the Expansion of
Arbitrary Functions in Series of Jacobi Polynomials /
442 \\
11.3.6 Evaluation and Estimation of the Coefficients in
the Expansion of a Given Function $f(x)$ in Series of
Jacobi Polynomials / 443 \\
11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
453 \\
11.5 The Chebyshev Polynomials $T_n^*(x)$ and
$U_n^*(x)$ / 459 \\
11.6 Coefficients for Expansion of Integrals of
Functions in Series of Chebyshev Polynomials of the
First Kind / 464 \\
11.6.1 Introduction / 464 \\
11.6.2 Series of Shifted Chebyshev Polynomials / 464
\\
11.6.3 Series of Chebyshev Polynomials of Even Order /
468 \\
11.6.4 Series of Chebyshev Polynomials of Odd Order /
468 \\
11.7 Orthogonality Properties of Chebyshev Polynomials
with Respect to Summation / 469 \\
11.8 A Nesting Procedure for the Computation of
Expansions in Series of Functions Where the Functions
Satisfy a Linear Finite Difference Equation / 475 \\
\\
XII. Computation by Use of Recurrence Formulas \\
\\
12.1 Introduction / 483 \\
12.2 Homogeneous Difference Equations / 483 \\
12.3 Inhomogeneous Difference Equations / 487 \\
\\
XIII. Some Aspects of Rational and Polynomial
Approximations \\
\\
13.1 Introduction / 490 \\
13.2 Approximations in Series of Chebyshev Polynomials
of the First Kind / 490 \\
13.3 The Pad{\'e} Table / 493 \\
13.4 Approximation of Functions Defined by a
Differential Equation --- The $\tau$-Method / 495 \\
13.5 Approximations of Functions Defined by a Series /
499 \\
13.6 Solution of Differential Equations in Series of
Chebyshev Polynomials of the First Kind / 500 \\
\\
XIV. Miscellaneous Topics \\
\\
14.1 Introduction / 505 \\
14.2 Bernoulli Polynomials and Numbers / 505 \\
14.3 $D$ and $\delta$ Operators / 507 \\
14.4 Computation and Check of the Tables / 509 \\
14.5 Mathematical Constants / 512 \\
14.6 Late Bibliography / 516 \\
\\
Bibliography / 517 \\
\\
Notation Index / 545 \\
\\
Subject Index / 551",
}
@Article{Luke:1975:SRU,
author = "Y. L. Luke",
title = "Some remarks on uniform asymptotic expansions for
{Bessel} functions",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "3--4",
pages = "285--290",
month = "????",
year = "1975",
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fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Book{Masser:1975:EFT,
author = "D. W. Masser",
title = "Elliptic Functions and Transcendence",
volume = "437",
publisher = pub-SV,
address = pub-SV:adr,
pages = "112 (est.)",
year = "1975",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0069432",
ISBN = "3-540-07136-9 (print), 3-540-37410-8 (e-book)",
ISBN-13 = "978-3-540-07136-5 (print), 978-3-540-37410-7
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
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MRclass = "11J81 (14K22; 33E05; 11G15; 11J17; 11-02)",
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https://www.math.utah.edu/pub/tex/bib/lnm1975.bib",
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URL = "http://link.springer.com/book/10.1007/BFb0069432;
http://www.springerlink.com/content/978-3-540-37410-7",
ZMnumber = "0312.10023",
acknowledgement = ack-nhfb,
series-URL = "http://link.springer.com/bookseries/304",
}
@Article{Midy:1975:ICG,
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integral of the second kind in the neighbourhood of $ x
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volume = "25",
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bibdate = "Sun Oct 17 16:12:48 MDT 1999",
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acknowledgement = ack-nhfb,
classification = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Centre de Calcul Paris Sud Informatique, Univ. Paris
XI, Orsay, France",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "elliptic integral; integration; Landen transformation;
second kind",
treatment = "T Theoretical or Mathematical",
}
@Article{Miller:1975:CCN,
author = "Webb Miller",
key = "Miller",
title = "Computational Complexity and Numerical Stability",
journal = j-SIAM-J-COMPUT,
volume = "4",
number = "2",
pages = "97--107",
month = jun,
year = "1975",
CODEN = "SMJCAT",
DOI = "https://doi.org/10.1137/0204009",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
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acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
keywords = "complexity; number of multiplications to evaluate a
polynomial; numerical analysis; rounding error",
}
@TechReport{Morris:1975:LRS,
author = "Robert Morris",
title = "A Library of Reference Standard Mathematical
Subroutines",
type = "Technical Memorandum",
number = "1074 (TM 75-1271-6)",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
pages = "??",
day = "1",
month = may,
year = "1975",
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bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
abstract = "This memo describes a set of mathematical library
functions to use arbitrary accuracy. Relevant error
analysis and subroutines listings are given.",
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author-dates = "Robert Morris (25 July 1932--26 June 2011)",
}
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title = "A Comparison of Computational Methods and Algorithms
for the Complex Gamma Function",
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volume = "1",
number = "1",
pages = "56--70",
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MRclass = "65D20",
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journal-URL = "https://dl.acm.org/loi/toms",
reviewer = "R. H. Bartels",
}
@Article{Oliver:1975:SME,
author = "J. Oliver",
title = "Stable methods for evaluating the points $ \cos (i \pi
/ n) $",
journal = j-J-INST-MATH-APPL,
volume = "16",
number = "2",
pages = "247--257",
month = oct,
year = "1975",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/16.2.247",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65D05",
MRnumber = "52 #12292 (391471)",
MRreviewer = "C. W. Clenshaw",
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reviewer-dates = "Charles William Clenshaw (15 March 1926--23
September 2004)",
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@Article{Prince:1975:AAF,
author = "P. J. Prince",
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Series Approximations",
journal = j-TOMS,
volume = "1",
number = "4",
pages = "372--379",
month = dec,
year = "1975",
CODEN = "ACMSCU",
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ISSN = "0098-3500 (print), 1557-7295 (electronic)",
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@Article{Rudnicki-Bujnowski:1975:EFC,
author = "Georges Rudnicki-Bujnowski",
title = "Explicit Formulas for {Clebsch--Gordan} Coefficients",
journal = j-COMP-PHYS-COMM,
volume = "10",
number = "4",
pages = "245--250",
month = oct,
year = "1975",
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citedby = "Fullerton:1980:BEM",
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remark = "Fullerton: A PL/I-FORMAC procedure is discussed.",
}
@Article{Skovgaard:1975:RAJ,
author = "Ove Skovgaard",
title = "Remark on ``{Algorithm 332}: {Jacobi} Polynomials''",
journal = j-CACM,
volume = "18",
number = "2",
pages = "116--117",
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:22:18 MST 2001",
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note = "See \cite{Witte:1968:AAJ}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Skovgaard75",
remark = "Fullerton: Modifications to an adjustable-precision
FORTRAN routine.",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Skovgaard75",
}
@Article{Skovgaard:1975:RBF,
author = "Ove Skovgaard",
title = "Remark on ``{Algorithm 236: Bessel Functions of the
First Kind [S17]}''",
journal = j-TOMS,
volume = "1",
number = "3",
pages = "282--284",
month = sep,
year = "1975",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
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acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Temme:1975:NEM,
author = "N. M. Temme",
title = "On the Numerical Evaluation of the Modified {Bessel}
Function of the Third Kind",
journal = j-J-COMPUT-PHYS,
volume = "19",
number = "3",
pages = "324--337",
month = nov,
year = "1975",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(75)90082-0",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 11:20:31 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Temme:1975:UAE,
author = "N. M. Temme",
title = "Uniform asymptotic expansions of the incomplete gamma
functions and the incomplete beta function",
journal = j-MATH-COMPUT,
volume = "29",
number = "132",
pages = "1109--1114",
month = oct,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Appl. Math., Amsterdam, Netherlands",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic expansions; asymptotic series;
complementary error function; function approximation;
incomplete beta function; incomplete gamma functions;
uniform",
treatment = "T Theoretical or Mathematical",
}
@Book{VanBuren:1975:TAS,
author = "A. L. (Arnie Lee) {Van Buren} and others",
title = "Tables of Angular Spheroidal Wave Functions",
publisher = "Naval Research Laboratory",
address = "Washington, DC, USA",
pages = "????",
year = "1975",
LCCN = "QC174.26.W3 T27",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Wave functions; Tables; Spheroidal functions",
tableofcontents = "v. 1. Prolate, m = O \\
v. 2. Oblate, m = O",
}
@TechReport{Warner:1975:PDG,
author = "D. D. Warner",
title = "A partial derivative generator",
type = "Computing Science Technical Report",
number = "28",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
year = "1975",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Theory/auto.diff.bib",
abstract = "A precompiler is described which takes a specification
of a function as input and produces a Fortran
subroutine which will evaluate the component functions
and the corresponding Jacobian. Many of the Fortran
elementary functions are provided, as well as a
facility which allows the user to specify their own
differentiation rules.",
acknowledgement = ack-nhfb,
keywords = "differentiation arithmetic; precompiler.",
referred = "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].",
}
@Article{Assmus:1976:NFS,
author = "E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and
Howard E. Sachar",
title = "A New Form of the Square Root Bound",
journal = j-SIAM-J-APPL-MATH,
volume = "30",
number = "2",
pages = "352--354",
month = mar,
year = "1976",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); C1160
(Combinatorial mathematics)",
corpsource = "Dept. of Math., Lehigh Univ., Bethlehem, PA, USA",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
keywords = "combinatorial mathematics; linear codes; square root
bound; sufficient combinatorial conditions",
treatment = "T Theoretical or Mathematical",
}
@Article{Badhe:1976:NAN,
author = "Sahadeo K. Badhe",
title = "New approximation of the normal distribution
function",
journal = j-COMMUN-STAT-SIMUL-COMPUT,
volume = "5",
number = "4",
pages = "173--176",
year = "1976",
CODEN = "CSSCDB",
DOI = "https://doi.org/10.1080/03610917608812017",
ISSN = "0361-0918",
ISSN-L = "0361-0918",
bibdate = "Sat Jan 30 06:32:08 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Simulation and
Computation",
journal-URL = "http://www.tandfonline.com/loi/lssp20",
}
@Article{Baker:1976:SFB,
author = "P. W. Baker",
title = "Suggestion for a fast binary sine\slash cosine
generator",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "11",
pages = "1134--1136",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674566",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674566",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "$\cos(x)$; $\sin(x)$; elementary function",
}
@Article{Barnett:1976:MRC,
author = "A. R. Barnett",
title = "{RCWFF} --- Modification of the Real {Coulomb}
Wavefunction Program {RCWFN}",
journal = j-COMP-PHYS-COMM,
volume = "11",
number = "1",
pages = "141--142",
month = jan # "\slash " # feb,
year = "1976",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(76)90045-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:24:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Barnett:1976:RMR,
author = "A. R. Barnett",
title = "{RCWFF} --- Modification of the Real {Coulomb}
Wavefunction Program {RCWFN}",
journal = j-COMP-PHYS-COMM,
volume = "11",
number = "1",
pages = "141--142",
month = jan # "\slash " # feb,
year = "1976",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(76)90045-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 06:01:19 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/001046557690045X",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
xxtitle = "{RCWFF} --- a modification of the real {Coulomb}
wavefunction program {RCWFN}",
}
@Article{Blagoveshchenskii:1976:MCM,
author = "Yu V. Blagoveshchenskii and B. A. Popov and G. S.
Tesler",
title = "Methods for computing mutually inverse functions",
journal = j-CYBER,
volume = "11",
number = "2",
pages = "252--256",
month = mar,
year = "1976",
CODEN = "CYBNAW",
DOI = "https://doi.org/10.1007/BF01069867",
ISSN = "0011-4235 (print), 2375-0189 (electronic)",
ISSN-L = "0011-4235",
bibdate = "Tue Jan 24 08:29:23 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/index/10.1007/BF01069867",
acknowledgement = ack-nhfb,
fjournal = "Cybernetics",
journal-URL = "http://link.springer.com/journal/10559",
remark = "Translated from \booktitle{Kibernetika}, No. 2, pp.
69--72, March--April, 1975.",
}
@Article{Blair:1976:RCA,
author = "J. M. Blair and C. A. Edwards and J. H. Johnson",
title = "Rational {Chebyshev} approximations for the inverse of
the error function",
journal = j-MATH-COMPUT,
volume = "30",
number = "136",
pages = "827--830",
month = oct,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Atomic Energy of Canada Ltd., Chalk River Nuclear
Lab., Chalk River, Ont., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Chebyshev approximation; Chebyshev approximations;
error function; inverse; rational",
remark = "Fullerton: With microfiche supplement.",
treatment = "T Theoretical or Mathematical",
}
@Article{Brent:1976:FMP,
author = "Richard P. Brent",
title = "Fast Multiple-Precision Evaluation of Elementary
Functions",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "242--251",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321941.321944",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "68A20 (68A10)",
MRnumber = "52 \#16111",
MRreviewer = "Amnon Barak",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Let $ f(x) $ be one of the usual elementary functions
($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $,
etc.), and let $ M(n) $ be the number of
single-precision operations required to multiply
$n$-bit integers. It is shown that $ f(x) $ can be
evaluated, with relative error $ O(2 - n) $, in $
O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
$, for any floating-point number $x$ (with an $n$-bit
fraction) in a suitable finite interval. From the
Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
that an $n$-bit approximation to $ f(x) $ may be
evaluated in $ O(n \log_(n) \log \log (n)) $
operations. Special cases include the evaluation of
constants such as $ \pi $ $e$, and $ e^\pi $. The
algorithms depend on the theory of elliptic integrals,
using the arithmetic-geometric mean iteration and
ascending Landen transformations.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
classification = "723",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
keywords = "computational complexity; computer arithmetic;
computer programming",
}
@InProceedings{Brent:1976:MPZ,
author = "Richard P. Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
crossref = "Traub:1976:ACC",
pages = "151--176",
year = "1976",
MRclass = "68A20",
MRnumber = "54 \#11843",
MRreviewer = "Claus-Peter Schnorr",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Buschman:1976:IHF,
author = "R. G. Buschman",
title = "Inequalities for Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "30",
number = "134",
pages = "303--305",
month = apr,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
corpsource = "Dept. of Math. and Statistics, Univ. of Guelph,
Guelph, Ont., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; classical orthogonal polynomials;
confluence; dominant diagonal matrix; function;
functions; Gauss' hypergeometric; hypergeometric
functions; Kummer's hypergeometric function; modified
Bessel function; principle",
treatment = "T Theoretical or Mathematical",
}
@Article{Davies:1976:IPS,
author = "M. Davies and B. Dawson",
title = "The incrementation parameter in square root
iteration",
journal = j-J-INST-MATH-APPL,
volume = "17",
number = "2",
pages = "219--223",
year = "1976",
CODEN = "JMTAA8",
ISSN = "0020-2932",
MRclass = "65H05",
MRnumber = "55 #9514",
MRreviewer = "Luciano Biasini",
bibdate = "Fri Apr 5 07:38:01 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0319.65039",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Article{Deuflhard:1976:ASC,
author = "P. Deuflhard",
title = "On Algorithms for the Summation of Certain Special
Functions",
journal = j-COMPUTING,
volume = "17",
number = "1",
pages = "37--48",
month = mar,
year = "1976",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02252258",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:52 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nhfb,
affiliation = "Inst. f{\"u}r Math., Tech. Univ. M{\"u}nchen,
M{\"u}nchen, West Germany",
citedby = "Fullerton:1980:BEM",
classification = "723; 921; B0290B; B0290H; C4110; C4140",
description = "error analysis; linear algebra",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "algorithms; backward error analysis; computer
programming; graph representation; mathematical
techniques; special functions; stability; summation",
remark = "Fullerton: An extension of Clenshaw's summation method
is discussed. Spherical harmonic sums are considered as
a special case.",
}
@TechReport{DiDonato:1976:CIG,
author = "Armido R. DiDonato and R. K. Hageman",
title = "Computation of the incomplete gamma function ratios",
type = "Report",
number = "NSWC/DL TR-3482",
institution = "Naval Surface Weapons Center",
address = "Dahlgren, VA, USA",
pages = "86",
month = apr,
year = "1976",
bibdate = "Mon Jun 03 12:24:32 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://apps.dtic.mil/sti/citations/tr/ADA031812",
acknowledgement = ack-nhfb,
}
@Article{Eckhardt:1976:RAW,
author = "Ulrich Eckhardt",
title = "A Rational Approximation to {Weierstrass}' $ \wp
$-Function",
journal = j-MATH-COMPUT,
volume = "30",
number = "136",
pages = "818--826",
month = oct,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "A0260 (Numerical approximation and analysis); C4130
(Interpolation and function approximation)",
corpsource = "Nuclear Res. Center, Central Inst. for Appl. Math.,
Julich, West Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "equianharmonic; function approximation; rational
approximation; unit period parallelogram; Weierstrass'
elliptic function; Weierstrass' p function",
remark = "Fullerton: A complex FORTRAN algorithm with accuracy
down to $ 10^{-18} $ is given.",
treatment = "T Theoretical or Mathematical",
}
@Article{Ellacott:1976:RCA,
author = "S. Ellacott and Jack Williams",
title = "Rational {Chebyshev} Approximation in the Complex
Plane",
journal = j-SIAM-J-NUMER-ANAL,
volume = "13",
number = "3",
pages = "310--323",
month = jun,
year = "1976",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{elLozy:1976:RAC,
author = "Mohamed el Lozy",
title = "Remark on {``Algorithm 299: Chi-Squared Integral
[S15]''}",
journal = j-TOMS,
volume = "2",
number = "4",
pages = "393--395",
month = dec,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Jul 05 16:47:38 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Hill:1967:ACS,Hill:1985:RCS}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Fettis:1976:CR,
author = "Henry E. Fettis",
title = "Complex Roots of $ \sin z = a z, \cos z = a z $, and $
\cosh z = a z $",
journal = j-MATH-COMPUT,
volume = "30",
number = "135",
pages = "541--545",
month = jul,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "complex roots; cos z=az; cosh z=az; functional
equations; sin z=az",
treatment = "T Theoretical or Mathematical",
}
@Article{Fullerton:1976:AEM,
author = "L. W. Fullerton and G. A. {Rinker, Jr.}",
title = "Accurate and Efficient Methods for the Evaluation of
Vacuum-Polarization Potentials of Order {$ Z \alpha $}
and {$ Z \alpha^2 $}",
journal = j-PHYS-REV-A,
volume = "13",
number = "3",
pages = "1283--1287",
month = mar,
year = "1976",
CODEN = "PLRAAN",
ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
ISSN-L = "1050-2947",
bibdate = "Sat Oct 30 06:32:26 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Physical Review A (Atomic, Molecular, and Optical
Physics)",
journal-URL = "http://pra.aps.org/browse",
remark = "Fullerton: Nine-figure approximations to $ K_n(x) =
\int_1^\infty e^{-x t} t^n (1 / r^3 + 1 / (2 r^5)) (r^2
- 1)^{1 / 2} \, d t $ for $ n = 0, 1, 3 $, and $5$.",
}
@Article{Ikebe:1976:CZB,
author = "Y. Ikebe",
title = "Computing Zeros of {Bessel} and Regular {Coulomb} Wave
Functions and of Their Derivatives by Matrix Theoretic
Approach --- Practical Accuracy Criteria",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "810--810",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Kerridge:1976:YAS,
author = "D. F. Kerridge and G. W. Cook",
title = "Yet Another Series for the Normal Integral",
journal = j-BIOMETRIKA,
volume = "63",
number = "2",
pages = "401--403",
month = aug,
year = "1976",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2335636",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
bibdate = "Sat Jun 21 14:34:06 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315483;
https://www.math.utah.edu/pub/tex/bib/biometrika1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2335636",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://www.jstor.org/journals/00063444.html",
}
@Article{Kononova:1976:CEF,
author = "N. F. Kononova",
title = "The computation of elementary functions by means of
polynomial approximations by the method of {V. K.
Dzjadik}. ({Russian})",
journal = "Vy{\v{c}}isl. Prikl. Mat. (Kiev)",
volume = "29",
pages = "27--39",
year = "1976",
ISSN = "0321-4117",
MRclass = "151. 65D15",
MRnumber = "57 \#18026",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Lentz:1976:GBF,
author = "William J. Lentz",
title = "Generating {Bessel} Functions in {Mie} Scattering
Calculations Using Continued Fractions",
journal = j-APPL-OPTICS,
volume = "15",
number = "3",
pages = "668--671",
month = mar,
year = "1976",
CODEN = "APOPAI",
DOI = "https://doi.org/10.1364/AO.15.000668",
ISSN = "0003-6935",
bibdate = "Sat Oct 30 08:41:40 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A new method of generating the Bessel functions and
ratios of Bessel functions necessary for Mie
calculations is presented. Accuracy is improved while
eliminating the need for extended precision word
lengths or large storage capability. The algorithm uses
a new technique of evaluating continued fractions that
starts at the beginning rather than the tail and has a
built-in error check. The continued fraction
representations for both spherical Bessel functions and
ratios of Bessel functions of consecutive order are
presented.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Applied Optics",
journal-URL = "http://www.osapublishing.org/ao/browse.cfm",
}
@Article{Luke:1976:CER,
author = "Yudell L. Luke",
title = "{Chebyshev} expansions and rational approximations",
journal = j-J-COMPUT-APPL-MATH,
volume = "2",
number = "2",
pages = "85--93",
month = jun,
year = "1976",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:14 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X76900139",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Morris:1976:RDF,
author = "Robert Morris",
title = "Remark on ``{Algorithm 490}: The Dilogarithm Function
of a Real Argument [{S22}]''",
journal = j-TOMS,
volume = "2",
number = "1",
pages = "112--112",
month = mar,
year = "1976",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355666.355680",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Aug 30 00:27:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Ginsberg:1975:AAD}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Paul:1976:SEF,
author = "George Paul and M. Wayne Wilson",
title = "Should the Elementary Function Library Be Incorporated
Into Computer Instruction Sets?",
journal = j-TOMS,
volume = "2",
number = "2",
pages = "132--142",
month = jun,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 00:30:21 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Pike:1976:RIB,
author = "Malcolm C. Pike and Jennie SooHoo and N. E. Bosten",
title = "Remark on {``Algorithm 179: Incomplete Beta Ratio
[S14]''}",
journal = j-TOMS,
volume = "2",
number = "2",
pages = "207--208",
month = jun,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Jul 05 16:45:39 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Ludwig:1963:AIB,Bosten:1974:RAI}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Pomeranz:1976:REC,
author = "J. Pomeranz",
title = "Remark on ``{Algorithm 487: Exact Cumulative
Distribution of the Kolmogorov--Smirnov Statistic for
Small Samples [S14]}''",
journal = j-TOMS,
volume = "2",
number = "1",
pages = "111--111",
month = mar,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Feb 06 05:28:05 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Pomeranz:1974:AAE}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Redding:1976:CPC,
author = "R. W. Redding and W. P. Latham",
title = "On the calculation of the parabolic cylinder
functions. {II}. {The} function {$ V(a, x) $}",
journal = j-J-COMPUT-PHYS,
volume = "20",
number = "2",
pages = "256--258",
month = feb,
year = "1976",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(76)90071-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:20 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999176900711",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Salamin:1976:CUA,
author = "Eugene Salamin",
title = "Computation of $ \pi $ Using Arithmetic-Geometric
Mean",
journal = j-MATH-COMPUT,
volume = "30",
number = "135",
pages = "565--570",
month = jul,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Charles Stark Draper Lab., Cambridge, MA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "arithmetic geometric mean; convergence; elliptic
integrals; error analysis; fast Fourier transform
multiplication; function evaluation; Landen's;
Legendre's relation; numerical computation of pi;
transformation",
remark = "Fullerton: A quadratically convergent algorithm.",
treatment = "A Application; T Theoretical or Mathematical",
}
@InCollection{Salimov:1976:OCE,
author = "F. I. Salimov",
booktitle = "Probabilistic methods and cybernetics",
title = "The organization of calculations of elementary
functions into tables. ({Russian})",
volume = "12--13",
publisher = "Kazan University",
address = "Kazan, USSR",
pages = "77--90",
year = "1976",
MRclass = "65A05",
MRnumber = "58 \#31706",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Schett:1976:PTS,
author = "Alois Schett",
title = "Properties of the {Taylor} series expansion
coefficients of the {Jacobian} elliptic functions",
journal = j-MATH-COMPUT,
volume = "30",
number = "133",
pages = "143--147",
month = jan,
year = "1976",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290P (Differential equations); C4170 (Differential
equations)",
corpsource = "CENS, Gif-sur-Yvette, France",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "differential equations; Jacobian elliptic functions;
randomisation distributions; series (mathematics);
Taylor series expansion",
remark = "Fullerton: The first several coefficients are
tabulated.",
treatment = "T Theoretical or Mathematical",
}
@Article{Schonfelder:1976:PSF,
author = "J. L. Schonfelder",
title = "The Production of Special Function Routines for a
Multi-Machine Library",
journal = j-SPE,
volume = "6",
number = "1",
pages = "71--82",
month = jan # "\slash " # mar,
year = "1976",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
remark = "Fullerton: The design of transportable routines for
the NAG library is discussed.",
}
@Article{Schulten:1976:REC,
author = "K. Schulten and R. G. Gordon",
title = "Recursive Evaluation of $ 3 j $ and $ 6 j $
Coefficients",
journal = j-COMP-PHYS-COMM,
volume = "11",
number = "2",
pages = "269--278",
month = mar # "\slash " # may,
year = "1976",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(76)90058-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:32:44 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Shanks:1976:TER,
author = "D. Shanks",
title = "Table errata: {``Regular continued fractions for $ \pi
$ and $ \gamma $'', (Math. Comp. {\bf 25} (1971), 403);
``Rational approximations to $ \pi $'' (ibid. {\bf 25}
(1971), 387--392) by K. Y. Choong, D. E. Daykin and C.
R. Rathbone}",
journal = j-MATH-COMPUT,
volume = "30",
number = "134",
pages = "381--381",
year = "1976",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1976-0386215-4",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05 (10-04 10F20)",
MRnumber = "0386215 (52 \#7073)",
bibdate = "Wed Jan 14 13:22:34 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://www.ams.org/journals/mcom/1976-30-134/S0025-5718-1976-0386215-4",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "The second paper in the title is actually a review of
a report containing table of partial quotients for a
simple continued fraction for $ \pi $.",
}
@Article{Sheorey:1976:DCE,
author = "V. B. Sheorey",
title = "Double {Chebyshev} Expansions for Wave Functions",
journal = j-COMP-PHYS-COMM,
volume = "12",
number = "2",
pages = "125--134",
month = nov,
year = "1976",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(76)90061-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:38:43 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465576900618",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Siemieniuch:1976:PCR,
author = "J. L. Siemieniuch",
title = "Properties of certain rational approximations to $
e^{-z} $",
journal = j-BIT,
volume = "16",
number = "2",
pages = "172--191",
month = jun,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01931369",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=172",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "elefunt; elementary functions",
}
@Article{Stegun:1976:ACM,
author = "I. A. Stegun and R. Zucker",
title = "Automatic Computing Methods for Special Functions.
{Part III}. {The} Sine, Cosine, Exponential Integrals,
and Related Functions",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "80B",
number = "2",
pages = "291--311",
month = apr,
year = "1976",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 11:07:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Adjustable double precision FORTRAN.
routines for $ \operatorname {Si} $, $ \operatorname
{Ci} $, $ \operatorname {Ei} $, $ \operatorname {Shi}
$, and $ \operatorname {Chi} $.",
}
@Article{Temme:1976:NEO,
author = "Nico M. Temme",
title = "On the numerical evaluation of the ordinary {Bessel}
function of the second kind",
journal = j-J-COMPUT-PHYS,
volume = "21",
number = "3",
pages = "343--350",
month = jul,
year = "1976",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(76)90032-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:21 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999176900322",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Tugov:1976:MCA,
author = "I. I. Tugov and Yu. L. Shitkov",
title = "A Method of Calculating the {Appell} Functions $
{F}_a(\alpha; \beta, \beta '; \gamma; x, y) $",
journal = j-USSR-COMP-MATH-MATH-PHYS,
volume = "16",
number = "6",
pages = "1587--1590",
year = "1976",
CODEN = "CMMPA9",
ISSN = "0041-5553, 0502-9902",
ISSN-L = "0041-5553",
bibdate = "Sat Oct 30 11:38:05 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "U.S.S.R. Computational Mathematics and Mathematical
Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00415553",
remark = "Fullerton: [English] translation of Russian-language
Zhurnal Vychislitel'noi Matematikii Matemancheskoi
Fiziki (1976).",
}
@Article{Alexander:1977:SRR,
author = "V. L. Alexander",
title = "Square Root Routine",
journal = j-IBM-TDB,
volume = "20",
number = "3",
pages = "1222",
month = aug,
year = "1977",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Amos:1977:ACS,
author = "D. E. Amos and S. L. Daniel and M. K. Weston",
title = "{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and
{JBESS} for {Bessel} Functions {$ I_\nu (x) $} and {$
J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $} [{S18}]",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "93--95",
month = mar,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355719.355727",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Apr 29 15:14:12 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See erratum \cite{Amos:1978:ECS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Amos:1977:CSI,
author = "D. E. Amos and S. L. Daniel and M. K. Weston",
title = "{CDC} 6600 Subroutines {IBESS} and {JBESS} for
{Bessel} Functions {$ I_\nu (x) $} and {$ J_\nu (x) $},
{$ x \ge 0, \nu \ge 0 $}",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "76--92",
month = mar,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355719.355726",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20",
MRnumber = "55 #6781",
bibdate = "Tue Sep 06 19:20:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
reviewer = "Sven-{\AA}ke Gustafson",
}
@Article{Ardill:1977:BFC,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "The {Bessel} Functions {$ J_0 $} and {$ J_1 $} of
Complex Argument",
journal = j-COMP-PHYS-COMM,
volume = "13",
number = "1",
pages = "17--24",
month = may,
year = "1977",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(77)90023-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:19:09 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465577900236",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Manual{Arnold:1977:SMF,
author = "Mark G. Arnold",
title = "{SCELBAL} Mathematical Functions Supplement
(8008\slash 8080)",
organization = "Scelbi Computer Consulting. Inc.",
address = "1322 Rear --- Boston Post Road, Milford, CT 0646,
USA",
pages = "31",
year = "1977",
bibdate = "Fri Dec 01 16:04:29 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.scelbi.com/files/docs/scelbal/SCELBAL%20Mathematical%20Functions%20Supplement.pdf",
acknowledgement = ack-nhfb,
remark = "Brief description of implementations of cos, sin, exp,
log, and atn functions.",
}
@Book{Brezinski:1977:ACA,
author = "Claude Brezinski",
title = "Acc{\'e}l{\'e}ration de la convergence en analyse
num{\'e}rique. ({French}) [{Convergence} acceleration
in numerical analysis]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "313",
year = "1977",
ISBN = "0-387-08241-7, 3-540-08241-7",
ISBN-13 = "978-0-387-08241-7, 978-3-540-08241-5",
LCCN = "????",
bibdate = "Thu Dec 1 10:17:17 MST 2011",
bibsource = "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
language = "French",
}
@Article{Carlson:1977:EIF,
author = "B. C. Carlson",
title = "Elliptic Integrals of the First Kind",
journal = j-SIAM-J-MATH-ANA,
volume = "8",
number = "2",
pages = "231--242",
month = "????",
year = "1977",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRnumber = "MR 0430341 (55:3346)",
bibdate = "Fri Oct 29 22:03:28 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Book{Carlson:1977:SFA,
author = "Bille Chandler Carlson",
title = "Special Functions of Applied Mathematics",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 335",
year = "1977",
ISBN = "0-12-160150-1",
ISBN-13 = "978-0-12-160150-8",
LCCN = "QA351 .C32",
bibdate = "Fri Jan 22 10:33:57 MST 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Functions, Special",
}
@Article{Cody:1977:CRF,
author = "W. J. Cody and Rose M. Motley and L. Wayne Fullerton",
title = "The Computation of Real Fractional Order {Bessel}
Functions of the Second Kind",
journal = j-TOMS,
volume = "3",
number = "3",
pages = "232--239",
month = sep,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355744.355747",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Sep 20 18:24:22 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Danilcenko:1977:ETC,
author = "L. S. Danil'{\v{c}}enko",
title = "An efficient technique for the construction of
rational approximations of elementary functions.
({Russian}) Optimization of computations (approximation
and minimization of functions)",
journal = "Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint",
volume = "18",
pages = "17--21",
year = "1977",
MRclass = "65D15",
MRnumber = "80b:65016",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{deAPMartins:1977:DSB,
author = "Pedro {de A.P.Martins}",
title = "Determination of spherical {Bessel} functions of an
order larger than the argument",
journal = j-J-COMPUT-PHYS,
volume = "25",
number = "2",
pages = "194--198",
month = oct,
year = "1977",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(77)90021-3",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999177900213",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
xxtitle = "Determination of spherical {Bessel}'s functions of an
order larger than the argument",
}
@Article{Derenzo:1977:AHC,
author = "Stephen E. Derenzo",
title = "Approximations for Hand Calculators Using Small
Integer Coefficients",
journal = j-MATH-COMPUT,
volume = "31",
number = "137",
pages = "214--222",
month = jan,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "B0290D (Functional analysis); B0290F (Interpolation
and function approximation); C4120 (Functional
analysis); C4130 (Interpolation and function
approximation); C7310 (Mathematics computing)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximations; function approximation; function
evaluation; hand calculators; programmable calculators;
small integer coefficients",
treatment = "A Application; T Theoretical or Mathematical",
}
@TechReport{DiDonato:1977:CPP,
author = "Armido R. DiDonato and R. K. Hageman",
title = "Computation of the percentage points of the chi-square
distribution",
type = "Report",
number = "NSWC/DL TR-3569",
institution = "Naval Surface Weapons Center",
address = "Dahlgren, VA, USA",
pages = "200",
year = "1977",
bibdate = "Mon Jun 03 12:24:32 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://apps.dtic.mil/sti/pdfs/ADA043997.pdf",
acknowledgement = ack-nhfb,
}
@Article{Dijkstra:1977:CFE,
author = "D. Dijkstra",
title = "A continued fraction expansion for a generalization of
{Dawson}'s integral",
journal = j-MATH-COMPUT,
volume = "31",
number = "138",
pages = "503--510",
month = apr,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4110 (Error analysis in numerical methods); C4120
(Functional analysis); C4160 (Numerical integration and
differentiation)",
corpsource = "Dept. of Math., Tech. Univ. Twente, Enschede,
Netherlands",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "confluent hypergeometric; continued fraction
expansion; Dawson's; error analysis; function; function
evaluation; generalization; integral; integration;
truncation error",
remark = "Fullerton: An expansion for $ F(p, x) = e^{-x^2}
\int_0^x e^{t^2} \, d t $ is given.",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Dzjadyk:1977:TPA,
author = "V. K. Dzjadyk and S. F. Karpenko",
title = "Tables of polynomials for the approximate solution of
elementary functions. ({Russian})",
number = "28",
institution = "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
pages = "28",
year = "1977",
MRclass = "65A05 (65D20)",
MRnumber = "58 \#19016",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@TechReport{Dzyadyk:1977:OPM,
author = "V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko
and N. F. Kononova",
title = "{{\cyr Ob {\`e}ffektivnom priblizhenii mnogochlenami
{\`e}lementarnykh funktsi{\u\i}.}} ({Russian})
[Efficient approximation by polynomials of elementary
functions]",
type = "Preprint",
number = "IM-77-21",
institution = "Akad. Nauk Ukrain. SSR Inst. Mat.",
address = "Kiev, USSR",
pages = "42",
year = "1977",
MRclass = "65L99",
MRnumber = "57 \#11075",
MRreviewer = "B. D. Donevski",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Eckhardt:1977:RAW,
author = "Ulrich Eckhardt",
title = "A rational approximation to {Weierstrass}' elliptic
function. {II}. {The} lemniscatic case",
journal = j-COMPUTING,
volume = "18",
number = "4",
pages = "341--349",
year = "1977",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:53 MST 2001",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nhfb,
affiliation = "Zentralinst. f{\"u}r Angewandte Math., Julich, West
Germany",
citedby = "Fullerton:1980:BEM",
classification = "C4130",
description = "function approximation",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "elliptic functions; lemniscatic case; rational
approximation; Weierstrass elliptic function",
remark = "Fullerton: Weierstrass' function and its derivative
are approximated in the complex plane to 16 S.",
}
@Article{Egbert:1977:PCAa,
author = "W. E. Egbert",
title = "Personal calculator algorithms. {I}. Square roots",
journal = j-HEWLETT-PACKARD-J,
volume = "28",
number = "9",
pages = "22--23",
month = may,
year = "1977",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Tue Mar 25 14:12:15 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5420 (Mainframes and minicomputers); C7310
(Mathematics computing)",
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
keywords = "electronic calculators; HP personal calculator; square
root algorithm",
treatment = "A Application; T Theoretical or Mathematical",
xxpages = "22--24",
}
@Article{Ercegovac:1977:GHO,
author = "Milo{\v{s}} D. Ercegovac",
title = "A General Hardware-Oriented Method for Evaluation of
Functions and Computations in a Digital Computer",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "667--680",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674900",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674900",
abstract = "A parallel computational method, amenable for
efficient hardware-level implementation, is described.
It provides a simple and fast algorithm for the
evaluation of polynomials, certain rational functions
and arithmetic expressions, solving a class of systems
of linear equations, or performing the basic arithmetic
operations in a fixed-point number representation
system. The time required to perform the computation is
of the order of $m$ carry-free addition operations, $m$
being the number of digits in the solution. In
particular, the method is suitable for fast evaluation
of mathematical functions in hardware.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Arithmetic expressions; digital computer arithmetic;
E-method; evaluation of real-valued functions;
fixed-point representation; hardware-level
implementation; integral powers; linear systems;
on-line algorithms; parallel computation; polynomials;
rational functions; redundant number systems",
}
@TechReport{Fox:1977:PMS,
author = "P. A. Fox and A. D. Hall and N. L. Schryer",
title = "The {PORT} Mathematical Subroutine Library",
type = "Computing Science Technical Report",
number = "47",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
pages = "ii + 50",
day = "22",
month = mar,
year = "1977",
bibdate = "Fri Sep 01 09:08:27 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
URL = "http://history.siam.org/%5C/sup/Fox_bell_subroutine.pdf",
abstract = "The development at Bell Laboratories of PORT, a
library of portable Fortran programs for numerical
computation, is discussed.\par
Portability is achieved by careful language
specification, together with the key technique of
specifying computer classes by means of pre-defined
machine constants.\par
The library is built around an automatic error-handling
facility and a dynamic storage allocation scheme, both
of which are implemented portably. These, together with
the modular structure of the library, lead to
simplified calling sequences and ease of use.",
acknowledgement = ack-nhfb,
remark = "May 1977 revision of version of September 1976.",
tableofcontents = "Part 1: Description \\
Part 2: Utility program listings: \\
Machine constants \\
Error handling \\
Stack allocation",
}
@InProceedings{Fullerton:1977:PSF,
author = "L. W. Fullerton",
title = "Portable Special Function Routines",
crossref = "Cowell:1977:PMS",
pages = "452--483",
year = "1977",
bibdate = "Sat Oct 30 06:40:00 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Gautschi:1977:ACC,
author = "Walter Gautschi",
title = "Anomalous convergence of a continued fraction for
ratios of {Kummer} functions",
journal = j-MATH-COMPUT,
volume = "31",
number = "140",
pages = "994--999",
month = oct,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1120 (Mathematical analysis); C4170 (Differential
equations)",
corpsource = "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "apparent; Bessel functions; continued fraction;
convergence; differential equations; gamma functions;
Kummer functions; wrong limit",
treatment = "T Theoretical or Mathematical",
}
@Article{Gautschi:1977:ERI,
author = "Walter Gautschi",
title = "Evaluation of Repeated Integrals of the Coerror
Function",
journal = j-TOMS,
volume = "3",
number = "3",
pages = "240--252",
month = sep,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355744.355748",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 22:26:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
remark = "Fullerton: An arbitrary-accuracy method for evaluating
$ i^n \erfc (x) $ is given.",
}
@Article{Harris:1977:CAT,
author = "F. E. Harris",
title = "Convergence acceleration technique for lattice sums
arising in electronic-structure studies of crystalline
solids",
journal = j-J-MATH-PHYS,
volume = "18",
number = "12",
pages = "2377--2381",
month = dec,
year = "1977",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Jan 2 14:59:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "A0260 (Numerical approximation and analysis); A6150L
(Crystal binding)",
corpsource = "Dept. of Chem., Univ. of Hawaii, Honolulu, HI, USA",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "convergence acceleration; convergence of numerical
methods; crystalline solids; electronic structure;
Laplace transform; Laplace transforms; lattice energy;
lattice sums; Poisson's summation formula",
pubcountry = "USA",
treatment = "T Theoretical or Mathematical",
}
@Book{Henrici:1977:ART,
author = "Peter Henrici",
title = "{Analytische Rechenverfahren f{\"u}r den
Taschenrechner HP-25}. ({German}) [{Analytical}
Calculations for the {HP-25} Calculator]",
publisher = "Oldenbourg",
address = "M{\"u}nchen, West Germany",
pages = "280",
year = "1977",
ISBN = "0-471-02938-6",
ISBN-13 = "978-0-471-02938-0",
LCCN = "????",
bibdate = "Mon Jan 28 08:25:06 MST 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "1923--1987",
language = "German",
subject = "Numerische Mathematik; Programmierung <EDV>;
Kleinrechner",
tableofcontents = "Einleitung / 9 \\
Teil I: Zahlentheorie / 13 \\
Primfaktorzerlegung / 14 \\
Euklidscher Algorithmus / 18 \\
Rationale Binomialkoeffizienten / 22 \\
Kettenbruchdarstellungen reeller Zahlen / 28 \\
Genaue Kettenbruchdarstellungen von quadratischen
Irrationalit{\"a}ten / 33 \\
Teil II: Iteration / 39 \\
Iteration / 40 \\
Iteration mit Aitken-Beschleunigung / 45 \\
Aitken--Steffensen-Iteration / 50 \\
Newton-Iteration f{\"u}r Wurzeln komplexer Zahlen / 55
\\
Teil III: Polynome / 61 \\
Der Horner-Algorithmus 6 / 2 \\
Das Newton-Verfahren bei Polynomen / 66 \\
Bernoulli-Verfahren: Eine reelle dominante Nullstelle /
71 \\
Bernoulli-Verfahren: Zwei konjugiert komplexe dominante
Nullstellen / 76 \\
Der Quotienten--Differenzen-Algorithmus / 82 \\
Der Routh-Algorithmus / 87 \\
Der Schur--Cohn-Algorithmus I / 92 \\
Der Schur--Cohn-Algorithmus II / 97 \\
Teil IV: Potenzreihen / 101 \\
Reziproke Potenzreihe / 102 \\
Potenz einer Potenzreihe / 111 \\
Exponentiation einer Potenzreihe / 118 \\
Teil V: Integration / 123 \\
Numerische Integration mit Schrittverfeinerung / 124
\\
Der Romberg-Algorithmus / 129 \\
Die Planasche Summationsformel / 136 \\
Eine Differentialgleichung erster Ordnung: Trapezregel
/ 143 \\
Autonome Differentialgleichung zweiter Ordnung ohne
erste Ableitung / 150 \\
Lineare Differentialgleichung zweiter Ordnung / 155 \\
Teil VI: Spezielle Konstanten und Funktionen / 161 \\
Log-Arcsinus-Algorithmus / 162 \\
Die Gamma-Funktion / 167 \\
Unvollst{\"a}ndige Gamma-Funktion / 174 \\
Die Fehlerfunktion / 181 \\
Vollst{\"a}ndige elliptische Integrale / 187 \\
Besselfunktionen ganzzahliger Ordnung / 191 \\
Besselfunktionen beliebiger Ordnung / 196 \\
Besselfunktionen: Asymptotische Reihe / 201 \\
Die Riemannsche Zetafunktion auf der kritischen Geraden
/ 207 \\
Stichwortverzeichnis / 213",
}
@Book{Higgins:1977:CBP,
author = "John Rowland Higgins",
title = "Completeness and basis properties of sets of special
functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 134",
year = "1977",
ISBN = "0-521-21376-2 (hardcover), 0-521-60488-5 (paperback)",
ISBN-13 = "978-0-521-21376-9 (hardcover), 978-0-521-60488-8
(paperback)",
LCCN = "????",
bibdate = "Sat Oct 30 16:52:55 MDT 2010",
bibsource = "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1977:AIB,
author = "G. W. Hill",
title = "{Algorithm 518}: Incomplete {Bessel} Function {$ I_0
$}. {The von Mises} Distribution [{S14}]",
journal = j-TOMS,
volume = "3",
number = "3",
pages = "279--284",
month = sep,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355744.355753",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Oct 24 15:46:06 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
remark = "Fullerton: Adjustable-accuracy 50-statement FORTRAN
subprogram.",
}
@Article{Hinden:1977:PAR,
author = "Harvey J. Hinden",
title = "Phi Again: a Relationship Between the Golden Ratio and
the Limit of a Ratio of Modified {Bessel} Functions",
journal = j-FIB-QUART,
volume = "15",
number = "2",
pages = "112, 152",
month = apr,
year = "1977",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:17 MDT 2011",
bibsource = "http://www.fq.math.ca/15-2.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/15-2/hinden-a.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Ismail:1977:IRC,
author = "Mourad E. H. Ismail",
title = "Integral representations and complete monotonicity of
various quotients of {Bessel} functions",
journal = j-CAN-J-MATH,
volume = "29",
number = "??",
pages = "1198--1207",
month = "????",
year = "1977",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1977-119-5",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:38:50 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v29/;
https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
}
@Article{Jansen:1977:RLF,
author = "J. K. M. Jansen",
title = "Remark on ``{Algorithm 259: Legendre Functions for
Arguments Larger than One}''",
journal = j-TOMS,
volume = "3",
number = "2",
pages = "204--250",
month = jun,
year = "1977",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Feb 06 05:28:08 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gautschi:1965:ALF}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Book{Luke:1977:ACM,
author = "Yudell L. Luke",
title = "Algorithms for the Computation of Mathematical
Functions",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiii + 284",
year = "1977",
ISBN = "0-12-459940-0",
ISBN-13 = "978-0-12-459940-6",
LCCN = "QA351 .L7961",
bibdate = "Wed Dec 15 10:38:19 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / xi \\
1: Basic Formulas / 1 \\
1.1 Introduction / 1 \\
1.2 The Generalized Hypergeometric Function and the
$G$-Function / 1 \\
1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1,
q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev
Polynomials of the First Kind / 4 \\
1.4 Efficient Evaluation of Series of Chebyshev
Polynomials / 17 \\
1.5 Rational Approximations for Generalized
Hypergeometric Functions / 20 \\
1.6 The Pad{\'e} Table / 27 \\
1.7 Computations of and Checks on Coefficients and
Tables / 29 \\
1.8 Tables of the Functions $e^{-\zeta}$, and
$e^{-\xi}$ / 35 \\
2: Identification of Functions / 41 \\
2.1 Introduction / 41 \\
2.2 The Generalized Hypergeometric Function $_pF_q(z)$
/ 41 \\
2.3 The G-Function / 47 \\
2.4 Miscellaneous Functions / 48 \\
3: General Remarks on the Algorithms and Programs / 49
\\
3.1 Introduction / 49 \\
3.2 Precision and Complex Arithmetic / 49 \\
4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\
5: Coefficients for the Expansion of the Confluent
Hypergeometric Function $_1F_1(a;c;z)$ in Ascending
Series of Chebyshev Polynomials / 70 \\
6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\
7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$
in Ascending Series of Chebyshev Polynomials / 82 \\
8: Coefficients for the Expansion of the Confluent
Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$
in Descending Series of Chebyshev Polynomials / 88 \\
9: Coefficients for the Expansion of the Functions
$G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$,
in Descending Series of Chebyshev Polynomials / 101 \\
10: Differential and Integral Properties of Expansions
in Series of Chebyshev Polynomials of the First Kind /
116 \\
11: Expansion of Exponential Type Integrals in Series
of Chebyshev Polynomials of the First Kind / 126 \\
11.1 Introduction / 126 \\
11.2 The Representation for $g(x)$ / 127 \\
11.3 The Representation for $G(x)$ / 129 \\
11.4 Exponential Type Integrals Involving Logarithms /
133 \\
11.5 Numerical Examples / 135 \\
11.6 Errata / 139 \\
12: Conversion of a Power Series into a Series of
Chebyshev Polynomials of the First Kind / 154 \\
13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159
\\
14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174
\\
15: Rational Approximations for $_1F_1(a;c;-z)$ / 182
\\
16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192
\\
17: Rational Approximations for Bessel Functions of the
First Kind / 203 \\
18: Pad{\'e} Approximations for $I_{\nu +
1}(z)/I_\nu(z)$ / 220 \\
19: Evaluation of Bessel Functions of the First Kind by
Use of the Backward Recurrence Formula \\
19.1 Introduction / 230 \\
19.2 Backward Recurrence Schemata for $I_\nu(z)$ and
$J_\nu(z)$ / 230 \\
19.3 Numerical Examples / 240 \\
19.4 Mathematical Description of Programs / 243 \\
19.4.1 Evaluation of Functions Related to $I_{m +
\nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\
19.4.2 Evaluation of Functions Related to $e^{-l}I_{m +
\nu}(z)$ / 245 \\
20: Rational Approximations for $z^aU(a;1 + a - b;z)$ /
252 \\
21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265
\\
Appendices \\
Bibliography / 280 \\
Notation Index / 281 \\
Subject Index / 283",
wrongisbn = "0-12-459940-6",
}
@Article{Marsaglia:1977:SMG,
author = "George Marsaglia",
title = "The squeeze method for generating gamma variates",
journal = j-COMPUT-MATH-APPL,
volume = "3",
number = "4",
pages = "321--325",
year = "1977",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(77)90089-X",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65C10",
MRnumber = "58 \#13613",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
ZMnumber = "0384.65005",
abstract = "This paper describes an exact method for computer
generation of random variables with a gamma
distribution. The method is based on the
Wilson--Hilferty transformation and an improvement on
the rejection technique. The idea is to ``squeeze'' a
target density between two functions, the top one easy
to sample from, the bottom one easy to evaluate.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
ZMclass = "*65C10 Random number generation 60E05 General theory
of probability distributions",
}
@Article{McCarthy:1977:OAE,
author = "D. P. McCarthy",
title = "The optimal algorithm to evaluate $ x^n $ using
elementary multiplication methods",
journal = j-MATH-COMPUT,
volume = "31",
number = "137",
pages = "251--256",
month = jan,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4120 (Functional analysis); C4240 (Programming and
algorithm theory)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computational complexity; function evaluation; optimal
multiplication chains; symbolic algebraic
manipulation",
treatment = "T Theoretical or Mathematical",
}
@Article{Ng:1977:CAL,
author = "E. W. Ng",
title = "Computations and Applications of Linear Hypergeometric
Transformations",
journal = j-COMPUT-MATH-APPL,
volume = "3",
number = "1",
pages = "65--70",
year = "1977",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(77)90115-8",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Sat Oct 30 09:27:55 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Linear transformations are well-known in the theory of
hypergeometric functions. In this note, it is
indicated, both by analyses and by supporting numerical
experiments, how these transformations can be applied
to the computation of Legendre's functions, the
incomplete Beta function, and the variance-ratio
probability distribution function. It is shown that a
simple transformation can in many cases cause dramatic
improvement in computation.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Page:1977:MAC,
author = "E. Page",
title = "Miscellanea: Approximations to the Cumulative Normal
Function and its Inverse for Use on a Pocket
Calculator",
journal = j-APPL-STAT,
volume = "26",
number = "1",
pages = "75--76",
year = "1977",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:21:55 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@Article{Pexton:1977:RTTa,
author = "Robert L. Pexton and Arno D. Steiger",
title = "Roots of two transcendental equations involving
spherical {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "31",
number = "139",
pages = "752--753",
month = jul,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1110 (Algebra)",
corpsource = "Univ. of California, Livermore, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; root; spherical Bessel functions;
transcendental equations",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Randazzo:1977:DFE,
author = "D. J. Randazzo",
booktitle = "Numerical analysis ({Proceedings of the Colloquium,
Lausanne, 1976})",
title = "Data fits with exponential functions",
volume = "37",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "77--94",
year = "1977",
ISBN = "3-7643-0939-3",
ISBN-13 = "978-3-7643-0939-8",
MRclass = "65D15",
MRnumber = "468111",
MRreviewer = "C. W. Clenshaw",
bibdate = "Mon Nov 13 08:14:42 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Internat. Ser. Numer. Math.",
acknowledgement = ack-nhfb,
reviewer-dates = "Charles William Clenshaw (15 March 1926--23
September 2004)",
}
@Article{Schett:1977:RFT,
author = "Alois Schett",
title = "Recurrence formula of the {Taylor} series expansion
coefficients of the {Jacobian} elliptic functions",
journal = j-MATH-COMPUT,
volume = "31",
number = "140",
pages = "1003--1005",
month = oct,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1110 (Algebra)",
corpsource = "CENS, Gif-sur-Yvette, France",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "elliptic functions; functions; Jacobian elliptic;
peak; recurrence formula; run up; Taylor series
expansion coefficients",
treatment = "T Theoretical or Mathematical",
}
@Article{Schindler:1977:CCS,
author = "Susan Schindler and R. Mirman",
title = "The {Clebsch--Gordan} coefficients of {$ S_n $}",
journal = j-J-MATH-PHYS,
volume = "18",
number = "8",
pages = "1697--1704",
month = aug,
year = "1977",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.523470",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Jan 2 14:59:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Ordering schemes for the frames and tableaux of $ S_n
$ are presented, and some results, expressible in terms
of these, are developed. A formula is derived for the
sign function on tableaux. A table of the nonzero
Clebsch--Gordon coefficients for the ''working
triplets'' is given. Methods are described, and a
needed table supplied, for finding the other
coefficients from the tabulated ones. The values are
for $ n = 2, \ldots {}, 6 $, with the coefficients for
$ n = 6 $ relegated to PAPS.",
acknowledgement = ack-nhfb,
classification = "A0365F (Algebraic methods in quantum theory); A1130L
(Other internal and higher symmetries in particle
physics)",
corpsource = "Baruch Coll., City Univ. of New York, NY, USA",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "$S_n$ group; Clebsch Gordan coefficients;
Clebsch--Gordan coefficients; working triplets",
pubcountry = "USA",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Schonfelder:1977:PTS,
author = "J. L. Schonfelder",
title = "The Production and Testing of Special Function
Software in the {NAG} Library",
crossref = "Cowell:1977:PMS",
pages = "425--451",
year = "1977",
bibdate = "Sat Oct 30 10:24:29 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Sharma:1977:GMA,
author = "R. R. Sharma and Bahman Zohuri",
title = "A general method for an accurate evaluation of
exponential integrals {$ E_1 (x), x > 0 $}",
journal = j-J-COMPUT-PHYS,
volume = "25",
number = "2",
pages = "199--204",
month = oct,
year = "1977",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(77)90022-5",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999177900225",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Verma:1977:CSF,
author = "Arun Verma",
title = "Certain summation formulae for basic hypergeometric
series",
journal = j-CAN-MATH-BULL,
volume = "20",
number = "??",
pages = "369--376",
month = "????",
year = "1977",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1977-055-8",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
bibdate = "Thu Sep 8 10:04:41 MDT 2011",
bibsource = "http://cms.math.ca/cmb/v20/;
https://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian mathematical bulletin = Bulletin canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
}
@Article{Amos:1978:ECS,
author = "Donald E. Amos",
title = "Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines
{IBESS} and {JBESS} for {Bessel} Functions {$ I_\nu (x)
$} and {$ J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $}
[{S18}]''",
journal = j-TOMS,
volume = "4",
number = "4",
pages = "411--411",
month = dec,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356502.356501",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Aug 30 00:28:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Amos:1977:ACS}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Andrews:1978:EFM,
author = "M. Andrews and S. F. McCormick and G. D. Taylor",
title = "Evaluation of Functions on Microcomputers: Square
Root",
journal = j-COMPUT-MATH-APPL,
volume = "4",
number = "4",
pages = "359--367",
year = "1978",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:40:29 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@Article{Andrews:1978:UEF,
author = "M. Andrews and T. Mraz",
title = "Unified elementary function generator",
journal = j-MICROPROC-MICROSYS,
volume = "2",
number = "5",
pages = "270--273",
month = oct,
year = "1978",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Ardill:1978:SBF,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "Spherical {Bessel} functions $ j_n $ and $ y_n $ of
integer order and real argument",
journal = j-COMP-PHYS-COMM,
volume = "14",
number = "3--4",
pages = "261--265",
month = may # "\slash " # jun,
year = "1978",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(78)90019-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/001046557890019X",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Benton:1978:CZT,
author = "T. C. Benton and H. D. Knoble",
title = "Common Zeros of Two {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "32",
number = "142",
pages = "533--535",
month = apr,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1110 (Algebra)",
corpsource = "Pennsylvania State Univ., University Park, PA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; common zeros; poles and zeros;
positive zeros; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Blair:1978:RCA,
author = "J. M. Blair and C. A. Edwards and J. H. Johnson",
title = "Rational {Chebyshev} approximations for the {Bickley}
functions {$ K i_n(x) $}",
journal = j-MATH-COMPUT,
volume = "32",
number = "143",
pages = "876--886",
month = jul,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Atomic Energy of Canada Ltd., Chalk River, Ont.,
Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximation; Bessel functions; Bickley functions;
Chebyshev approximation; Chebyshev approximations;
function; recurrence; relation",
remark = "Fullerton: Approximations accurate to 23 digits of
repeated integrals of the Bessel function $ K_0 (x) $
for $ n = 1, 2, \ldots {}, 10 $.",
treatment = "T Theoretical or Mathematical",
}
@Article{Bowman:1978:ASS,
author = "K. O. Bowman and L. R. Shenton",
title = "Asymptotic series and {Stieltjes} continued fractions
for a gamma function ratio",
journal = j-J-COMPUT-APPL-MATH,
volume = "4",
number = "2",
pages = "105--111",
month = jun,
year = "1978",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:17 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X78900347",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Book{Brezinski:1978:AAC,
author = "Claude Brezinski",
title = "Algorithmes d'acc{\'e}l{\'e}ration de la convergence:
{\'e}tude num{\'e}rique. ({French}) [Algorithms for
convergence acceleration: numerical study]",
publisher = "{\'E}ditions Technip",
address = "Paris, France",
pages = "xi + 392",
year = "1978",
ISBN = "2-7108-0341-0 (paperback)",
ISBN-13 = "978-2-7108-0341-6 (paperback)",
LCCN = "????",
bibdate = "Thu Dec 1 10:20:23 MST 2011",
bibsource = "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
language = "French",
}
@Article{Brezinski:1978:CAS,
author = "C. Brezinski",
title = "Convergence acceleration of some sequences by the $
\epsilon $-algorithm",
journal = j-NUM-MATH,
volume = "29",
number = "2",
pages = "173--177",
month = jan,
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra)",
corpsource = "UER d'IEEA-Informatique, Univ. de Lille I, Villeneuve
d'Ascq, France",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "acceleration; converge; convergence acceleration;
convergence of numerical methods; epsilon-algorithm;
sequences",
treatment = "T Theoretical or Mathematical",
}
@Article{Brezinski:1978:SCA,
author = "C. Brezinski",
title = "Survey on convergence acceleration methods in
numerical analysis",
journal = j-MATH-STUDENT,
volume = "46",
number = "1",
pages = "28--41 (1979)",
year = "1978",
CODEN = "MTHSBH",
ISSN = "0025-5742",
MRclass = "65B99",
MRnumber = "698176 (84d:65003)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematics Student",
keywords = "convergence acceleration",
}
@Article{Chin:1978:DAD,
author = "R. C. Y. Chin and G. W. Hedstrom",
title = "A dispersion analysis for difference schemes: tables
of generalized {Airy} functions",
journal = j-MATH-COMPUT,
volume = "32",
number = "144",
pages = "1163--1170",
month = oct,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation);
C4170 (Differential equations)",
corpsource = "Univ. of California, Lawrence Livermore Lab.,
Livermore, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "artificial viscosity; difference schemes; dispersion
analysis; function approximation; functions;
generalized Airy; linear hyperbolic equation",
treatment = "T Theoretical or Mathematical",
}
@Article{Coleman:1978:RSN,
author = "John P. Coleman",
title = "Remark on {``Algorithm 49: Spherical Neumann
Function''}",
journal = j-TOMS,
volume = "4",
number = "3",
pages = "295--295",
month = sep,
year = "1978",
CODEN = "ACMSCU",
ISSN = "0098-3500",
bibdate = "Sat Jul 05 16:48:40 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Herndon:1961:ASN}.",
acknowledgement = ack-nhfb,
keywords = "Neumann functions; special functions",
}
@Article{DiDonato:1978:AR,
author = "A. R. DiDonato",
title = "An Approximation for $ \int^\infty_x e^{-t^2 / 2} t^p
d t, x > 0, p $ Real",
journal = j-MATH-COMPUT,
volume = "32",
number = "141",
pages = "271--275",
month = jan,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation)",
corpsource = "Naval Surface Weapons Center, Dahlgren, VA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "integral approximation; integration; numerical
analysis",
remark = "Fullerton: Closely related to the complementary
incomplete gamma function.",
treatment = "A Application; N New Development; T Theoretical or
Mathematical",
}
@Article{Drezner:1978:CBN,
author = "Z. Drezner",
title = "Computation of the Bivariate Normal Integral",
journal = j-MATH-COMPUT,
volume = "32",
number = "141",
pages = "277--279",
month = jan,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Faculty of Business, McMaster Univ., Hamilton, Ont.,
Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "bivariate normal integral; computation; Gauss
quadrature method; integration; numerical analysis",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Dzjadyk:1978:CRP,
author = "V. K. Dzjadyk and L. {\=I}. F{\'\i}lozof",
title = "The convergence rate of {Pad{\'e}} approximants for
some elementary functions. ({Russian})",
journal = "Mat. Sb. (N.S.)",
volume = "107(149)",
number = "3",
pages = "347--363, 463",
year = "1978",
ISSN = "0368-8666",
MRclass = "41A21 (30E10 41A25)",
MRnumber = "81b:41043",
MRreviewer = "B. D. Donevski",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@InProceedings{Ercegovac:1978:LSR,
author = "Milo{\v{s}} D. Ercegovac",
title = "An On-Line Square Rooting Algorithm",
crossref = "IEEE:1978:PSC",
pages = "183--189",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
abstract = "An on-line algorithm for computing square roots in a
radix 2, normalized floating-point number system with
the redundant digit set $ \{ - 1, 0, 1 \} $ is
described. The algorithm has on-line delay of one and
it is amenable for modular implementation. A systematic
approach, used in deriving this algorithm, is presented
in detail.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Book{Feinsilver:1978:SFP,
author = "Philip J. (Philip Joel) Feinsilver",
title = "Special functions, probability semigroups, and
{Hamiltonian} flows",
volume = "696",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 112",
year = "1978",
ISBN = "0-387-09100-9",
ISBN-13 = "978-0-387-09100-6",
LCCN = "QA3 .L28 no. 696; QA273",
bibdate = "Sat Oct 30 19:22:05 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Lecture notes in mathematics",
acknowledgement = ack-nhfb,
subject = "probabilities; semigroups; functions, special;
Hamiltonian systems",
}
@InProceedings{Frankowski:1978:RME,
author = "Krzysztof S. Frankowski",
title = "A Realistic Model for Error Estimates in the
Evaluation of Elementary Functions",
crossref = "IEEE:1978:PSC",
pages = "70--74",
year = "1978",
MRclass = "65G05 (65D20)",
MRnumber = "80g:65050",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gautschi:1978:CMB,
author = "Walter Gautschi and Josef Slavik",
title = "On the computation of modified {Bessel} function
ratios",
journal = j-MATH-COMPUT,
volume = "32",
number = "143",
pages = "865--875",
month = jul,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1120 (Mathematical analysis); C4130 (Interpolation
and function approximation)",
corpsource = "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel; Bessel functions; continued fraction;
fraction; function approximation; functions; Gauss'
continued; modified Bessel function ratios; Perron's
continued fraction",
treatment = "T Theoretical or Mathematical",
}
@Article{Gustafson:1978:ATC,
author = "S.-{\AA}. Gustafson",
title = "Algorithm $ 38 $. {Two} computer codes for convergence
acceleration",
journal = j-COMPUTING,
volume = "21",
number = "1",
pages = "87--91",
year = "1978",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65B10",
MRnumber = "83a:65005",
bibdate = "Tue Jan 2 17:40:53 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "Australian Nat. Univ., Canberra, ACT, Australia",
classification = "723; C4140",
description = "convergence of numerical methods",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "codes, symbolic; convergence acceleration; power
series sum",
}
@Article{Gustafson:1978:CAG,
author = "S.-{\AA}. Gustafson",
title = "Convergence acceleration on a general class of power
series",
journal = j-COMPUTING,
volume = "21",
number = "1",
pages = "53--69",
year = "1978",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65B10 (40A05)",
MRnumber = "83m:65005",
MRreviewer = "A. M. Cohen",
bibdate = "Tue Jan 2 17:40:53 MST 2001",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "Australian Nat. Univ., Canberra, ACT, Australia",
classification = "C4120",
description = "convergence of numerical methods; function
evaluation",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "algorithms; convergence acceleration; power series",
}
@Article{Hamaker:1978:MAC,
author = "Hugo C. Hamaker",
title = "Miscellanea: Approximating the Cumulative Normal
Distribution and its Inverse",
journal = j-APPL-STAT,
volume = "27",
number = "1",
pages = "76--77",
month = jan,
year = "1978",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:22:12 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@InProceedings{Hull:1978:DFP,
author = "T. E. Hull",
title = "Desirable Floating-Point Arithmetic and Elementary
Functions for Numerical Computation",
crossref = "IEEE:1978:PSC",
pages = "63--69",
year = "1978",
bibdate = "Thu Sep 01 12:14:34 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Katholi:1978:CVP,
author = "Charles R. Katholi",
title = "On the computation of values of the psi function from
rapidly converging power series expansions",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "8",
number = "1",
pages = "25--42",
year = "1978",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657808810245",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:10:43 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Ling:1978:EWZ,
author = "Chin-Bing Ling",
title = "Evaluation of {Weierstrass} Zeta Functions",
journal = j-SIAM-REVIEW,
volume = "20",
number = "1",
pages = "183--183",
month = "????",
year = "1978",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1020017",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:52:48 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/20/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1978",
}
@Article{Morita:1978:CCE,
author = "T. Morita",
title = "Calculation of the complete elliptic integrals with
complex modulus",
journal = j-NUM-MATH,
volume = "29",
number = "2",
pages = "233--236",
month = jan,
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classification = "C4160 (Numerical integration and differentiation)",
corpsource = "Dept. of Appl. Sci., Faculty of Engng., Tohoku Univ.,
Sendai, Japan",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "complete elliptic integrals; complex modulus;
integration",
remark = "Fullerton: Addendum to a paper by Morita and
Horiguchi.",
treatment = "T Theoretical or Mathematical",
}
@Article{Pexton:1978:RTT,
author = "Robert L. Pexton and Arno D. Steiger",
title = "Roots of two transcendental equations as functions of
a continuous real parameter",
journal = j-MATH-COMPUT,
volume = "32",
number = "142",
pages = "511--518",
month = apr,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1110 (Algebra)",
corpsource = "Lawrence Livermore Lab., Univ. of California,
Livermore, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "continuous real parameter; equations; roots; spherical
Bessel functions; transcendental equations",
treatment = "T Theoretical or Mathematical",
}
@Article{Preston:1978:NAT,
author = "F. S. Preston",
title = "A New Algorithm for the Tangent",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "2",
pages = "167--167",
month = feb,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675052",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:26 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675052",
abstract = "A new mathematical algorithm has been developed for
the tangent. The form of the equation guarantees that
the error is zero at $ 0^\circ $, $ 45^\circ $, and $
90^\circ $ corresponding to tangents of $0$, $1$, and
infinity. With only one constant the error is brought
to zero at two more points and the maximum error is
less than one part in $ 3000 $. By adding a second
constant, the error is reduced to less than one in $
720 \, 000 $. Further terms improve the accuracy
geometrically.",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Schindler:1978:GCG,
author = "Susan Schindler and R. Mirman",
title = "Generation of the {Clebsch-Gordan} coefficients for {$
S_n $}",
journal = j-COMP-PHYS-COMM,
volume = "15",
number = "1--2",
pages = "131--145",
month = sep,
year = "1978",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(78)90087-5",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sun Oct 31 09:20:58 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Schmidt:1978:EI,
author = "Paul W. Schmidt",
title = "Evaluation of the Integral $ \int^\infty_0 \frac {t^{2
\alpha - 1} J_\nu (x \sqrt {1 + t^2})(1 + t^2)^{\alpha
+ \beta - 1}} d t $",
journal = j-MATH-COMPUT,
volume = "32",
number = "141",
pages = "265--269",
month = jan,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Phys. Dept., Univ. of Missouri, Columbia, MO, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "cylinder diameter distribution; first kind Bessel
function; integral evaluation; integration; long
circular; neutron scattering data; numerical analysis;
power series expansions; recurrence; relations",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Schoene:1978:RMI,
author = "Andrew Y. Schoene",
title = "Remark on ``{Algorithm 435}: Modified Incomplete Gamma
Function [{S14}]''",
journal = j-TOMS,
volume = "4",
number = "3",
pages = "296--304",
month = sep,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355791.355803",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Aug 30 00:28:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Fullerton:1972:MIG}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Schonfelder:1978:CEE,
author = "J. L. Schonfelder",
title = "{Chebyshev} expansions for the error and related
functions",
journal = j-MATH-COMPUT,
volume = "32",
number = "144",
pages = "1232--1240",
month = oct,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4110 (Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
corpsource = "Computer Centre, Univ. of Birmingham, Birmingham, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximations; Chebyshev approximation; Chebyshev
expansions; error analysis; error function; mappings;
NAG library",
remark = "Fullerton: Approximations for $ \erf (x) $, $ \erfc
(x) $, and probability functions $ P(x) $, $ Q(x) $
with accuracy down to $ 10^{-30} $.",
treatment = "T Theoretical or Mathematical",
}
@Article{Skovgaard:1978:RCE,
author = "Ove Skovgaard",
title = "Remark on ``{Algorithm 149: Complete Elliptic Integral
[S21]}''",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "95--95",
month = mar,
year = "1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Feb 06 05:28:13 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Merner:1962:AAC}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Slepian:1978:PSW,
author = "D. Slepian",
title = "Prolate Spheroidal Wave Functions, {Fourier} Analysis,
and Uncertainty --- {V}: The Discrete Case",
journal = j-BELL-SYST-TECH-J,
volume = "57",
number = "5",
pages = "1371--1430",
month = may # "--" # jun,
year = "1978",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:56 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1978/BSTJ.1978.5705.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol57/bstj57-5-1371.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Temme:1978:UAE,
author = "N. M. Temme",
title = "Uniform asymptotic expansions of confluent
hypergeometric functions",
journal = j-J-INST-MATH-APPL,
volume = "22",
number = "2",
pages = "215--223",
year = "1978",
CODEN = "JMTAA8",
ISSN = "0020-2932",
MRclass = "33A30",
MRnumber = "80a:33004",
MRreviewer = "F. W. J. Olver",
bibdate = "Fri Apr 5 05:48:27 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Article{Wang:1978:EPF,
author = "J. Y. Wang",
title = "The Evaluation of Periodic Functions with Large Input
Arguments",
journal = j-SIGNUM,
volume = "13",
number = "4",
pages = "7--8",
month = dec,
year = "1978",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1053412.1053413",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:05 MDT 2005",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
abstract = "The argument reduction scheme plays an important role
in the evaluation of periodic functions. In this report
we discuss the criteria for determining the domain of
computer routines that evaluate periodic functions, and
apply the results to the widely used sine and cosine
functions.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C4120 (Functional analysis); C4240 (Programming and
algorithm theory)",
corpsource = "Appl. Math. Div., Argonne Nat. Lab., Argonne, IL,
USA",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "argument; computational complexity; computer routines;
cosine functions; FORTRAN IV; function evaluation;
large input arguments; periodic functions; reduction
scheme",
remark-1 = "From page 7: ``In this report, we will examine bounds
on the domain that guarantees that the computed
function values retain half of the significant
digits.''",
remark-2 = "From page 8: ``Improvement: \ldots{} this can he
accomplished by storing PI/4 in two words, i.e., PI/4 =
C1 + C2.",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Wang:1978:SMR,
author = "J. Y. Wang and J. Boyer",
title = "A Studv of the Mathematical Routines in the {IBM
System/360 FORTRAN IV} and {FORTRAN IV (Mod II)}
Libraries",
type = "Report",
number = "AMD-TM 304",
institution = "Applied Mathematics Division, Argonne National
Laboratory",
address = "Argonne, IL, USA",
month = jan,
year = "1978",
bibdate = "Fri Sep 20 14:26:48 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Cited in \cite[Reference 8]{Agarwal:1986:NSV} in
elefunt.bib and fparith.bib.",
acknowledgement = ack-nhfb,
}
@Article{Alt:1979:SRD,
author = "H. Alt",
title = "Square Rooting Is as Difficult as Multiplication",
journal = j-COMPUTING,
volume = "21",
number = "3",
pages = "221--232",
month = sep,
year = "1979",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68C25",
MRnumber = "82m:68081",
bibdate = "Tue Jan 2 17:40:54 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Math. \& Information, Univ. of Saarlandes,
Saarbrucken, West Germany",
classification = "723; C5230",
description = "digital arithmetic",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "algorithm; computer programming; square rooting",
}
@Article{Ardill:1979:ABF,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "Accurate {Bessel} functions {$ J_n(z) $}, {$ Y_n(z)
$}, {$ H_n^{(1)}(z) $} and {$ H_n^{(2)}(z) $} of
integer order and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "17",
number = "3",
pages = "321--336",
month = jun,
year = "1979",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(79)90060-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "Fullerton: Description of a program with accuracy
about $ 10^{-10} $.",
}
@Article{Atkins:1979:FSC,
author = "D. E. Atkins",
title = "{Fourth Symposium on Computer Arithmetic}: crunching
with quality and {LSI}",
journal = j-COMPUTER,
volume = "12",
number = "4",
pages = "94--97",
month = apr,
year = "1979",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Thu Dec 12 07:20:54 MST 1996",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Computer arithmetic problems --- faster computation
rates and more efficient representations of real
numbers --- are considered in the paper. Floating-point
arithmetic standardization, novel implementation of
basic arithmetic operators, evaluation of elementary
functions --- these are the main considerations of the
conference review.",
acknowledgement = ack-nhfb,
classification = "722; 723",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabr = "Computer",
keywords = "computer arithmetic; computer systems, digital; data
processing --- data description; mathematical
techniques --- digital arithmetic",
}
@Article{Babb:1979:OEC,
author = "Stanley E. {Babb, Jr.} and James W. Cafky",
title = "Operational evaluation of certain infinite {Bessel}
function integrals",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1033--1039",
month = jul,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "44A99",
MRnumber = "80e:44002",
MRreviewer = "L. Arteaga",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4180 (Integral equations)",
corpsource = "Dept. of Phys. and Astron., Univ. of Oklahoma, Norman,
OK, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel function integral; integration; numerical
methods; Schafheitlin method; trigonometric function;
Weber",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Borjesson:1979:SAE,
author = "P. B{\"o}rjesson and C.-E. Sundberg",
title = "Simple Approximations of the Error Function {$ Q(x) $}
for Communications Applications",
journal = j-IEEE-TRANS-COMM,
volume = "27",
number = "3",
pages = "639--643",
month = mar,
year = "1979",
CODEN = "IECMBT",
DOI = "https://doi.org/10.1109/tcom.1979.1094433",
ISSN = "0090-6778 (print), 1558-0857 (electronic)",
ISSN-L = "0090-6778",
bibdate = "Sat Dec 16 15:29:00 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Communications",
}
@Article{Campbell:1979:BFR,
author = "J. B. Campbell",
title = "{Bessel} functions {$ J_\nu (x) $} and {$ Y_\nu (x) $}
of real order and real argument",
journal = j-COMP-PHYS-COMM,
volume = "18",
number = "1",
pages = "133--142",
month = sep,
year = "1979",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(79)90030-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 06:01:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465579900304",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Carlson:1979:CEI,
author = "B. C. Carlson",
title = "Computing elliptic integrals by duplication",
journal = j-NUM-MATH,
volume = "33",
number = "1",
pages = "1--16",
month = mar,
year = "1979",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D20",
MRnumber = "80h:65008",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Logarithms, arctangents, and elliptic integrals of all
three kinds (including complete integrals) are
evaluated numerically by successive applications of the
duplication theorem. When the convergence is improved
by including a fixed number of terms of Taylor's
series, the error ultimately decreases by a factor of
4096 in each cycle of iteration. Except for Cauchy
principal values there is no separation of cases
according to the values of the variables, and no
serious cancellations occur if the variables are real
and nonnegative. Only rational operations and square
roots are required. An appendix contains a recurrence
relation and two new representations (in terms of
elementary symmetric functions and power sums) for
$R$-polynomials, as well as an upper bound for the
error made in truncating the Taylor series of an
$R$-function.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classification = "C4180 (Integral equations)",
corpsource = "Dept. of Math. and Phys., Iowa Univ., Ames, IA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence; duplication theory; elliptic integral;
integration; numerical methods; R-polynomial; Taylor
series",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Cole:1979:EI,
author = "R. J. Cole and C. Pescatore",
title = "Evaluation of the Integral $ \int_0^\infty t^n \exp (
- t^2 - x / t) \, d t $",
journal = j-J-COMPUT-PHYS,
volume = "32",
number = "2",
pages = "280--287",
month = aug,
year = "1979",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(79)90135-9",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:34 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999179901359",
abstract = "The main purpose of this paper is to provide a unified
approach to the treatment of linear recurrence
relations for single or pairs of order statistics.
Suppose such a relation has been proved in the simplest
case when $ X_1, \ldots {}, X_n $ are independent
variates having an arbitrary absolutely continuous
distribution. It is pointed out that the same relation
continues to hold when the $X$'s are exchangeable,
whether continuous or not. As has recently become well
known, further generalizations are possible when the
$X$'s have any joint distribution. Attention is also
drawn to a useful nonlinear recurrence relation due to
Boncelet (1987).",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Conde:1979:Z,
author = "S. Conde and Shyam L. Kalla",
title = "The $ \nu $-zeros of {$ J_{- \nu }(x) $}",
journal = j-MATH-COMPUT,
volume = "33",
number = "145",
pages = "423--426",
month = jan,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20",
MRnumber = "80b:65021",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4170 (Differential equations); C4190 (Other numerical
methods)",
corpsource = "Facultad de Ingenieria, Univ. del Zulia, Maracaibo,
Venezuela",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel function; boundary value; boundary-value
problems; J/sub -v/(x); partial differential equations;
poles and zeros; problems; transforms; v-zeros",
remark = "Fullerton: With a microfiche supplement.",
treatment = "T Theoretical or Mathematical",
}
@Article{Delic:1979:CSS,
author = "G. Delic",
title = "{Chebyshev} series for the spherical {Bessel} function
$ j_l(r) $",
journal = j-COMP-PHYS-COMM,
volume = "18",
number = "1",
pages = "73--86",
month = sep,
year = "1979",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(79)90025-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 06:01:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465579900250",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Divgi:1979:CUB,
author = "D. R. Divgi",
title = "Calculation of Univariate and Bivariate Normal
Probability Functions",
journal = j-ANN-STAT,
volume = "7",
number = "4",
pages = "903--910",
month = jul,
year = "1979",
CODEN = "ASTSC7",
DOI = "https://doi.org/10.1214/aos/1176344739",
ISSN = "0090-5364 (print), 2168-8966 (electronic)",
ISSN-L = "0090-5364",
bibdate = "Wed Jun 4 06:39:50 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annstat1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://projecteuclid.org/euclid.aos/1176344739",
acknowledgement = ack-nhfb,
fjournal = "Annals of Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aos/",
}
@Article{Einarsson:1979:BEN,
author = "Bo Einarsson",
title = "Bibliography on the evaluation of numerical software",
journal = j-J-COMPUT-APPL-MATH,
volume = "5",
number = "2",
pages = "145--159",
month = jun,
year = "1979",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0771-050X(79)90011-1",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Thu Oct 28 17:14:49 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This bibliography on the evaluation of numerical
software has been written at the request of the IFIP
Working Group on Numerical Software (IFIP WG 2.5), and
is divided into nine different sections. Within each
section the references are given in alphabetical order
by the first author. The aim of the bibliography is to
be useful in the production and evaluation of good
software for numerical mathematics.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
tableofcontents = "2. Miscellaneous evaluations \\
3. Linear algebra \\
4. Optimization and nonlinear equations \\
5. Functions \\
6. Quadrature \\
7. Integral equations \\
8. Ordinary differential equations \\
9. Partial differential equations",
}
@Article{elLozy:1979:RAS,
author = "Mohamed el Lozy",
title = "Remark on ``{Algorithm 395: Student's
$t$-Distribution}'' and Remark on ``{Algorithm 396:
Student's Quantiles [S14]}''",
journal = j-TOMS,
volume = "5",
number = "2",
pages = "238--239",
month = jun,
year = "1979",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Feb 06 05:28:16 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
remark = "Fullerton: The algorithms are corrected for computers
with anomalously small word lengths (e.g., IBM and
Interdata).",
}
@Article{Epstein:1979:STE,
author = "H. I. Epstein and B. F. Caviness",
title = "A structure theorem for the elementary functions and
its application to the identity problem",
journal = j-INT-J-COMPUT-INF-SCI,
volume = "8",
number = "1",
pages = "9--37",
year = "1979",
CODEN = "IJCIAH",
ISSN = "0091-7036",
MRclass = "12H05 (68C05)",
MRnumber = "80k:12032",
MRreviewer = "Michael F. Singer",
bibdate = "Sat Apr 26 12:45:53 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Computer and Information
Sciences",
journal-URL = "http://link.springer.com/journal/10766",
}
@Article{Fettis:1979:AEU,
author = "Henry E. Fettis",
title = "An asymptotic expansion for the upper percentage
points of the $ \chi^2 $-distribution",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1059--1064",
month = jul,
year = "1979",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2006079",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "62E20",
MRnumber = "80h:62014",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation)",
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximation theory; asymptotic expansion; upper
percentage point",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Gabutti:1979:HPM,
author = "Bruno Gabutti",
title = "On high precision methods for computing integrals
involving {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1049--1057",
month = jul,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D30",
MRnumber = "80c:65048",
MRreviewer = "K. Jetter",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4180 (Integral equations); C4240 (Programming and
algorithm theory)",
corpsource = "Istituto di Calcoli Numerici, Univ. di Torino, Torino,
Italy",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel function integral; computational complexity;
exponential function integral; integration",
treatment = "T Theoretical or Mathematical",
}
@Article{Gargantini:1979:NSS,
author = "Irene Gargantini",
title = "The Numerical Stability of Simultaneous Iterations Via
Square-Rooting",
journal = j-COMPUT-MATH-APPL,
volume = "5",
number = "1",
pages = "25--31",
month = "????",
year = "1979",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(81)90136-X",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812218190136X",
acknowledgement = ack-jr # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Gautschi:1979:AIG,
author = "W. Gautschi",
title = "{Algorithm 542}: Incomplete Gamma Functions [{S14}]",
journal = j-TOMS,
volume = "5",
number = "4",
pages = "482--489",
month = dec,
year = "1979",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355853.355864",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Aug 28 00:39:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
remark = "Fullerton: FORTRAN routines of adjustable accuracy.",
}
@Article{Gautschi:1979:CPI,
author = "Walter Gautschi",
title = "A Computational Procedure for Incomplete Gamma
Functions",
journal = j-TOMS,
volume = "5",
number = "4",
pages = "466--481",
month = dec,
year = "1979",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355853.355863",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Aug 28 00:32:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
remark = "Fullerton: Algorithms for the incomplete gamma
function, $ \gamma (a, x) $, the complementary
function, $ \Gamma (a, x) $, and Tricomi's form, $
\gamma '(a, x) $, are given.",
}
@Article{Glasser:1979:NI,
author = "M. L. Glasser",
title = "A Note on the Integral $ \int^\infty_0 t^{2 \alpha -
1}(1 + t^2)^{1 - \alpha - \beta } {J}_\nu (x \sqrt {1 +
t^2}) d t $",
journal = j-MATH-COMPUT,
volume = "33",
number = "146",
pages = "792--793",
month = apr,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A40",
MRnumber = "80d:33004",
MRreviewer = "T. Erber",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1120 (Mathematical analysis); C4180 (Integral
equations)",
corpsource = "Math. and Computer Sci. Dept., Clarkson Coll. of
Technol., Potsdam, NY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; hypergeometric series; integral;
integral equations",
treatment = "T Theoretical or Mathematical",
}
@Article{Haavie:1979:GNT,
author = "Tore H{\aa}vie",
title = "Generalized {Neville} type extrapolation schemes",
journal = j-BIT,
volume = "19",
number = "2",
pages = "204--213",
month = jun,
year = "1979",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01930850",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65B05 (65D05 65D30)",
MRnumber = "80f:65005",
MRreviewer = "Siegfried Filippi",
bibdate = "Wed Jan 4 18:52:16 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=2&spage=204",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Johnson:1979:RAF,
author = "Donald B. Johnson and Webb Miller and Brian Minnihan
and Celia Wrathall",
title = "Reducibility Among Floating-Point Graphs",
journal = j-J-ACM,
volume = "26",
number = "4",
pages = "739--760",
month = oct,
year = "1979",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "80i:65045",
bibdate = "Fri Dec 08 11:55:10 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The graph-theoretic models of this paper can be used
to compare the rounding-error behavior of numerical
programs. The models follow the approach, popularized
by Wilkinson, of assuming independent rounding errors
in each arithmetic operation. Models constructed on
this assumption are more tractable than would be the
case under more realistic assumptions. There are
identified two easily tested conditions on programs
which guarantee that error analyses are relatively
insensitive to the particular graph model employed. The
development has the additional benefit of sometimes
providing an elementary proof that one program is
comparable in stability to another. Examples of such
results are given.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Kusterer:1979:SEP,
author = "Roland Kusterer and Manfred Reimer",
title = "Stable Evaluation of Polynomials in Time $ \log n $",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1019--1031",
month = jul,
year = "1979",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1979-0528054-X;
https://doi.org/10.2307/2006075",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G05 (68C25)",
MRnumber = "80d:65050 (528054)",
MRreviewer = "C. W. Clenshaw",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Math. Inst., University of Dortmund, Dortmund, West
Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithm; approximation theory; number of
multiplications to evaluate a polynomial; polynomials",
reviewer-dates = "Charles William Clenshaw (15 March 1926--23
September 2004)",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Leung:1979:AFE,
author = "K. V. Leung and S. S. Ghaderpanah",
title = "An application of the finite element approximation
method to find the complex zeros of the modified
{Bessel} function $ {K}_n(z) $",
journal = j-MATH-COMPUT,
volume = "33",
number = "148",
pages = "1299--1306",
month = oct,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33-04)",
MRnumber = "80e:65024",
MRreviewer = "R. P. Boas, Jr.",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4140 (Linear algebra)",
corpsource = "Dept. of Computer Sci., Concordia Univ., Montreal,
Que., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel function; complex zeros; finite element
analysis; finite element approximation method;
iterative optimisation scheme; modified; poles and
zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Lindstrom:1979:MSM,
author = "F. T. Lindstrom",
title = "A Modified $3$-Spline Method for Evaluating the
{Euler} Digamma Function",
journal = j-TECHNOMETRICS,
volume = "21",
number = "3",
pages = "307--311",
month = aug,
year = "1979",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1267752",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:18:50 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254300;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
URL = "http://www.jstor.org/stable/1267752",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Ling:1979:EWZ,
author = "C. B. Ling",
title = "Evaluation of {Weierstrass} Zeta Functions",
journal = j-SIAM-REVIEW,
volume = "21",
number = "1",
pages = "146--147",
month = "????",
year = "1979",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1021020",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Maurone:1979:ABD,
author = "Philip A. Maurone and Alain J. Phares",
title = "On the asymptotic behavior of the derivatives of
{Airy} functions",
journal = j-J-MATH-PHYS,
volume = "20",
number = "11",
pages = "2191--2191",
month = nov,
year = "1979",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.523997",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33A60",
MRnumber = "80j:33014",
bibdate = "Sat Oct 29 11:28:40 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1975.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v20/i11/p2191_s1",
acknowledgement = ack-nhfb,
classification = "A0230 (Function theory, analysis); A0365D
(Functional analytical methods in quantum theory);
A1235 (Composite models of particles)",
corpsource = "Dept. of Phys., Villanova Univ., Villanova, PA, USA",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "Airy functions; angular momentum theory; asymptotic
behavior; derivatives; functional analysis;
noniterative functional solution; quantum theory; quark
confinement; recursion relation",
onlinedate = "29 July 2008",
pagecount = "1",
treatment = "T Theoretical or Mathematical",
}
@Article{Morris:1979:DFR,
author = "Robert Morris",
title = "The Dilogarithm Function of a Real Argument",
journal = j-MATH-COMPUT,
volume = "33",
number = "146",
pages = "778--787",
month = apr,
year = "1979",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1979-0521291-X",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33A70)",
MRnumber = "80e:65025",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4240 (Programming and algorithm theory)",
corpsource = "Bell Labs., Murray Hill, NJ, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithm theory; dilogarithm function; real
argument",
received = "22 May 1978",
remark = "Fullerton: Relative errors down to $ 10^{-24} $ for $
\operatorname {Li}_2 (z) = - \int_0^z \frac {\log (1 -
z)z} \, d z $. $ \operatorname {Li}_2 (z) $ is a form
of Spence's integral.",
treatment = "T Theoretical or Mathematical",
}
@Article{Pexton:1979:DRT,
author = "Robert L. Pexton and Arno D. Steiger",
title = "Degenerate roots of three transcendental equations
involving spherical {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1041--1048",
month = jul,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "loose microfiche suppl. 65H10 (65D20)",
MRnumber = "80g:65057",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Lawrence Livermore Lab., Univ. of California,
Livermore, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "function approximation; spherical Bessel function;
transcendental equation",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Phillips:1979:FAC,
author = "G. Phillips",
title = "A fast approximation to the complementary error
function for use in fitting gamma-ray peaks",
journal = j-NUCL-INSTR-METH,
volume = "164",
number = "??",
pages = "561--563",
month = sep,
year = "1979",
CODEN = "NUIMAL",
DOI = "https://doi.org/10.1016/0029-554X(79)90094-6",
ISSN = "0029-554x (print), 1878-3759 (electronic)",
ISSN-L = "0029-554X",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://adsabs.harvard.edu/abs/1979NucIM.164..561P",
abstract = "A fast approximation to the complementary error
function has been programmed and tested for use in the
peak-shape function for fitting peaks in gamma-ray
spectra. The function was compared for speed and
accuracy on the NRL ASC 7 computer to the mathematical
library version of the complementary error function.
The approximation has resulted in a 50\% time savings
in the computer program HYPERMET which was developed at
NRL for automatic analysis of gamma-ray spectra from
germanium detectors.",
acknowledgement = ack-nhfb,
fjournal = "Nuclear Instruments and Methods",
}
@Article{Risch:1979:APE,
author = "Robert H. Risch",
title = "Algebraic properties of the elementary functions of
analysis",
journal = j-AM-J-MATH,
volume = "101",
number = "4",
pages = "743--759",
year = "1979",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
MRclass = "12H05",
MRnumber = "81b:12029",
MRreviewer = "J. L. Johnson",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Mathematics",
}
@Article{Schulten:1979:AEC,
author = "Z. (or K. ??) Schulten and D. G. M. Anderson and R. G.
Gordon",
title = "An Algorithm for the Evaluation of the Complex {Airy}
Functions",
journal = j-J-COMPUT-PHYS,
volume = "31",
number = "1",
pages = "60--75",
month = apr,
year = "1979",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(79)90062-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 10:34:34 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
remark = "Fullerton: Simple formulae over the whole complex
plane are presented.",
}
@Article{Smith:1979:ALL,
author = "David A. Smith and William F. Ford",
title = "Acceleration of Linear and Logarithmic Convergence",
journal = j-SIAM-J-NUMER-ANAL,
volume = "16",
number = "2",
pages = "223--240",
month = apr,
year = "1979",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65B10",
MRnumber = "82a:65012",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Takemasa:1979:CFC,
author = "T. Takemasa and T. Tamura and H. H. Wolter",
title = "{Coulomb} Functions with Complex Angular Momenta",
journal = j-COMP-PHYS-COMM,
volume = "17",
number = "4",
pages = "351--355",
month = jul # "\slash " # aug,
year = "1979",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(79)90097-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 11:14:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "Fullerton: Description of program CCOULOM, which works
only in the part of the $ (\rho, \eta) $-plane where $
\eta^2 \ll \rho $ and $ | \ell |^2 \ll \rho $.",
}
@Article{Temme:1979:AAP,
author = "N. M. Temme",
title = "An Algorithm with {ALGOL 60} Program for the
Computation of the Zeros of Ordinary {Bessel} Functions
and those of their Derivatives",
journal = j-J-COMPUT-PHYS,
volume = "32",
number = "2",
pages = "270--279",
month = aug,
year = "1979",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(79)90134-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 11:23:13 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
remark = "Fullerton: An adjustable-accuracy 100 line Algol
procedure is discussed.",
}
@Article{Temme:1979:AEI,
author = "N. M. Temme",
title = "The asymptotic expansion of the incomplete gamma
functions",
journal = j-SIAM-J-MATH-ANA,
volume = "10",
number = "4",
pages = "757--766",
month = jul,
year = "1979",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A15",
MRnumber = "80i:33002",
MRreviewer = "E. Rieksti\lfhook n{\v{s}}",
bibdate = "Sun Nov 28 19:22:16 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/10/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Terras:1979:DIG,
author = "Riho Terras",
title = "The determination of incomplete gamma functions
through analytic integration",
journal = j-J-COMPUT-PHYS,
volume = "31",
number = "1",
pages = "146--151",
month = apr,
year = "1979",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(79)90066-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:33 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999179900664",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Thacher:1979:NBR,
author = "Henry C. {Thacher, Jr.}",
title = "New Backward Recurrences for {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "33",
number = "146",
pages = "744--764",
month = apr,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33A40)",
MRnumber = "81b:65019",
MRreviewer = "R. G. Langebartel",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C1120 (Mathematical analysis)",
corpsource = "Dept. of Computer Sci., Univ. of Kentucky, Lexington,
KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "backward recurrences; Bessel functions; converges",
treatment = "N New Development; T Theoretical or Mathematical",
}
@Article{Brent:1980:SNA,
author = "Richard P. Brent and Edwin M. McMillan",
title = "Some new algorithms for high-precision computation of
{Euler}'s constant",
journal = j-MATH-COMPUT,
volume = "34",
number = "149",
pages = "305--312",
month = jan,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "10-04 (10A40 68C05)",
MRnumber = "82g:10002",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Univ. of California, Berkeley, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; computation; Euler's constant;
function evaluation; high precision",
remark = "Fullerton: Calculation to 30,100 places is discussed,
but only a 3-digit value appears in the paper.",
treatment = "N New Development; T Theoretical or Mathematical",
}
@InProceedings{Brent:1980:UAE,
author = "R. P. Brent",
title = "Unrestricted Algorithms for Elementary and Special
Functions",
crossref = "Lavington:1980:IPP",
pages = "613--619",
year = "1980",
bibdate = "Thu Sep 01 11:55:31 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://maths-people.anu.edu.au/~brent/pub/pub052.html",
acknowledgement = ack-nj,
remark = "From the author's Web site: Errata for original
version:\par Page 615, remove the absolute value signs
in equation (13) and the following paragraph (x should
be large and positive here).\par
Page 616, second half of equation (26): insert a minus
sign after the equals sign.\par
Page 617, equation (39): delete `` / j ! ''.\par
Page 617, equation (42): the assumption ``j < k''
should be added. Also, the contour C needs to be
enlarged slightly.\par
Page 617, left-hand-side of equation (44): replace
``Sj,k'' by ``S2j,k''.\par
Page 617, ten lines after equation (44): replace
``O(jn2)'' by ``O(j2n)''.",
}
@Article{Brezinski:1980:GEA,
author = "C. Brezinski",
title = "A general extrapolation algorithm",
journal = j-NUM-MATH,
volume = "35",
number = "2",
pages = "175--187",
month = jun,
year = "1980",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65B05",
MRnumber = "81j:65015",
MRreviewer = "L. Fox",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation)",
corpsource = "UER IEEA, Univ. de Lille 1, Villeneuve d'Ascq,
France",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration; extrapolation; extrapolation
algorithm; linear extrapolation; rational
extrapolation; recursive algorithm; sequence
transformations",
treatment = "T Theoretical or Mathematical",
}
@Article{Char:1980:SCF,
author = "Bruce W. Char",
title = "On {Stieltjes}' continued fraction for the gamma
function",
journal = j-MATH-COMPUT,
volume = "34",
number = "150",
pages = "547--551",
month = apr,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05 (65D20)",
MRnumber = "81b:65008",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: The first 41 coefficients to 40 digits are
given.",
}
@Article{Clenshaw:1980:UAE,
author = "C. W. Clenshaw and Frank W. J. Olver",
title = "An unrestricted algorithm for the exponential
function",
journal = j-SIAM-J-NUMER-ANAL,
volume = "17",
number = "2",
pages = "310--331",
month = apr,
year = "1980",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0717026",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65D20",
MRnumber = "567276",
MRreviewer = "A. M. Cohen",
bibdate = "Sun Nov 12 06:18:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "An algorithm is presented for the computation of the
exponential function of real argument. There are no
restrictions on the range of the argument or on the
precision that may be demanded in the results.",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004); Frank William John Olver (15 December 1924--23
April 2013)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Book{Cody:1980:SME,
author = "William J. {Cody, Jr.} and William Waite",
title = "Software Manual for the Elementary Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "x + 269",
year = "1980",
ISBN = "0-13-822064-6",
ISBN-13 = "978-0-13-822064-8",
LCCN = "QA331 .C635 1980",
bibdate = "Tue Dec 14 23:28:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
acknowledgement = ack-nhfb,
shorttableofcontents = "Preface / ix \\
1. Introduction / 1 \\
2. Preliminaries / 3 \\
3. Performance Testing / 11 \\
4. SQRT / 17 \\
5. ALOG/ALOG10 / 35 \\
6. EXP / 60 \\
7. POWER (**) / 84 \\
8. SIN/COS / 125 \\
9. TAN/COT / 150 \\
10. ASIN/ACOS / 174 \\
11. ATAN/ATAN2 / 194 \\
12. SINH/COSH / 217",
tableofcontents = "Preface / ix \\
1. Introduction / 1 \\
2. Preliminaries / 3 \\
3. Performance Testing / 11 \\
4. SQRT / 17 \\
a. General Discussion / 17 \\
b. Flow Chart for SQRT(X) / 18 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 19 \\
d. Implementation Notes, Binary Floating-Point Machines
/ 23 \\
e. Implementation Notes, Non-Binary Floating-Point
Machines / 25 \\
f. Testing / 28 \\
5. ALOG/ALOG10 / 35 \\
a. General Discussion / 35 \\
b. Flow Chart for ALOG(X)/ALOG10(X) / 37 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 38 \\
d. Implementation Notes, Non-Decimal Floating-Point
Machines / 42 \\
e. Implementation Notes, Decimal Floating-Point
Machines / 46 \\
f. Testing / 49 \\
6. EXP / 60 \\
a. General Discussion / 60 \\
b. Flow Chart for EXP(X) / 62 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 63 \\
d. Implementation Notes, Non-Decimal Floating-Point
Machines / 67 \\
e. Implementation Notes, Decimal Floating-Point
Machines / 71 \\
f. Testing / 75 \\
7. POWER (**) / 84 \\
a. General Discussion / 84 \\
b. Flow Chart for POWER(X,Y) / 88 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 90 \\
d. Implementation Notes, Non-Decimal Floating-Point
Machines / 97 \\
e. Implementation Notes, Decimal Floating-Point
Machines / 106 \\
f. Testing / 113 \\
8. SIN/COS / 125 \\
a. General Discussion / 125 \\
b. Flow Chart for SIN(X)/COS(X) / 127 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 129 \\
d. Implementation Notes, All Floating-Point Machines /
134 \\
e. Testing / 139 \\
9. TAN/COT / 150 \\
a. General Discussion / 150 \\
b. Flow Chart for TAN(X)/COTAN(X) / 152 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 154 \\
d. Implementation Notes, All Floating-Point Machines /
159 \\
e. Testing / 164 \\
10. ASIN/ACOS / 174 \\
a. General Discuss i on / 174 \\
b. Flow Chart for AS IN(X)/ACOS(X) / 176 \\
c. Implementation Not es, Non-Decimal Fixed-Point
Machines / 177 \\
d. Implementation Notes, All Floating-Point Machines /
181 \\
e. Testing / 185 \\
11. ATAN/ATAN2 / 194 \\
a. General Discussion / 194 \\
b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 198 \\
d. Implementation Notes, All Floating-Point Machines /
203 \\
e. Testing / 207 \\
12. SINH/COSH / 217 \\
a. General Discussion / 217 \\
b. Flow Chart for SINH(X)/COSH(X) / 220 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 221 \\
d. Implementation Notes, All Floating-Point Machines /
225 \\
e. Testing / 229",
}
@Article{Coleman:1980:FSB,
author = "J. P. Coleman",
title = "A {Fortran} subroutine for the {Bessel} function {$
J_n(x) $} of order $0$ to $ 10 $",
journal = j-COMP-PHYS-COMM,
volume = "21",
number = "1",
pages = "109--118",
day = "1",
month = dec,
year = "1980",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(80)90080-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 06:01:19 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465580900806",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Delahaye:1980:RNA,
author = "J. P. Delahaye and B. Germain-Bonne",
title = "{R}{\'e}sultats n{\'e}gatifs en acc{\'e}l{\'e}ration
de la convergence. ({French}) [{Negative} results in
convergence acceleration]",
journal = j-NUM-MATH,
volume = "35",
number = "4",
pages = "443--457",
month = nov,
year = "1980",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65B99 (40A99)",
MRnumber = "81k:65007",
MRreviewer = "Claude Brezinski",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
corpsource = "Univ. des Sci. et Tech. de Lille I, Villeneuve d'Ascq,
France",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "acceleration; algorithm; approximation theory;
computational complexity; convergence; convergence
acceleration; convergence of numerical methods",
language = "French",
treatment = "T Theoretical or Mathematical",
}
@Article{Ditkin:1980:CSF,
author = "V. A. Ditkin and K. A. Karpov and M. K. Kerimov",
title = "The computation of special functions",
journal = j-USSR-COMP-MATH-MATH-PHYS,
volume = "20",
number = "5",
pages = "3--12",
year = "1980",
CODEN = "CMMPA9",
ISSN = "0041-5553, 0502-9902",
ISSN-L = "0041-5553",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.2.1; G.1.2",
CRclass = "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Generating functions; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
fjournal = "U.S.S.R. Computational Mathematics and Mathematical
Physics",
genterm = "algorithms; design",
guideno = "09092",
journal-URL = "http://www.sciencedirect.com/science/journal/00415553",
journalabr = "USSR Comput. Math. Math. Phys",
jrldate = "1980",
subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Eckhardt:1980:AWE,
author = "Ulrich Eckhardt",
title = "{Algorithm 549}: {Weierstrass}' Elliptic Functions
[{S21}]",
journal = j-TOMS,
volume = "6",
number = "1",
pages = "112--120",
month = mar,
year = "1980",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355873.355884",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Aug 29 10:31:24 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Weierstrass' elliptic functions",
remark = "Fullerton: A complex FORTRAN algorithm with accuracy
down to $ 10^{-18} $ is given",
}
@Article{Fransen:1980:HPV,
author = "Arne Frans{\'e}n and Staffan Wrigge",
title = "High-precision values of the gamma function and of
some related coefficients",
journal = j-MATH-COMPUT,
volume = "34",
number = "150",
pages = "553--566",
month = apr,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05 (65D20)",
MRnumber = "81f:65004",
MRreviewer = "F. W. J. Olver",
bibdate = "Sat Apr 01 10:12:58 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
note = "See addendum and corrigendum
\cite{Fransen:1981:ACH}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 80D values of coefficients in the Taylor
series for $ \Gamma^m(s + x) $ are given.",
}
@TechReport{Fullerton:1980:BEM,
author = "L. W. Fullerton",
title = "A Bibliography on the Evaluation of Mathematical
Functions",
type = "Technical report",
number = "TM 80-1274-4 and CSTR 86",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
month = sep,
year = "1980",
bibdate = "Sat Feb 05 17:39:14 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gargantini:1980:PSR,
author = "Irene Gargantini",
title = "Parallel Square-Root Iterations for Multiple Roots",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "3",
pages = "279--288",
month = "????",
year = "1980",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122180900358",
acknowledgement = ack-jr # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@Unpublished{Kahan:1980:SPI,
author = "W. Kahan",
title = "Software $ \sqrt x $ for the Proposed {IEEE
Floating-Point Standard}",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
pages = "????",
day = "25",
month = aug,
year = "1980",
bibdate = "Mon Apr 25 18:24:02 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript",
acknowledgement = ack-nhfb,
mynote = "Dated August 25 1980",
}
@Article{Kasperkovitz:1980:AAM,
author = "P. Kasperkovitz",
title = "Asymptotic approximations for modified {Bessel}
functions",
journal = j-J-MATH-PHYS,
volume = "21",
number = "1",
pages = "6--13",
month = jan,
year = "1980",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.524310",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33A40",
MRnumber = "81a:33012",
MRreviewer = "N. Hayek Calil",
bibdate = "Sat Oct 29 18:18:22 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v21/i1/p6_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "21 July 2008",
pagecount = "8",
}
@Article{Langebartel:1980:FER,
author = "R. G. Langebartel",
title = "{Fourier} expansions of rational fractions of elliptic
integrals and {Jacobian} elliptic functions",
journal = j-SIAM-J-MATH-ANA,
volume = "11",
number = "3",
pages = "506--513",
month = may,
year = "1980",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "42A16 (33A25)",
MRnumber = "81e:42008",
MRreviewer = "R. C. Varma",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@InProceedings{Maksymiv:1980:APT,
author = "E. M. Maksymiv",
booktitle = "Differentsialnye Uravneniya i ikh Prilozhen",
title = "Approximate properties of {Thiele}'s formula in a
class of elementary functions. ({Russian})",
volume = "141",
publisher = "Vestnik L'vov. Politekhn. Inst.",
address = "L'vov, USSR",
pages = "55--56",
year = "1980",
MRclass = "119.65D20",
MRnumber = "81i:65021",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Moran:1980:CND,
author = "P. A. P. Moran",
title = "Calculation of the Normal Distribution Function",
journal = j-BIOMETRIKA,
volume = "67",
number = "3",
pages = "675--676",
month = dec,
year = "1980",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.1093/biomet/67.3.675;
https://doi.org/10.2307/2335138",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
MRclass = "62E30",
MRnumber = "601106 (82d:62044)",
MRreviewer = "G. P. Bhattacharjee",
bibdate = "Sat Jun 21 14:34:26 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315495;
https://www.math.utah.edu/pub/tex/bib/biometrika1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2335138",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://biomet.oxfordjournals.org/content/by/year;
http://www.jstor.org/journals/00063444.html",
}
@Article{OBrien:1980:SBF,
author = "D. M. O'Brien",
title = "Spherical {Bessel} functions of large order",
journal = j-J-COMPUT-PHYS,
volume = "36",
number = "1",
pages = "128--132",
month = jun,
year = "1980",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(80)90177-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:01 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999180901771",
abstract = "This note introduces functions $ b_n(x) $, related to
spherical Bessel functions $ j_n(x) $ and $ y_n(x) $.
They are scaled so that they are bounded functions of
$n$ and polynomially bounded functions of $x$, and
therefore avoid the problems of underflow and overflow
which are so common with Bessel functions. They can be
generated from a stable recurrence relation for which
starting values are readily computable.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@InProceedings{Olver:1980:UAG,
author = "F. W. J. Olver",
title = "Unrestricted algorithms for generating elementary
functions",
crossref = "Alefeld:1980:PSE",
pages = "131--140",
year = "1980",
MRclass = "65G05 (65D15)",
MRnumber = "82b:65034",
MRreviewer = "John Todd",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pedersen:1980:HBM,
author = "P. W. Pedersen",
title = "Hvordan beregner man kvadratroden? \toenglish {How do
you calculate the square root?} \endtoenglish",
journal = "Elektronik (Denmark)",
volume = "??",
number = "4",
pages = "18--21",
month = apr,
year = "1980",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Popov:1980:PFD,
author = "B. A. Popov and G. S. Tesler",
title = "Priblizhenie funktsii dlya tekhnicheskikh prilozhenii.
({Russian}) [{Approximation} of functions for technical
applications]",
publisher = "Naukova Dumka",
address = "Kiev, USSR",
pages = "351",
year = "1980",
MRclass = "65D15 (41-02 65D07)",
MRnumber = "602955",
bibdate = "Tue Jan 24 08:23:12 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Nauka i tekhnicheskii progress. [Science and technical
progress]",
acknowledgement = ack-nhfb # " and " # ack-mv,
}
@Article{Rengarajan:1980:MFI,
author = "S. R. Rengarajan and J. E. Lewis",
title = "{Mathieu} Functions of Integral Order and Real
Arguments",
journal = j-IEEE-TRANS-MICROWAVE-THEORY-TECH,
volume = "28",
number = "3",
pages = "276--277",
month = mar,
year = "1980",
CODEN = "IETMAB",
DOI = "https://doi.org/10.1109/TMTT.1980.1130060",
ISSN = "0018-9480 (print), 1557-9670 (electronic)",
ISSN-L = "0018-9480",
bibdate = "Sat Oct 30 10:09:01 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "To compute Mathieu functions, modified Mathieu
functions and related parameters for integral orders
and real arguments, encountered in wave propagation
involving elliptic geometries.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "IEEE transactions on microwave theory and techniques",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=22",
remark = "Fullerton: A long FORTRAN program is very briefly
described. This work is superior to that of Clemm
(1969), because $q$ may be negative.",
}
@Article{Schell:1980:AEU,
author = "Hans-Joachim Schell",
title = "{Asymptotische Entwicklungen f{\"u}r die
unvollst{\"a}ndige Gammafunktion}. ({German})
[{Asymptotic} developments for the incomplete gamma
function]",
journal = "{Wissenschaftliche Zeitschrift der Technischen
Hochschule Karl-Marx-Stadt}",
volume = "22",
number = "5",
pages = "477 485",
month = "????",
year = "1980",
bibdate = "Sat Feb 18 15:11:46 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "{Wiss. Schr. Tech. Univ. Karl-Marx-Stadt}",
keywords = "incomplete gamma function; uniform asymptotic
expansions",
language = "German",
}
@Article{Schonfelder:1980:VHA,
author = "J. L. Schonfelder",
title = "Very high accuracy {Chebyshev} expansions for the
basic trigonometric functions",
journal = j-MATH-COMPUT,
volume = "34",
number = "149",
pages = "237--244",
month = jan,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20",
MRnumber = "81f:65016",
MRreviewer = "Claude Carasso",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 40D coefficients for the sine, cosine and
tangent are given.",
}
@Book{Sneddon:1980:SFM,
author = "Ian Naismith Sneddon",
title = "Special Functions of Mathematical Physics and
Chemistry",
publisher = "Longman",
address = "London, UK",
edition = "Third",
pages = "ix + 182",
year = "1980",
ISBN = "0-582-44396-2 (paperback)",
ISBN-13 = "978-0-582-44396-9 (paperback)",
LCCN = "QA351 .S64 1980",
bibdate = "Sat Oct 30 18:25:01 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Longman mathematical texts",
acknowledgement = ack-nhfb,
remark = "See first edition \cite{Sneddon:1956:SFM} and second
edition \cite{Sneddon:1961:SFM}.",
subject = "Functions, Special",
}
@InCollection{Tretjakov:1980:PSE,
author = "V. A. Tret'jakov",
booktitle = "Mathematical analysis and the theory of functions
({Russian})",
title = "On the properties of some elementary functions that
are defined on the algebra of bicomplex numbers.
({Russian})",
publisher = "Moskov. Oblast. Ped. Inst.",
address = "Moscow, USSR",
pages = "99--106",
year = "1980",
MRclass = "30G35 (78A35)",
MRnumber = "82i:30069",
MRreviewer = "Toma V. Tonev",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Tretter:1980:ASA,
author = "Marietta J. Tretter and G. W. Walster",
title = "Analytic subtraction applied to the incomplete gamma
and beta functions",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "1",
number = "3",
pages = "321--326",
month = sep,
year = "1980",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0901022",
ISSN = "0196-5204",
ISSN-L = "0196-5204",
MRclass = "65D20 (33A15)",
MRnumber = "81m:65029",
MRreviewer = "Anton Hut'a",
bibdate = "Mon Mar 31 09:58:49 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sjoce3",
keywords = "analytic subtraction; continued fraction; incomplete
beta function; incomplete gamma function",
onlinedate = "September 1980",
}
@PhdThesis{vonGudenberg:1980:EAR,
author = "J. Wolff {von Gudenberg}",
title = "{Einbettung allgemeiner Rechnerarithmetik in Pascal
mittels eines Operatorkonzepts und Implementierung der
Standardfunktionen mit optimaler Genauigkeit}
\toenglish {Embedding a General Computer Arithmetic in
Pascal by Means of an Operator Concept and the
Implementation of Elementary Functions with Optimal
Accuracy} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1980",
bibdate = "Sun Oct 25 10:29:29 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Waldecker:1980:NSR,
author = "D. E. Waldecker",
title = "Nonrestoring Square Root with Simplified Answer
Generation",
journal = j-IBM-TDB,
volume = "22",
number = "11",
pages = "4807--4808",
month = apr,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InCollection{Wang:1980:ISM,
author = "J. Y. Wang",
booktitle = "{SHARE-54}, Anaheim, {CA}, March 3, 1980",
title = "On the Improvement of Some Mathematical Subroutines in
the {IBM S/360 FORTRAN IV} Libraries",
volume = "1",
publisher = "????",
address = "????",
pages = "75--77",
year = "1980",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Fri Sep 20 14:23:46 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[Reference 7]{Agarwal:1986:NSV} in
elefunt.bib and fparith.bib.",
}
@Article{Andrews:1981:EFM,
author = "M. Andrews and D. Jaeger and S. F. McCormick and G. D.
Taylor",
title = "Evaluation of Functions on Microcomputers: $ \exp (x)
$",
journal = j-COMPUT-MATH-APPL,
volume = "7",
number = "6",
pages = "503--508",
month = "????",
year = "1981",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:21 MST 2017",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122181900341",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
xxmonth = "(none)",
}
@Article{Arscott:1981:LBB,
author = "F. M. Arscott",
title = "The land beyond {Bessel}: a survey of higher special
functions",
journal = j-LECT-NOTES-MATH,
volume = "846",
pages = "26--45",
year = "1981",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0089822",
ISBN = "3-540-10569-7 (print), 3-540-38538-X (e-book)",
ISBN-13 = "978-3-540-10569-5 (print), 978-3-540-38538-7
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Fri May 9 19:07:31 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0089822/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0089819",
book-URL = "http://www.springerlink.com/content/978-3-540-38538-7",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Banuelos:1981:PCF,
author = "Alicia Ba{\~n}uelos and Ricardo Angel Depine and
Roberto Claudio Mancini",
title = "A program for computing the {Fermi--Dirac} functions",
journal = j-COMP-PHYS-COMM,
volume = "21",
number = "3",
pages = "315--322",
month = jan,
year = "1981",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Wed Feb 5 09:02:18 MST 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465581900126",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655/",
}
@Article{Baratella:1981:ABF,
author = "P. Baratella and M. Garetto and G. Vinardi",
title = "Approximation of the {Bessel} function {$ J_\nu (x) $}
by numerical integration",
journal = j-J-COMPUT-APPL-MATH,
volume = "7",
number = "2",
pages = "87--91",
month = jun,
year = "1981",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:21 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X81900401",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Barnett:1981:ARI,
author = "A. R. Barnett",
title = "An algorithm for regular and irregular {Coulomb} and
{Bessel} functions of real order to machine accuracy",
journal = j-COMP-PHYS-COMM,
volume = "21",
number = "3",
pages = "297--314",
month = jan,
year = "1981",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(81)90011-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "We describe an algorithm to evaluate a wide class of
functions and their derivatives, to extreme precision
(25--30S) if required, which does not use any function
calls other than square root. The functions are the
Coulomb functions of positive argument ($ F_\lambda (x,
\eta) $, $ G_\lambda (x, \eta) $, $ x > 0 $, $ \eta $,
$ \lambda $ real) and hence, as special cases with $
\eta = 0 $, the cylindrical Bessel functions ($ J_\mu
(x) $, $ Y_\mu (x) $, $ x > 0 $, $ \mu $ real), the
spherical Bessel functions ($ i_\lambda (x) $, $
y_\lambda (x) $, $ x > 0 $, $ \lambda $ real), Airy
functions of negative argument $ \textrm {Ai}( - x) $,
$ \textrm {Bi}( - x) $ and others. The present method
has a number of attractive features: both the regular
and irregular solution are calculated, all others of
the functions can be produced from a specified minimum
(not necessarily zero) to a specified maximum,
functions of a single order can be found without all of
the orders from zero, the derivatives of the functions
arise naturally in the solution and are readily
available, the results are available to different
precisions from the same subroutine (in contrast to
rational approximation techniques) and the methods can
be used for estimating final accuracies. In addition,
the sole constant required in the algorithm is $ \pi $,
no precalculated arrays of coefficients are needed, and
the final accuracy is not dependent on that of other
subroutines. The method works most efficiently in the
region $ x \approx 0.5 $ to $ x \approx 1000 $ but
outside this region the results are still reliable,
even though the number of iterations within the
subroutine rises. Even in these more asymptotic regions
the unchanged algorithm can be used with known accuracy
to test other specific subroutines more appropriate to
these regions. The algorithm uses the recursion
relations satisfied by the Coulomb functions and
contains a significant advance over Miller's method for
evaluating the ratio of successive minimal solutions ($
F_\lambda + 1 / F_\lambda $ ). It relies on the
evaluation of two continued fractions and no infinite
series is required for normalisation: instead the
Wronskian is used.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Bice:1981:AAS,
author = "P. K. Bice",
title = "Algorithm adds square root to micro's arithmetic
capability",
journal = j-ELECTRONIC-DESIGN,
volume = "29",
number = "11",
pages = "146",
month = may,
year = "1981",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Branrers:1981:RAZ,
author = "M. Branrers and R. Piessens and M. {De Meue}",
title = "Rational approximations for zeros of {Bessel}
functions",
journal = j-J-COMPUT-PHYS,
volume = "42",
number = "2",
pages = "403--405",
month = aug,
year = "1981",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(81)90253-9",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:07 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181902539",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Campbell:1981:BFR,
author = "J. B. Campbell",
title = "{Bessel} functions {$ I_\nu (z) $} and {$ K_\nu (z) $}
of real order and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "24",
number = "1",
pages = "97--105",
month = sep # "\slash " # oct,
year = "1981",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(81)90109-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:27:59 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465581901090",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Carlson:1981:AAI,
author = "B. C. Carlson and Elaine M. Notis",
title = "{Algorithm 577}: Algorithms for Incomplete Elliptic
Integrals [{S21}]",
journal = j-TOMS,
volume = "7",
number = "3",
pages = "398--403",
month = sep,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355958.355970",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Aug 29 22:58:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "$R$-functions; elliptic integrals; inverse circular
functions; inverse hyperbolic functions; logarithms",
}
@Article{Chen:1981:AFD,
author = "Gang Chen",
title = "An attempt to find the derivatives of elementary
functions using the algorithmic language {BCY}.
({Chinese})",
journal = "Zhejiang Daxue Xuebao",
volume = "3",
pages = "141--149",
year = "1981",
MRclass = "26A09",
MRnumber = "714 524",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Davis:1981:EFA,
author = "Diane F. Davis",
title = "Elementary Functions on an Array Processor",
crossref = "IEEE:1981:PIS",
pages = "170--178",
year = "1981",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Delahaye:1981:ACS,
author = "J.-P. Delahaye",
title = "Acc{\'e}l{\'e}ration de la convergence des suites dont
le rapport des erreurs est born{\'e}. ({French})
[{Convergence} acceleration for sequences with bounded
error ratios]",
journal = j-CALCOLO,
volume = "18",
number = "2",
pages = "1--116",
year = "1981",
CODEN = "CDABAE",
DOI = "https://doi.org/10.1007/BF02576491",
ISSN = "0008-0624 (print), 1126-5434 (electronic)",
ISSN-L = "0008-0624",
MRclass = "65B05",
MRnumber = "647821 (83a:65004)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Calcolo",
journal-URL = "http://link.springer.com/journal/10092",
keywords = "convergence acceleration",
language = "{French}",
}
@Article{Drachman:1981:TTH,
author = "B. Drachman and C. I. Chuang",
title = "A table of two hundred zeros of the derivative of the
modified {Bessel} function {$ K_n(z) $} and a graph of
their distribution",
journal = j-J-COMPUT-APPL-MATH,
volume = "7",
number = "3",
pages = "167--171",
month = sep,
year = "1981",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X81900140",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Farmwald:1981:HBE,
author = "P. Michael Farmwald",
title = "High Bandwidth Evaluation of Elementary Functions",
crossref = "IEEE:1981:PIS",
pages = "139--142",
year = "1981",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Fettis:1981:TEHb,
author = "Henry E. Fettis",
title = "Table errata: {{\em Handbook of elliptic integrals for
engineers and physicists} [second edition, Springer,
New York, 1971 and MR {\bf 43} \#3506] by P. F. Byrd
and M. D. Friedman}",
journal = j-MATH-COMPUT,
volume = "36",
number = "153",
pages = "317--317",
month = jan,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05",
MRnumber = "82a:65008a",
bibdate = "Sat Apr 12 15:32:35 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fettis:1981:TETb,
author = "Henry E. Fettis",
title = "Table errata: {{\em A table of the complete elliptic
integral of the first kind for complex values of the
modulus, Part I} [Rep. No. ARL 69-0172, Aerospace Res.
Lab., Wright--Patterson Air Force Base, Ohio, 1969; MR
{\bf 40} \#6725] by Fettis and J. C. Caslin}",
journal = j-MATH-COMPUT,
volume = "36",
number = "153",
pages = "318",
month = jan,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "318.65A05",
MRnumber = "82a:65010",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fransen:1981:ACH,
author = "Arne Frans{\'e}n",
title = "Addendum and corrigendum to: {``High-precision values
of the gamma function and of some related
coefficients''} {[Math. Comp. {\bf 34} (1980), no. 150,
553--566, MR 81f:65004] by Frans{\'e}n and S. Wrigge}",
journal = j-MATH-COMPUT,
volume = "37",
number = "155",
pages = "233--235",
month = jul,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05 (65D20)",
MRnumber = "82m:65002",
bibdate = "Sat Apr 01 10:12:58 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
note = "See \cite{Fransen:1980:HPV}.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fredette:1981:RES,
author = "G. Fredette",
title = "68000 routine extracts square roots",
journal = j-EDN,
volume = "26",
number = "16",
pages = "185--194",
month = aug,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@TechReport{Fullerton:1981:FUMa,
author = "L. W. Fullerton",
title = "{FNLIB} User's Manual Explanatory Table of Contents",
type = "Technical report",
number = "CSTR 92",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
month = mar,
year = "1981",
bibdate = "Sat Feb 05 17:39:14 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Fullerton:1981:FUMb,
author = "L. W. Fullerton",
title = "{FNLIB} User's Manual",
type = "Technical report",
number = "CSTR 95",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
month = mar,
year = "1981",
bibdate = "Sat Feb 05 17:39:14 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gasper:1981:SFB,
author = "George Gasper",
title = "Summation Formulas for Basic Hypergeometric Series",
journal = j-SIAM-J-MATH-ANA,
volume = "12",
number = "2",
pages = "196--200",
month = mar,
year = "1981",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A30",
MRnumber = "82a:33005",
MRreviewer = "L. J. Slater",
bibdate = "Sun Nov 28 19:22:39 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/12/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Gatto:1981:NEM,
author = "M. A. Gatto and J. B. Seery",
title = "Numerical evaluation of the modified {Bessel}
functions {$I$} and {$K$}",
journal = j-COMPUT-MATH-APPL,
volume = "7",
number = "3",
pages = "203--209",
month = "????",
year = "1981",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:20 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122181900808",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@Article{Glasser:1981:CBS,
author = "M. L. Glasser",
title = "A Class of {Bessel} Summations",
journal = j-MATH-COMPUT,
volume = "37",
number = "156",
pages = "499--501",
month = oct,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A40 (42A16 44A15)",
MRnumber = "82j:33015",
MRreviewer = "B. D. Agrawal",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
corpsource = "Dept. of Math. and Computer Sci., Clarkson Coll.,
Potsdam, NY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; Bessel summations; infinite series",
treatment = "T Theoretical or Mathematical",
}
@Article{Haavie:1981:RUT,
author = "Tore H{\aa}vie",
title = "Remarks on a unified theory for classical and
generalized interpolation and extrapolation",
journal = j-BIT,
volume = "21",
number = "4",
pages = "465--474",
month = dec,
year = "1981",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932843",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "41A05 (65D05)",
MRnumber = "83d:41004",
MRreviewer = "G. M{\"u}hlbach",
bibdate = "Wed Jan 4 18:52:17 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=4&spage=465",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Hill:1981:RSD,
author = "G. W. Hill",
title = "Remark on ``{Algorithm 395: Student's
$t$-Distribution}''",
journal = j-TOMS,
volume = "7",
number = "2",
pages = "247--249",
month = jun,
year = "1981",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Feb 06 05:28:18 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Hill:1970:AASa,Hill:1970:AASb,elLozy:1979:RAS}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Hill:1981:RSQ,
author = "G. W. Hill",
title = "Remark on ``{Algorithm 396: Student's
$t$-Quantiles}''",
journal = j-TOMS,
volume = "7",
number = "2",
pages = "250--251",
month = jun,
year = "1981",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Feb 06 05:28:19 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Hill:1970:AASb}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Hough:1981:API,
author = "D. Hough",
title = "Application of the proposed {IEEE 754} standard for
floating-point arithmetic",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "70--74",
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1981.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
annote = "Various features of the proposed standard provide an
especially convenient environment for programming
numerical procedures such as the familiar elementary
functions.",
bydate = "MB",
byrev = "Le",
country = "USA",
date = "14/06/82",
descriptors = "Computer arithmetic; floating point; computation
structure; method; application; standard",
enum = "1418",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
location = "RWTH-AC-DFV: Bibl.",
references = "10",
revision = "21/04/91",
}
@Article{Iserles:1981:ARA,
author = "A. Iserles and M. J. D. Powell",
title = "On the {$A$}-acceptability of rational approximations
that interpolate the exponential function",
journal = j-IMA-J-NUMER-ANAL,
volume = "1",
number = "3",
pages = "241--251",
month = jul,
year = "1981",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/1.3.241",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65D15 (30E10)",
MRnumber = "83a:65015 (641308)",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
author-dates = "Michael James David Powell (29 July 1936--19 April
2015)",
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{James:1981:LTS,
author = "D. G. James",
title = "Linear transformations of the second elementary
function",
journal = j-LIN-AND-MULT-ALGEBRA,
volume = "10",
number = "4",
pages = "347--349",
year = "1981",
CODEN = "LNMLAZ",
ISSN = "0308-1087 (print), 1563-5139 (electronic)",
ISSN-L = "0308-1087",
MRclass = "15A69 (10C15)",
MRnumber = "83c:15023",
MRreviewer = "E. W. Ellers",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear and Multilinear Algebra",
journal-URL = "http://www.tandfonline.com/loi/glma20",
}
@Article{Kunz:1981:QZ,
author = "W. Kunz",
title = "{Quadratwurzel mit dem $ \mu $P Z80} \toenglish
{Square Roots with the Z80 Microprocessor}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "7",
pages = "109--110",
year = "1981",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Book{Lewin:1981:PAF,
author = "Leonard Lewin",
title = "Polylogarithms and Associated Functions",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xvii + 359",
year = "1981",
ISBN = "0-444-00550-1",
ISBN-13 = "978-0-444-00550-2",
LCCN = "QA342 .L47",
bibdate = "Fri Jun 16 13:56:23 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "22-Jul-1919--13-Aug-2007",
author-url = "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
remark = "Lightly revised and retitled edition of
\cite{Lewin:1958:DAF}.",
subject = "Logarithmic functions",
}
@InCollection{Longman:1981:DCA,
author = "I. M. Longman",
booktitle = "{Pad{\'e} approximation and its applications,
Amsterdam 1980 (Amsterdam, 1980)}",
title = "Difficulties of convergence acceleration",
volume = "888",
publisher = pub-SV,
address = pub-SV:adr,
pages = "273--289",
year = "1981",
MRclass = "65B10",
MRnumber = "649102 (83d:65013)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture Notes in Mathematics",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Maino:1981:CPC,
author = "G. Maino and E. Menapace and A. Ventura",
title = "Computation of parabolic cylinder functions by means
of a {Tricomi} expansion",
journal = j-J-COMPUT-PHYS,
volume = "40",
number = "2",
pages = "294--304",
month = apr,
year = "1981",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(81)90211-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:06 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181902114",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Markov:1981:ICE,
author = "S. M. Markov",
title = "On the interval computation of elementary functions",
journal = j-C-R-ACAD-BULGARE-SCI,
volume = "34",
number = "3",
pages = "319--322",
year = "1981",
CODEN = "DBANAD",
ISSN = "0366-8681",
MRclass = "65G10",
MRnumber = "83e:65084",
MRreviewer = "David F. Griffiths",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes rendus de l'Acad{\'e}mie bulgare des
sciences",
}
@Article{McCullagh:1981:RCS,
author = "Peter McCullagh",
title = "A rapidly convergent series for computing $ \psi (z) $
and its derivatives",
journal = j-MATH-COMPUT,
volume = "36",
number = "153",
pages = "247--248",
month = jan,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33A15)",
MRnumber = "81m:65028",
MRreviewer = "J. Gregor",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2007741",
acknowledgement = ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Imperial Coll. of Sci. and Technol., London, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "(mathematics); convergence; function evaluation; log
gamma function; poles; poles and zeros; rapidly
convergent series; series; series expansion; uniformly
convergent",
treatment = "T Theoretical or Mathematical",
}
@Article{Moon:1981:AFC,
author = "Wooil Moon",
title = "{Airy} function with complex arguments",
journal = j-COMP-PHYS-COMM,
volume = "22",
number = "4",
pages = "411--417",
month = may,
year = "1981",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(81)90138-7",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 09:27:06 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465581901387",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@TechReport{Morris:1981:NDL,
author = "Alfred H. {Morris, Jr.}",
title = "{NSWC\slash DL} Library of Mathematics Subroutines",
type = "Report",
number = "NSWC/TR-79-338",
institution = "Naval Surface Warfare Center",
address = "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
20903-5000, USA",
pages = "235",
year = "1981",
bibdate = "Tue Jun 13 08:47:19 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
note = "See also later editions
\cite{Morris:1990:NLM,Morris:1993:NLM}.",
URL = "https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA108106.xhtml",
abstract = "The NSWC/DL library is a library of general-purpose
FORTRAN subroutines that provide a basic computational
capability in a variety of mathematical activities.
Although intended for use on the CDC 6000 series
computers, emphasis has been placed on the
transportability of the codes. Subroutines are
available in the following areas: Elementary
Operations, Geometry, Special Functions, Polynomials,
Solutions of Nonlinear Equations, Vectors, Matrices,
Sparse Matrices, Eigenvalues and Eigenvectors, Least
Squares Solutions of Linear Equations, Optimization,
Transforms, Approximation of Functions, Curve Fitting,
Surface Fitting over Rectangular Grids, Surface Fitting
over Arbitrarily Positioned Data Points, Numerical
Integration, Ordinary Differential Equations/Initial
Value Problems, and Random Number Generation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Peng:1981:AES,
author = "Hong Peng",
title = "Algorithms for extracting square roots and cube
roots",
crossref = "IEEE:1981:PSC",
pages = "121--126",
year = "1981",
bibdate = "Thu Sep 01 11:37:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf",
abstract = "This paper describes a kind of algorithms for fast
extracting square roots and cube roots, their
mathematical proofs, their revised algorithm formulae,
and hardware implementation of the square root
algorithm. These algorithms may be of no significance
for large scale computer with fast division. But I am
sure that it is effective and economical to apply these
algorithms to the circuit designs of some mini- and
microcomputers with general multiplication and
division, such as nonrestoring division.",
acknowledgement = ack-nj,
keywords = "ARITH-5",
}
@Article{Razaz:1981:RAF,
author = "M. Razaz and J. L. Schonfelder",
title = "Remark on ``{Algorithm} 498: {Airy} Functions Using
{Chebyshev} Series Approximations''",
journal = j-TOMS,
volume = "7",
number = "3",
pages = "404--405",
month = sep,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355958.355971",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Aug 30 00:28:07 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Prince:1975:AAF}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Schulten:1981:NAE,
author = "Z. Schulten and R. G. Gordon and D. G. M. Anderson",
title = "A numerical algorithm for the evaluation of {Weber}
parabolic cylinder functions {$ U(a, x) $}, {$ V(a, x)
$}, and {$ W(a, \pm x) $}",
journal = j-J-COMPUT-PHYS,
volume = "42",
number = "2",
pages = "213--237",
month = aug,
year = "1981",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(81)90241-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:07 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181902412",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Shepherd:1981:CA,
author = "M. M. Shepherd and J. G. Laframboise",
title = "{Chebyshev} Approximation of $ (1 + 2 x) \exp (x^2)
\erfc (x) $ in $ 0 \leq x < \infty $",
journal = j-MATH-COMPUT,
volume = "36",
number = "153",
pages = "249--253",
month = jan,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20",
MRnumber = "83c:65029",
MRreviewer = "John P. Coleman",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "York Univ., Toronto, Ont., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "(1+2x)exp(x/sup 2/)erfc x; Chebyshev approximation;
Chebyshev expansion; erfc x; single",
treatment = "T Theoretical or Mathematical",
}
@Article{Smith:1981:ERA,
author = "J. M. Smith and F. W. J. Olver and D. W. Lozier",
title = "Extended-Range Arithmetic and Normalized {Legendre}
Polynomials",
journal = j-TOMS,
volume = "7",
number = "1",
pages = "93--105",
month = mar,
year = "1981",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65G05)",
MRnumber = "83a:65017",
bibdate = "Mon Aug 29 22:02:12 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/355934.355940",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "angular momentum; extended-range arithmetic; Legendre
polynomials; overflow; underflow",
}
@Article{Steinberg:1981:LSE,
author = "D. Steinberg and M. Rodeh",
title = "A layout for the shuffle-exchange network with {$
O(N^2 / \log^{3 / 2N}) $} area",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-30",
number = "12",
pages = "977--982",
month = dec,
year = "1981",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1981.1675738",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
catcode = "C.1.2; G.1.2",
CRclass = "C.1.2 Multiple Data Stream Architectures
(Multiprocessors); C.1.2 Interconnection architectures;
G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Interconnection architectures;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "IEEE Transactions on Computers",
genterm = "design",
guideno = "06519",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
jrldate = "Dec. 1981",
subject = "C. Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Article{Steinhardt:1981:ASF,
author = "Paul J. Steinhardt and P. Chaudhari",
title = "{Airy} stress function for atomic models",
journal = j-J-COMPUT-PHYS,
volume = "42",
number = "2",
pages = "266--276",
month = aug,
year = "1981",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(81)90244-8",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:07 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181902448",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@InProceedings{Taylor:1981:CHD,
author = "George S. Taylor",
title = "Compatible hardware for division and square root",
crossref = "IEEE:1981:PSC",
pages = "127--134",
year = "1981",
bibdate = "Mon Sep 16 16:30:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf",
abstract = "Hardware for radix four division and radix two square
root is shared in a processor designed to implement the
proposed IEEE floating-point standard. The division
hardware looks ahead to find the next quotient digit in
parallel with the next partial remainder. An 8-bit ALU
estimates the next remainder's leading bits. The
quotient digit look-up table is addressed with a
truncation of the estimate rather than a truncation of
the full partial remainder. The estimation ALU and the
look-up table are asymmetric for positive and negative
remainders. This asymmetry reduces the width of the ALU
and the number of minterms in the logic equations for
the look-up table. The square root algorithm obtains
the correctly rounded result in about two division
times using small extensions to the division
hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Temme:1981:ECH,
author = "N. M. Temme",
title = "On the expansion of confluent hypergeometric functions
in terms of {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "7",
number = "1",
pages = "27--32",
month = mar,
year = "1981",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:21 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X81900048",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Terras:1981:ASI,
author = "Riho Terras",
title = "Algorithms for some integrals of {Bessel} functions
and multivariate {Gaussian} integrals",
journal = j-J-COMPUT-PHYS,
volume = "41",
number = "1",
pages = "192--199",
month = may,
year = "1981",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(81)90087-5",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:06 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181900875",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Terras:1981:MAI,
author = "Riho Terras",
title = "A {Miller} algorithm for an incomplete {Bessel}
function",
journal = j-J-COMPUT-PHYS,
volume = "39",
number = "1",
pages = "233--240",
month = jan,
year = "1981",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(81)90147-9",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:04 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181901479",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Vogelius:1981:DRM,
author = "M. Vogelius and I. Babuska",
title = "On a dimensional reduction method. {II}. {Some}
approximation-theoretic results",
journal = j-MATH-COMPUT,
volume = "37",
number = "155",
pages = "47--68",
month = jul,
year = "1981",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.7",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.7 Ordinary Differential Equations;
G.1.7 Boundary value problems",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Boundary value problems",
fjournal = "Mathematics of Computation",
genterm = "theory",
guideno = "09396",
journal-URL = "http://www.ams.org/mcom/",
jrldate = "July 1981",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Wimp:1981:STT,
author = "Jet Wimp",
title = "Sequence Transformations and Their Applications",
volume = "154",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xix + 257",
year = "1981",
ISBN = "0-08-095662-9 (e-book), 0-12-757940-0",
ISBN-13 = "978-0-08-095662-6 (e-book), 978-0-12-757940-5",
LCCN = "QA292 .W54",
bibdate = "Thu Dec 1 11:08:47 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in Science and Engineering",
URL = "http://public.eblib.com/EBLPublic/PublicView.do?ptiID=453177",
acknowledgement = ack-nhfb,
subject = "Sequences (Mathematics) Transformations (Mathematics)
Numerical analysis; Acceleration of convergence",
tableofcontents = "Front Cover \\
Sequence Transformations and Their Applications \\
Copyright Page \\
Contents \\
Preface \\
Acknowledgments \\
Notation \\
Chapter 1. Sequences and Series \\
Chapter 2. Linear Transformations \\
Chapter 3. Linear Lozenge Methods \\
Chapter 4. Optimal Methods and Methods Based on Power
Series \\
Chapter 5. Nonlinear Lozenges \\
Iteration Sequences \\
Chapter 6. The Schmidt Transformation \\
The e-Algorithm \\
Chapter 7. Aitken's $d^2$-Process and Related Methods
\\
Chapter 8. Lozenge Algorithms and the Theory of
Continued Fractions \\
Chapter 9. Other Lozenge Algorithms and Nonlinear
MethodsChapter 10. The Brezinski--H{\aa}vie
ProtocolChapter 11. The Brezinski--H{\aa}vie Protocol
and Numerical Quadrature \\
Chapter 12. Probabilistic Methods \\
Chapter 13. Multiple Sequences \\
Appendix \\
Bibliography \\
Index",
}
@Article{Andrews:1982:MMS,
author = "M. Andrews",
title = "Mathematical Microprocessor Software: a $ \sqrt (x) $
Comparison",
journal = j-IEEE-MICRO,
volume = "2",
number = "3",
pages = "63--79",
month = may # "\slash " # jun,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.290970",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation);
C6150G (Diagnostic, testing, debugging and evaluating
systems)",
corpsource = "Colorado State Univ., Fort Collins, CO, USA",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "16-bit machines; 8-bit machine; accuracy; Chen method;
computer testing; Cordic method; direct method;
function approximation; hardware; Intel 8080; Newton
method; PDP-11/20; software requirements; speed;
square-roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Armengou:1982:ASQ,
author = "Santiago Zarzuela Armengou",
title = "About some questions of differential algebra
concerning to elementary functions",
journal = "Publ. Sec. Mat. Univ. Aut{\`o}noma Barcelona",
volume = "26",
number = "1",
pages = "5--15",
year = "1982",
MRclass = "12H05",
MRnumber = "86i:12009",
MRreviewer = "Michael F. Singer",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Barnett:1982:CCB,
author = "A. R. Barnett",
title = "{COULFG}: {Coulomb} and {Bessel} functions and their
derivatives, for real arguments, by {Steed}'s method",
journal = j-COMP-PHYS-COMM,
volume = "27",
number = "2",
pages = "147--166",
month = aug,
year = "1982",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(82)90070-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:03 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465582900704",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Barnett:1982:CFE,
author = "A. R. Barnett",
title = "Continued-fraction evaluation of {Coulomb} functions
{$ F_\lambda (\eta, x) $}, {$ G_\lambda (\eta, x) $}
and their derivatives",
journal = j-J-COMPUT-PHYS,
volume = "46",
number = "2",
pages = "171--188",
month = may,
year = "1982",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(82)90012-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:11 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999182900122",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Barnett:1982:HPE,
author = "A. R. Barnett",
title = "High-precision evaluation of the regular and irregular
{Coulomb} wavefunctions",
journal = j-J-COMPUT-APPL-MATH,
volume = "8",
number = "1",
pages = "29--33",
month = mar,
year = "1982",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X82900043",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@TechReport{Bazarov:1982:EEF,
author = "M. B. Bazarov and Yu. I. Shokin and Z. Kh. Yuldashev",
title = "On the Evaluation of Elementary Functions in Interval
Analysis (In {Russian})",
institution = "Applied Mathematics and Mechanics, Tashkent State
Univ.",
address = "Tashkent, USSR",
pages = "26--31",
year = "1982",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-jr # "\slash " # ack-nhfb,
}
@Article{Belevitch:1982:SIT,
author = "V. Belevitch and J. Boersma",
title = "On {Stieltjes} integral transforms involving {$ \Gamma
$}-functions",
journal = j-MATH-COMPUT,
volume = "38",
number = "157",
pages = "223--226",
month = jan,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "44A15 (33A15 33A45)",
MRnumber = "83d:44001",
MRreviewer = "V. M. Bhise",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0230 (Integral transforms); C1130 (Integral
transforms)",
corpsource = "Philips Res Lab., Brussels, Belgium",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Gamma functions; integral transforms; Stieltjes
transforms; systematic classification; transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Borwein:1982:MNT,
author = "P. B. Borwein",
title = "On a method of {Newman} and a theorem of {Bernstein}",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "1",
pages = "37--41",
month = jan,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "06012",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "Jan. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Brezinski:1982:ASG,
author = "C. Brezinski",
title = "{Algorithm 585}: a Subroutine for the General
Interpolation and Extrapolation Problems",
journal = j-TOMS,
volume = "8",
number = "3",
pages = "290--301",
month = sep,
year = "1982",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356004.356008",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Aug 29 23:49:19 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; convergence acceleration; extrapolation;
interpolation; least squares approximation;
Neville--Aitken scheme",
}
@Article{Brezinski:1982:SNC,
author = "Claude Brezinski",
title = "Some New Convergence Acceleration Methods",
journal = j-MATH-COMPUT,
volume = "39",
number = "159",
pages = "133--145",
month = jul,
year = "1982",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007624",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65B05",
MRnumber = "658218 (83f:65003)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "convergence acceleration",
}
@Article{Burr:1982:CCR,
author = "S. A. Burr",
title = "Computing cube roots when a fast square root is
available",
journal = j-COMPUT-MATH-APPL,
volume = "8",
number = "3",
pages = "181--183",
month = "????",
year = "1982",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(82)90041-4",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122182900414",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@Book{Carroll:1982:TST,
author = "Robert Wayne Carroll",
title = "Transmutation, scattering theory, and special
functions",
volume = "87; 69",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "x + 457",
year = "1982",
ISBN = "0-444-86426-1 (paperback)",
ISBN-13 = "978-0-444-86426-0 (paperback)",
LCCN = "QA1 .N86 no. 87; QA329",
bibdate = "Sat Oct 30 18:29:29 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "North-Holland mathematics studies",
acknowledgement = ack-nhfb,
subject = "Transmutation operators; Scattering (Mathematics);
Inverse problems (Differential equations); Functions,
Special",
}
@Article{Chambers:1982:UBF,
author = "Ll. G. Chambers",
title = "An upper bound for the first zero of {Bessel}
functions",
journal = j-MATH-COMPUT,
volume = "38",
number = "158",
pages = "589--591",
month = apr,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A65",
MRnumber = "83h:33011",
MRreviewer = "S. Ahmed",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Cody:1982:TTP,
author = "W. J. Cody",
title = "Transportable test procedures for elementary function
software",
crossref = "Mulvey:1982:EMP",
pages = "236--247",
year = "1982",
bibdate = "Thu Nov 17 06:39:08 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
}
@Article{Crick:1982:IRB,
author = "S. E. Crick",
title = "Inclusion relations for {Bernstein} quasi-analytic
classes",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "4",
pages = "375--379",
month = apr,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "algorithms; theory",
guideno = "07841",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "April 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Cruz:1982:ZHF,
author = "Andr{\'e}s Cruz and Javier Sesma",
title = "Zeros of the {Hankel} function of real order and of
its derivative",
journal = j-MATH-COMPUT,
volume = "39",
number = "160",
pages = "639--645",
month = oct,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A40",
MRnumber = "83j:33005",
MRreviewer = "S. Ahmed",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); B0290F (Interpolation
and function approximation); C4120 (Functional
analysis); C4130 (Interpolation and function
approximation)",
corpsource = "Dept. de Fisica Teorica, Univ. de Zaragoza, Zaragoza,
Spain",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximation; derivative; evaluation; function
approximation; function evaluation; Hankel function;
poles and zeros; real order; trajectories; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Danielopoulos:1982:CEP,
author = "S. D. Danielopoulos",
title = "On the Cost of Evaluating Polynomials and Their
Derivatives",
journal = j-COMPUTING,
volume = "29",
number = "4",
pages = "373--380",
year = "1982",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68C25 (68C20)",
MRnumber = "84a:68039",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Univ of Ioannina, Greece",
catcode = "G.1.2; G.4; G.1.0",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.4 Algorithm analysis; G.1.0 General;
G.1.0 Computer arithmetic",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic",
fjournal = "Computing",
genterm = "economics; theory",
guideno = "04049",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
jrldate = "1982",
keywords = "mathematical techniques",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Decker:1982:CAN,
author = "D. W. Decker and C. T. Kelley",
title = "Convergence acceleration for {Newton}'s method at
singular points",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "1",
pages = "219--229",
month = feb,
year = "1982",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65H05 (58E07 65J15)",
MRnumber = "83e:65090",
MRreviewer = "Michael Pr{\"u}fer",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "convergence acceleration",
}
@Article{Delahaye:1982:SLC,
author = "J. P. Delahaye and B. Germain-Bonne",
title = "The set of logarithmically convergent sequences cannot
be accelerated",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "4",
pages = "840--844",
month = aug,
year = "1982",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65B99",
MRnumber = "83f:65005",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "convergence acceleration",
}
@Article{Epstein:1982:UAF,
author = "C. Epstein and W. L. Miranker and T. J. Rivlin",
title = "Ultra-arithmetic {I}: function data types",
journal = j-MATH-COMP-SIM,
volume = "24",
number = "1",
pages = "1--18",
month = feb,
year = "1982",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1; G.1.2; G.1.2",
CRclass = "G.1.5 Roots of Nonlinear Equations; G.1.2
Approximation; G.1.2 Chebyshev approximation and
theory; G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Chebyshev
approximation and theory; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Mathematics and Computers in Simulation",
genterm = "algorithms",
guideno = "09324",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Epstein:1982:UAI,
author = "C. Epstein and W. L. Miranker and T. J. Rivlin",
title = "Ultra-arithmetic {II}: intervals of polynomials",
journal = j-MATH-COMP-SIM,
volume = "24",
number = "1",
pages = "19--29",
month = feb,
year = "1982",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.1; G.1.0",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.1 Interpolation; G.1.1 Spline and
piecewise polynomial interpolation; G.1.0 General;
G.1.0 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Spline and piecewise polynomial
interpolation; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Error analysis",
fjournal = "Mathematics and Computers in Simulation",
genterm = "algorithms",
guideno = "09325",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Fenton:1982:RCM,
author = "J. D. Fenton and R. S. Gardiner-Garden",
title = "Rapidly-convergent methods for evaluating elliptic
integrals and theta and elliptic functions",
journal = j-J-AUSTRAL-MATH-SOC-SER-B,
volume = "24",
number = "1",
pages = "47--58",
month = jul,
year = "1982",
CODEN = "JAMMDU",
DOI = "https://doi.org/10.1017/S0334270000003301",
ISSN = "0334-2700",
ISSN-L = "0334-2700",
bibdate = "Fri Apr 26 16:13:14 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.cambridge.org/core/journals/anziam-journal/article/rapidlyconvergent-methods-for-evaluating-elliptic-integrals-and-theta-and-elliptic-functions/2D993C9A7C9EB1D4B61B856E22B45A34",
acknowledgement = ack-nhfb,
ajournal = "J. Austral Math. Soc. Ser. B",
fjournal = "Journal of the Australian Mathematical Society. Series
B, Applied Mathematics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
onlinedate = "17 February 2009",
}
@Article{Fernandez:1982:HCI,
author = "F. M. Fern{\'a}ndez and A. Mes{\'o}n and E. A.
Castro",
title = "Hypervirial calculation of integrals involving
{Bessel} functions",
journal = j-J-MATH-PHYS,
volume = "23",
number = "2",
pages = "254--255",
month = feb,
year = "1982",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.525345",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "81C05 (33A40 82A51)",
MRnumber = "83c:81010",
bibdate = "Sat Oct 29 18:19:03 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v23/i2/p254_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "2",
}
@Article{Gawronski:1982:ACF,
author = "W. Gawronski and U. Stadtm{\"u}ller",
title = "Approximation of continuous functions by generalized
{Favard} operators",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "4",
pages = "384--396",
month = apr,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory; algorithms",
guideno = "06038",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "April 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Gessel:1982:SEH,
author = "Ira Gessel and Dennis Stanton",
title = "Strange Evaluations of Hypergeometric Series",
journal = j-SIAM-J-MATH-ANA,
volume = "13",
number = "2",
pages = "295--308",
month = mar,
year = "1982",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A30",
MRnumber = "83c:33002",
MRreviewer = "C. L. Parihar",
bibdate = "Sun Nov 28 19:22:53 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/13/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Gordon:1982:RAN,
author = "H. T. Gordon",
title = "Rough approximation numerical algorithms",
journal = j-DDJ,
volume = "7",
number = "7",
pages = "54--56",
month = jul,
year = "1982",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; G.1.2",
CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Dr. Dobb's Journal of Software Tools",
guideno = "04547",
jrldate = "July 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Greaves:1982:AHM,
author = "G. Greaves",
title = "An algorithm for the {Hausdorff} moment problem",
journal = j-NUM-MATH,
volume = "39",
number = "2",
pages = "231--238",
month = aug,
year = "1982",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Numerische Mathematik",
genterm = "algorithms",
guideno = "07489",
journal-URL = "http://link.springer.com/journal/211",
jrldate = "Aug. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Hawkes:1982:ANT,
author = "Alan G. Hawkes",
title = "Approximating the Normal Tail",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "31",
number = "3",
pages = "231--236",
month = sep,
year = "1982",
CODEN = "????",
DOI = "https://doi.org/10.2307/2987989",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Thu Jan 22 18:10:21 MST 2015",
bibsource = "http://www.jstor.org/stable/i349970;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-d-1980.bib",
URL = "http://www.jstor.org/stable/2987989",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
journal-URL = "http://www.jstor.org/journals/00390526.html",
}
@Article{Hermann:1982:SAG,
author = "Robert Hermann",
title = "Some algebraic, geometric, and system-theoretic
properties of the {Special Functions} of mathematical
physics",
journal = j-J-MATH-PHYS,
volume = "23",
number = "7",
pages = "1282--1294",
month = jul,
year = "1982",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.525511",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Sat Oct 29 18:19:10 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v23/i7/p1282_s1",
abstract = "It is known that many of the Special Functions of
mathematical physics appear as matrix elements of Lie
group representations. This paper is concerned with a
beginning attack on the converse problem, i.e., finding
conditions that a given function be a matrix element.
The methods used are based on a combination of ideas
from system theory, functional analysis, Lie theory,
differential algebra, and linear ordinary differential
equation theory. A key idea is to attach a symbol as an
element of a commutative algebra. In favorable cases,
this symbol defines a Riemann surface, and a
meromorphic differential form on that surface. The
topological and analytical invariants attached to this
form play a key role in system theory. The Lie algebras
of the groups appear as linear differential operators
on this Riemann surface. Finally, it is shown how the
Picard--Vessiot--Infeld--Hull theory of factorization
of linear differential operators leads to realization
of many Special Functions as matrix representations of
group representations.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "13",
}
@TechReport{Kahan:1982:BCC,
author = "W. Kahan",
title = "Branch Cuts for Complex Elementary Functions",
type = "Technical Report",
number = "PAM-105",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
year = "1982",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/Matrix.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "na, elementary function",
}
@Article{Keener:1982:CLB,
author = "L. L. Keener",
title = "Characterizing local best {SAIN} approximations",
journal = j-J-APPROX-THEORY,
volume = "36",
number = "1",
pages = "55--63",
month = sep,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Chebyshev approximation and
theory; G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Chebyshev approximation and theory;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "06074",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "Sept. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Lassey:1982:CCI,
author = "Keith R. Lassey",
title = "On the computation of certain integrals containing the
modified {Bessel} function $ {I}_0 (\xi) $",
journal = j-MATH-COMPUT,
volume = "39",
number = "160",
pages = "625--637",
month = oct,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20",
MRnumber = "83j:65029",
MRreviewer = "Walter Gautschi",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
B0290M (Numerical integration and differentiation);
C4130 (Interpolation and function approximation); C4160
(Numerical integration and differentiation)",
corpsource = "Inst. of Nuclear Sci., DSIR, Lower Hutt, New Zealand",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximation; approximation theory; convergence of
numerical methods; convergent series; function;
function approximation; integration; limiting
behaviour; modified Bessel; numerical integration;
one-dimensional integrals; two-dimensional integrals",
treatment = "T Theoretical or Mathematical",
}
@Article{Ling:1982:EIH,
author = "Chih Bing Ling and Ming Jing Wu",
title = "Evaluation of integrals of {Howland} type involving a
{Bessel} function",
journal = j-MATH-COMPUT,
volume = "38",
number = "157",
pages = "215--222",
month = jan,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05 (65D20)",
MRnumber = "82m:65003",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0220 (Mathematical analysis); B0290M (Numerical
integration and differentiation); C1120 (Mathematical
analysis); C4160 (Numerical integration and
differentiation)",
corpsource = "Dept. of Maths., Virginia Polytech. Inst. and State
Univ., Blacksburg, VA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "10D; 20D; accuracy; Bessel function; Bessel functions;
Howland type; integrals; integration; tabulated
values",
treatment = "T Theoretical or Mathematical",
}
@Article{McCormick:1982:EFM,
author = "S. F. McCormick and G. D. Taylor and D. V. Pryor",
title = "Evaluation of Functions on Microcomputers: $ \ln (x)
$",
journal = j-COMPUT-MATH-APPL,
volume = "8",
number = "5",
pages = "389--392",
month = "????",
year = "1982",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:23 MST 2017",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122182900323",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
xxmonth = "(none)",
}
@InCollection{Mori:1982:ARS,
author = "S. Mori and C. Y. Suen",
editor = "Ching Y. Suen and Renato {De Mori}",
key = "Scanners",
booktitle = "Computer analysis and perception: vol. I, {Visual}
signals",
title = "Automatic recognition of symbols and architecture of
the recognition unit",
publisher = pub-CRC,
address = pub-CRC:adr,
bookpages = "various",
pages = "17--40",
year = "1982",
ISBN = "0-8493-6305-5 (vol. 1), 0-8493-6306-3 (vol. 2)",
ISBN-13 = "978-0-8493-6305-4 (vol. 1), 978-0-8493-6306-1 (vol.
2)",
LCCN = "TA1650 .C65 1982",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "I.5; G.1.2; C.3; B.7; I.5.4",
CRclass = "I.5.2 Design Methodology; G.1.2 Approximation; G.1.2
Elementary function approximation; C.3 Signal
processing systems; B.7.1 Types and Design Styles;
I.5.4 Applications; I.5.4 Signal processing",
descriptor = "Computing Methodologies, PATTERN RECOGNITION, Design
Methodology; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Computer Systems Organization,
SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal
processing systems; Hardware, INTEGRATED CIRCUITS,
Types and Design Styles; Computing Methodologies,
PATTERN RECOGNITION, Applications, Signal processing",
genterm = "documentation; theory; design",
guideno = "01691",
subject = "I. Computing Methodologies; I.5 PATTERN RECOGNITION;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; C.
Computer Systems Organization; C.3 SPECIAL-PURPOSE AND
APPLICATION-BASED SYSTEMS; B. Hardware; B.7 INTEGRATED
CIRCUITS; I. Computing Methodologies; I.5 PATTERN
RECOGNITION",
}
@Article{Oklobdzija:1982:LSR,
author = "V. G. Oklobdzija and M. D. Ercegovac",
title = "An On-Line Square Root Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "1",
pages = "70--75",
month = jan,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675887",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ollin:1982:CFE,
author = "H. Z. Ollin and I. Gerst",
title = "Classes of functions with explicit best uniform
approximations",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "3",
pages = "264--276",
month = mar,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "06030",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "March 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Patel:1982:HND,
author = "Jagdish K. Patel and Campbell B. Read",
title = "Handbook of the Normal Distribution",
volume = "40",
publisher = pub-DEKKER,
address = pub-DEKKER:adr,
pages = "ix + 337",
year = "1982",
ISBN = "0-8247-1541-1",
ISBN-13 = "978-0-8247-1541-0",
LCCN = "QA273.6 .P373",
bibdate = "Sat Dec 16 17:22:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Statistics, textbooks and monographs",
acknowledgement = ack-nhfb,
subject = "Gaussian distribution",
}
@Article{Piessens:1982:ABF,
author = "R. Piessens and Maria Branders",
title = "Approximation for {Bessel} functions and their
application in the computation of {Hankel} transforms",
journal = j-COMPUT-MATH-APPL,
volume = "8",
number = "4",
pages = "305--311",
month = "????",
year = "1982",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122182900128",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@Article{Piessens:1982:ACB,
author = "R. Piessens",
title = "Automatic computation of {Bessel} function integrals",
journal = j-COMP-PHYS-COMM,
volume = "25",
number = "3",
pages = "289--295",
month = mar,
year = "1982",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(82)90024-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:01 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465582900248",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Rack:1982:GIV,
author = "H.-J Rack",
title = "A generalization of an inequality of {V. Markov} to
multivariate polynomials",
journal = j-J-APPROX-THEORY,
volume = "35",
number = "1",
pages = "94--97",
month = may,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "06047",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "May 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Rix:1982:UQA,
author = "P. Rix",
title = "{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus}
\toenglish {Universal Square Root Algorithms}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "23",
pages = "81--82",
year = "1982",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@PhdThesis{Rockey:1982:DMS,
author = "S. A. Rockey",
title = "Discrete methods of state approximation, parameter
identification and optimal control for hereditary
systems",
type = "{Ph.D} Thesis",
school = "Brown University",
address = "Providence, RI",
pages = "208",
year = "1982",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.2; G.1.5",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Linear
approximation; G.1.5 Roots of Nonlinear Equations;
G.1.5 Convergence",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Linear approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
Equations, Convergence",
guideno = "15449",
source = "UMI order no. DA8228325",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Sommer:1982:EPL,
author = "M. Sommer",
title = "Existence of pointwise-{Lipschitz}-continuous
selections of the metric projection for a class of
{$Z$}-spaces",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "2",
pages = "115--130",
month = feb,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "06018",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@PhdThesis{Wang:1982:AME,
author = "J.-L Wang",
title = "Asymptotically minimax estimators for distributions
with increasing failure rate",
type = "{Ph.D} Thesis",
school = "University of California, Berkeley",
address = "Berkeley, CA, USA",
pages = "42",
year = "1982",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "design",
guideno = "15084",
source = "UMI order no. DA8300696",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Whitley:1982:MBI,
author = "R. Whitley",
title = "{Markov} and {Bernstein}'s inequalities, and compact
and strictly singular operators",
journal = j-J-APPROX-THEORY,
volume = "34",
number = "3",
pages = "277--285",
month = mar,
year = "1982",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "06031",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "March 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Wilkes:1982:PPE,
author = "M. V. (Maurice Vincent) Wilkes and David J. Wheeler
and Stanley Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer: with Special Reference to the {EDSAC} and the
Use of a Library of Subroutines",
volume = "1",
publisher = pub-TOMASH,
address = pub-TOMASH:adr,
pages = "xxxi + 167",
year = "1982",
ISBN = "0-262-23118-2 (MIT Press 1984), 0-938228-03-X",
ISBN-13 = "978-0-262-23118-3 (MIT Press 1984),
978-0-938228-03-5",
LCCN = "QA76.6 .W545 1982",
bibdate = "Mon Feb 10 11:33:59 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With a new introduction by Martin Campbell-Kelly.",
series = "Charles Babbage Institute reprint series for the
history of computing",
acknowledgement = ack-nhfb,
}
@Article{Wills:1982:RCA,
author = "C. A. Wills and J. M. Blair and P. L. Ragde",
title = "Rational {Chebyshev} approximations for the {Bessel}
functions $ {J}_0 (x) $, $ {J}_1 (x) $, $ {Y}_0 (x) $,
$ {Y}_1 (x) $",
journal = j-MATH-COMPUT,
volume = "39",
number = "160",
pages = "617--623",
month = oct,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33A40 41A50)",
MRnumber = "83j:65030",
MRreviewer = "C. W. Clenshaw",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0260 (Optimisation techniques); B0290F (Interpolation
and function approximation); C1180 (Optimisation
techniques); C4130 (Interpolation and function
approximation)",
corpsource = "AEG Ltd., Chalk River Nuclear Labs., Ont., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximations; Bessel functions; Chebyshev; Chebyshev
approximation; formulae; McMahon asymptotic; minimax
techniques; near-minimax rational approximation",
treatment = "T Theoretical or Mathematical",
}
@PhdThesis{Wimp:1982:CMS,
author = "Jet (Jesse Jet) Wimp",
title = "Computational methods and special functions",
type = "{D.Sc.} thesis",
school = "University of Edinburgh",
address = "Edinburgh, UK",
year = "1982",
bibdate = "Thu Dec 01 11:15:32 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Amos:1983:APFa,
author = "D. E. Amos",
title = "{Algorithm 609}: a Portable {FORTRAN} Subroutine for
the {Bickley} Functions {$ \hbox {Ki}_n(x) $}",
journal = j-TOMS,
volume = "9",
number = "4",
pages = "480--493",
month = dec,
year = "1983",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356056.356064",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (33A70 65-04)",
MRnumber = "87a:65044",
bibdate = "Sun Sep 4 20:00:39 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
reviewer = "Marietta J. Tretter",
}
@Article{Amos:1983:APFb,
author = "Donald E. Amos",
title = "{Algorithm 610}: a Portable {FORTRAN} Subroutine for
Derivatives of the Psi Function",
journal = j-TOMS,
volume = "9",
number = "4",
pages = "494--502",
month = dec,
year = "1983",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356056.356065",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20",
MRnumber = "791 979",
bibdate = "Sun Sep 4 20:00:39 1994",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; G.1; G; D.3.2",
CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.m
Miscellaneous; D.3.2 Language Classifications; D.3.2
FORTRAN",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Miscellaneous; Mathematics of
Computing, MISCELLANEOUS; Software, PROGRAMMING
LANGUAGES, Language Classifications, FORTRAN",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
genterm = "ALGORITHMS",
guideno = "02212",
journal-URL = "https://dl.acm.org/loi/toms",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.m MISCELLANEOUS; D.
Software; D.3 PROGRAMMING LANGUAGES",
}
@Article{Benton:1983:CZT,
author = "T. C. Benton",
title = "Common Zeros of Two {Bessel} Functions. {Part II}.
{Approximations} and Tables",
journal = j-MATH-COMPUT,
volume = "41",
number = "163",
pages = "203--217",
month = jul,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A40 (65A05)",
MRnumber = "85a:33010",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
corpsource = "Dept. of Math., Pennsylvania State Univ., University
Park, PA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; computer program; poles and zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Bowman:1983:CFP,
author = "K. O. Bowman and L. R. Shenton",
title = "Continued fractions and the polygamma functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "9",
number = "1",
pages = "29--39",
month = mar,
year = "1983",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:24 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042783900262",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Brezinski:1983:CAE,
author = "C. Brezinski and J. P. Delahaye and B. Germain-Bonne",
title = "Convergence acceleration by extraction of linear
subsequences",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "6",
pages = "1099--1105",
month = dec,
year = "1983",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0720079",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65B99 (40A05)",
MRnumber = "723826 (85g:65014)",
MRreviewer = "John H. McCabe",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "convergence acceleration",
}
@Article{Brezinski:1983:ECC,
author = "Claude Brezinski",
title = "Error control in convergence acceleration processes",
journal = j-IMA-J-NUMER-ANAL,
volume = "3",
number = "1",
pages = "65--80",
year = "1983",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/3.1.65",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65B99 (65D32 65G05)",
MRnumber = "705081 (85a:65004)",
MRreviewer = "John P. Coleman",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "convergence acceleration",
}
@Article{Cash:1983:BRKa,
author = "J. R. Cash",
title = "Block {Runge--Kutta} Methods for the Numerical
Integration of Initial Value Problems in Ordinary
Differential Equations. {Part I}. {The} Nonstiff Case",
journal = j-MATH-COMPUT,
volume = "40",
number = "161",
pages = "175--191",
month = jan,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65L05",
MRnumber = "84d:65044a",
MRreviewer = "W. C. Rheinboldt",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
B0290M (Numerical integration and differentiation);
B0290P (Differential equations); C4130 (Interpolation
and function approximation); C4160 (Numerical
integration and differentiation); C4170 (Differential
equations)",
corpsource = "Dept. of Math., Imperial Coll., London, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximate numerical integration; approximation
theory; block implicit formulae; block Runge--Kutta
formulae; C. W. Gear; differential equations;
equations; first order; formulae; initial value;
initial value problems; integration; linear multistep
methods; nonstiff problems; order; ordinary
differential; problems; Runge--Kutta methods;
Runge--Kutta starters; stepsize; stiff problems;
systems; variable order; variable order block
explicit",
treatment = "T Theoretical or Mathematical",
}
@Article{Cody:1983:ASM,
author = "W. J. Cody",
title = "Algorithm 597: Sequence of Modified {Bessel} Functions
of the First Kind",
journal = j-TOMS,
volume = "9",
number = "2",
pages = "242--245",
month = jun,
year = "1983",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, MISCELLANEOUS",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
genterm = "algorithms",
guideno = "02186",
journal-URL = "https://dl.acm.org/loi/toms",
jrldate = "June 1983",
keywords = "algorithms",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation G
Mathematics of Computing, MISCELLANEOUS",
}
@Article{Coleman:1983:CEB,
author = "J. P. Coleman and A. J. Monaghan",
title = "{Chebyshev} expansions for the {Bessel} function $
{J}_n(z) $ in the complex plane",
journal = j-MATH-COMPUT,
volume = "40",
number = "161",
pages = "343--366",
month = jan,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05 (30E10 33A40 65D20)",
MRnumber = "84c:65013",
MRreviewer = "C. W. Clenshaw",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cruz:1983:MPR,
author = "Andr{\'e}s Cruz and Javier Sesma",
title = "Modulus and phase of the reduced logarithmic
derivative of the {Hankel} function",
journal = j-MATH-COMPUT,
volume = "41",
number = "164",
pages = "597--605",
month = oct,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A40 (65H05 81F10)",
MRnumber = "85b:33006",
MRreviewer = "H. E. Fettis",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cusick:1983:CCL,
author = "David Cusick",
title = "Computers \& Calculators: a Logarithm Algorithm for
Four-Function Calculators",
journal = j-TWO-YEAR-COLL-MATH-J,
volume = "14",
number = "4",
pages = "322--324",
month = sep,
year = "1983",
CODEN = "????",
DOI = "https://doi.org/10.1080/00494925.1983.11972706",
ISSN = "0049-4925 (print), 2325-9116 (electronic)",
ISSN-L = "0049-4925",
bibdate = "Thu Feb 14 09:49:45 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00494925.1983.11972706;
https://www.jstor.org/stable/3027283",
acknowledgement = ack-nhfb,
fjournal = "Two-Year College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
http://www.jstor.org/journals/00494925.html",
onlinedate = "30 Jan 2018",
}
@Article{Demsky:1983:MMC,
author = "J. Demsky and M. Schlesinger and R. D. Kent",
title = "Micro/mini computer program for calculating the square
root of rationals at arbitrary precision",
journal = j-COMP-PHYS-COMM,
volume = "29",
number = "3",
pages = "237--244",
month = may,
year = "1983",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(83)90004-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:04 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583900048",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Dietrich:1983:VQF,
author = "D. Dietrich",
title = "{Verfahren zur L{\"o}sung von Quadratwurzeln f{\"u}r
Mikrorechnerprozeduren} \toenglish {Methods for the
Solution of Square Roots for Microprocessor
Subroutines} \endtoenglish",
journal = j-ELEKTRONIKER,
volume = "8",
pages = "EL-1--EL-6",
year = "1983",
CODEN = "ELKRBL",
ISSN = "0531-9218",
bibdate = "Fri Dec 08 13:05:49 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektroniker (Switzerland)",
}
@Article{Dubrulle:1983:CNM,
author = "Augustin A. Dubrulle",
title = "Class of Numerical Methods for the Computation of
{Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "582--589",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Moler:1983:RSR} and generalization
\cite{Jamieson:1989:RCI}.",
abstract = "Moler and Morrison have described an iterative
algorithm for the computation of the Pythagorean sum
(a**2 plus b**2)** one-half of two real numbers a and
b. This algorithm is immune to unwarranted
floating-point overflows, has a cubic rate of
convergence, and is easily transportable. This paper,
which shows that the algorithm is essentially Halley's
method applied to the computation of square roots,
provides a generalization to any order of convergence.
Formulas of orders 2 through 9 are illustrated with
numerical examples. The generalization keeps the number
of floating-point divisions constant and should be
particularly useful for computation in high-precision
floating-point arithmetic.",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C5230 (Digital
arithmetic methods)",
classification = "723; 921",
corpsource = "IBM Sci. Centre, Palo Alto, CA, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
journalabr = "IBM J Res Dev",
keywords = "computer programming; digital arithmetic;
floating-point divisions; Halley's method;
high-precision floating-point arithmetic; iterative
algorithm; iterative methods; mathematical techniques
--- Numerical Methods; Pythagorean sums; rate of
convergence; square roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Ellacott:1983:FTE,
author = "S. W. Ellacott",
title = "On the {Faber} transform and efficient numerical
rational approximation",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "5",
pages = "989--1000",
month = oct,
year = "1983",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "41A20 (41A21)",
MRnumber = "85f:41010",
MRreviewer = "Lee L. Keener",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Fessler:1983:HAA,
author = "Theodore Fessler and William F. Ford and David A.
Smith",
title = "{HURRY}: An Acceleration Algorithm for Scalar
Sequences and Series",
journal = j-TOMS,
volume = "9",
number = "3",
pages = "346--354",
month = sep,
year = "1983",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356044.356051",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65B10",
MRnumber = "791 970",
bibdate = "Sun Sep 04 19:50:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Fukushima:1983:OAA,
author = "M. Fukushima",
title = "An outer approximation algorithm for solving general
convex programs",
journal = j-OPER-RES,
volume = "31",
number = "1",
pages = "101--113",
month = feb,
year = "1983",
CODEN = "OPREAI",
ISSN = "0030-364X (print), 1526-5463 (electronic)",
ISSN-L = "0030-364X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.4",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.4 Efficiency",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Efficiency",
fjournal = "Operations Research",
genterm = "algorithms; documentation; performance; reliability;
theory",
guideno = "09992",
journal-URL = "http://pubsonline.informs.org/loi/opre",
jrldate = "Jan./Feb. 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.4 MATHEMATICAL
SOFTWARE",
}
@Article{Giordano:1983:EAZ,
author = "C. Giordano and A. Laforgia",
title = "Elementary approximations for zeros of {Bessel}
functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "9",
number = "3",
pages = "221--228",
month = sep,
year = "1983",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Computational and Applied Mathematics",
genterm = "theory",
guideno = "08115",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
jrldate = "Sept. 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Hasson:1983:C,
author = "M. Hasson and O. Shisha",
title = "On the condition {$ \sum^{\infty }_{n = 1}n^{p -
1}E^*_n(f) < \infty $}",
journal = j-J-APPROX-THEORY,
volume = "39",
number = "4",
pages = "389--398",
month = dec,
year = "1983",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "42A10 (41A10)",
MRnumber = "85a:42002",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "07952",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "Dec. 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Johnson:1983:MGC,
author = "Gary M. Johnson",
title = "Multiple-grid convergence acceleration of viscous and
inviscid flow computations",
journal = j-APPL-MATH-COMP,
volume = "13",
number = "3--4",
pages = "375--398",
month = nov,
year = "1983",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "76-08",
MRnumber = "84m:76010",
bibdate = "Thu Feb 27 09:47:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "convergence acceleration",
}
@Article{Kershaw:1983:SEW,
author = "D. Kershaw",
title = "Some extensions of {W. Gautschi}'s inequalities for
the gamma function",
journal = j-MATH-COMPUT,
volume = "41",
number = "164",
pages = "607--611",
month = oct,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A15 (26D20 65D20)",
MRnumber = "84m:33003",
MRreviewer = "P. Anandani",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lehnhoff:1983:NPT,
author = "H.-G Lehnhoff",
title = "A new proof of {Teljakowskii}'s theorem",
journal = j-J-APPROX-THEORY,
volume = "38",
number = "2",
pages = "177--181",
month = jun,
year = "1983",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "07897",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "June 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Lehnhoff:1983:SPF,
author = "H.-G Lehnhoff",
title = "A simple proof of a {A. F. Timan}'s theorem",
journal = j-J-APPROX-THEORY,
volume = "38",
number = "2",
pages = "172--176",
month = jun,
year = "1983",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory",
guideno = "07896",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
jrldate = "June 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Little:1983:CCS,
author = "F. Little",
editor = "Robert E. Barnhill and Wolfgang Boehm",
booktitle = "Surfaces in computer aided geometric design:
proceedings of a conference held at Mathematisches
Forschungsinstitut Oberwolfach, {F.R.G.}, April 25--30,
1982, organized by Wolfgang Boehm and Josef Hoschek",
title = "Convex combination surfaces",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
bookpages = "xvi + 215",
pages = "99--109",
year = "1983",
ISBN = "0-444-86550-0",
ISBN-13 = "978-0-444-86550-2",
LCCN = "T385 .S827 1982",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.1; G.1.1; G.1.2",
CRclass = "G.1.1 Interpolation; G.1.1 Interpolation formulas;
G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Interpolation formulas; Mathematics of
Computing, NUMERICAL ANALYSIS, Interpolation,
Smoothing; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "theory",
guideno = "13093",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@TechReport{Lutskii:1983:VFT,
author = "G. M. Lutski{\u\i} and O. I. Penchev",
title = "{{\cyr Vychislenie {\`e}lementarnykh funktsi{\u\i}
metodom tsifra za tsifro{\u\i} v izbytochnykh sistemakh
schisleniya}}. ({Russian}) [Calculation of elementary
functions by the digit-by-digit method in redundant
number systems]",
type = "Preprint",
number = "83-22",
institution = "Akad. Nauk Ukrain. SSR, Inst. Kibernet.",
address = "Kiev, USSR",
pages = "30",
year = "1983",
MRclass = "65D20",
MRnumber = "719 021",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Mason:1983:CBF,
author = "Janet P. Mason",
title = "Cylindrical {Bessel} functions for a large range of
complex arguments",
journal = j-COMP-PHYS-COMM,
volume = "30",
number = "1",
pages = "1--11",
month = jul # "\slash " # aug,
year = "1983",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(83)90116-9",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:05 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583901169",
abstract = "The evaluation of Bessel functions of the first and
second kinds, covering a wide range of complex
arguments and integer orders, is required in the
determination of the intensity of acoustic reflection
from absorbing bodies. Numerical problems associated
with the calculations are discussed and various means
by which these problems have been overcome are
explained. The numerical methods used in calculating
the Bessel functions of the first, second and third
kinds are given, as well as sample results and
numerical checks in the form of computer plots and
printouts.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{McCabe:1983:ASC,
author = "J. H. McCabe",
title = "On an asymptotic series and corresponding continued
fraction for a gamma function ratio",
journal = j-J-COMPUT-APPL-MATH,
volume = "9",
number = "2",
pages = "125--130",
month = jun,
year = "1983",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:24 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042783900353",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@TechReport{McCurdy:1983:ACD,
author = "A. McCurdy and K. C. Ng and Beresford N. Parlett",
title = "Accurate computation of divided differences of the
exponential function",
type = "Report",
number = "PAM-160",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1983",
bibdate = "Fri Nov 11 09:06:19 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Meister:1983:MYF,
author = "B. Meister",
title = "On {Murphy}'s yield formula",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "545--548",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "B.7.1; G.1.2",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Input/Output
circuits; G.1.2 Approximation; G.1.2 Elementary
function approximation",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Input/Output circuits; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
fjournal = "IBM Journal of Research and Development",
genterm = "theory; design; reliability",
guideno = "06316",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
jrldate = "Nov. 1983",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; G. Mathematics
of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Mlodzki:1983:PPC,
author = "J. Mlodzki and J. Kuszkowski and M. Suffczynski",
title = "A {Pascal} program for calculating the reduced
{Coulomb} {Green}'s functions and their partial waves",
journal = j-COMP-PHYS-COMM,
volume = "29",
number = "4",
pages = "341--350",
month = jun,
year = "1983",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(83)90013-9",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Feb 24 18:49:59 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583900139",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Moler:1983:MSV,
author = "C. Moler",
editor = "????",
booktitle = "{SIAM Conference on Parallel Processing for Scientific
Computing, Norfolk, VA, November 10--11, 1983}",
title = "Mathematical Software for Vector Computers",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "??--??",
year = "1983",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Fri Sep 20 14:42:46 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[Reference 11]{Agarwal:1986:NSV} in
elefunt.bib and fparith.bib.",
}
@Article{Moler:1983:RSR,
author = "Cleve B. Moler and Donald Morrison",
title = "Replacing Square Roots by {Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "577--581",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Dubrulle:1983:CNM} and generalization
\cite{Jamieson:1989:RCI}.",
URL = "http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf",
abstract = "An algorithm is presented for computing a 'Pythagorean
sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from
a and b without computing their squares or taking a
square root. No destructive floating point overflows or
underflows are possible. The algorithm can be extended
to compute the Euclidean norm of a vector. The
resulting subroutine is short, portable, robust, and
accurate, but not as efficient as some other
possibilities. The algorithm is particularly attractive
for computers where space and reliability are more
important than speed",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4190 (Other numerical methods); C5230 (Digital
arithmetic methods)",
corpsource = "Dept. of Computer Sci., Univ. of New Mexico,
Albuquerque, NM, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "algorithms; digital arithmetic; Euclidean norm;
floating-point arithmetic; iterative methods;
performance; Pythagorean sums; subroutine; vector",
review = "ACM CR 8406-0463",
subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations \\ F.2.1 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials \\ F.2.2 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations",
treatment = "T Theoretical or Mathematical",
}
@PhdThesis{Monk:1983:SFE,
author = "P. B. Monk",
title = "Some finite element methods for the approximation of
the biharmonic equation",
type = "{Ph.D} Thesis",
school = "Rutgers University, The State University of New
Jersey",
address = "New Brunswick, NJ, USA",
pages = "242",
year = "1983",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.8; G.1.2",
CRclass = "G.1.8 Partial Differential Equations; G.1.8 Finite
element methods; G.1.2 Approximation; G.1.2 Elementary
function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations, Finite element methods;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "design; algorithms; experimentation",
guideno = "15929",
source = "UMI order no. DA8308441",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Muench:1983:LAF,
author = "Donald L. Muench and Gerald Wildenberg",
title = "A Logarithm Algorithm for a Five-Function Calculator",
journal = j-TWO-YEAR-COLL-MATH-J,
volume = "14",
number = "4",
pages = "324--326",
month = sep,
year = "1983",
CODEN = "????",
DOI = "https://doi.org/10.1080/00494925.1983.11972707",
ISSN = "0049-4925 (print), 2325-9116 (electronic)",
ISSN-L = "0049-4925",
bibdate = "Thu Feb 14 09:49:45 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00494925.1983.11972707",
acknowledgement = ack-nhfb,
fjournal = "Two-Year College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
http://www.jstor.org/journals/00494925.html",
onlinedate = "30 Jan 2018",
}
@Article{Nave:1983:ITF,
author = "Rafi Nave",
key = "Nav83",
title = "Implementation of Transcendental Functions on a
Numerics Processor",
journal = j-MICROPROC-MICROPROG,
volume = "11",
pages = "221--225",
year = "1983",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Microprocessing and Microprogramming",
}
@Article{Piessens:1983:MCC,
author = "Robert Piessens and Maria Branders",
title = "Modified {Clenshaw--Curtis} method for the computation
of {Bessel} function integrals",
journal = j-BIT,
volume = "23",
number = "3",
pages = "370--381",
month = sep,
year = "1983",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934465",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D30 (65R10)",
MRnumber = "85b:65019 (705003)",
MRreviewer = "H. E. Fettis",
bibdate = "Sun Nov 12 06:18:24 2023",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=23&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=23&issue=3&spage=370",
acknowledgement = ack-nhfb,
fjournal = "BIT. Nordisk Tidskrift for Informationsbehandling
(BIT)",
journal-URL = "http://link.springer.com/journal/10543",
subject-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
}
@Article{Prosser:1983:NCS,
author = "C. J. Prosser",
title = "A note on computing the square root of an integer",
journal = j-COMP-J,
volume = "26",
number = "2",
pages = "187--188",
month = may,
year = "1983",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C7310 (Mathematics
computing)",
corpsource = "Rutherford and Appleton Lab., Chilton, Didcot, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary; computer; fixed-point number; integer;
interactive methods; iterative methods; PASCAL; Pascal
implementation; square root; subroutines; successive
subtraction",
treatment = "P Practical",
}
@Article{Salzer:1983:NDG,
author = "Herbert E. Salzer",
title = "Note on the {Do{\v{c}}ev--Grosswald} asymptotic series
for generalized {Bessel} polynomials",
journal = j-J-COMPUT-APPL-MATH,
volume = "9",
number = "2",
pages = "131--135",
month = jun,
year = "1983",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:24 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
note = "See errata \cite{Anonymous:1984:EJCb}.",
URL = "http://www.sciencedirect.com/science/article/pii/0377042783900365",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Sidi:1983:ZSP,
author = "Avram Sidi and Doron S. Lubinsky",
title = "On the zeros of some polynomials that arise in
numerical quadrature and convergence acceleration",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "2",
pages = "400--405",
month = apr,
year = "1983",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0720028",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65H05 (65D30)",
MRnumber = "694528 (84f:65046)",
MRreviewer = "J. G. Herriot",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "convergence acceleration",
}
@Article{Talman:1983:LSC,
author = "James D. Talman",
title = "{LSFBTR}: a subroutine for calculating spherical
{Bessel} transforms",
journal = j-COMP-PHYS-COMM,
volume = "30",
number = "1",
pages = "93--99",
month = jul # "\slash " # aug,
year = "1983",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(83)90126-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:05 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583901261",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Temme:1983:NCC,
author = "N. M. Temme",
title = "The numerical computation of the confluent
hypergeometric function $ {U}(a, \, b, \, z) $",
journal = j-NUM-MATH,
volume = "41",
number = "1",
pages = "63--82",
month = apr,
year = "1983",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D20 (33A30 65D15)",
MRnumber = "84g:65030",
MRreviewer = "H. E. Fettis",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "Math. Centrum, Amsterdam, Netherlands",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "ALGOL 60 procedures; asymptotic expansions; confluent
hypergeometric function; function computation; function
evaluation; Miller algorithm; subroutines",
treatment = "P Practical; T Theoretical or Mathematical",
}
@TechReport{Temme:1983:TTR,
author = "N. M. Temme",
title = "Traces to {Tricomi} in recent work on special
functions and asymptotics of integrals",
type = "Report",
number = "TW 239/83",
institution = "Stichting mathematisch Centrum",
address = "Amsterdam, The Netherlands",
pages = "15",
year = "1983",
LCCN = "A1 M462 TW239/83",
bibdate = "Sat Oct 30 18:29:48 2010",
bibsource = "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Temme:1983:UAE,
author = "Nico M. Temme",
title = "Uniform asymptotic expansions of {Laplace} integrals",
journal = "Analysis",
volume = "3",
number = "1--4",
pages = "221--249",
year = "1983",
ISSN = "0174-4747 (print), 2196-6753 (electronic)",
ISSN-L = "0174-4747",
MRclass = "41A60 (44A10)",
MRnumber = "756117",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Feb 6 11:39:36 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Analysis. International Journal of Analysis and its
Application",
}
@Article{Volz:1983:CAA,
author = "H. V{\"o}lz",
title = "{CORDIC und {\"a}hnliche Algorithmen der elementaren
Funktionen mit besonderer Eignung f{\"u}r Mikrorechner}
\toenglish {CORDIC and Similar Algorithms for
Elementary Functions with Particular Aptitude for
Microcomputers} \endtoenglish",
journal = j-NACH-ELEK,
volume = "33",
number = "12",
pages = "506--510",
month = "????",
year = "1983",
CODEN = "NTELAP",
ISSN = "0323-4657",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
fjournal = "Nachrichtentechnik Elektronik",
}
@Article{Wejntrob:1983:ASR,
author = "Leon Wejntrob",
title = "Approximation of Square Roots",
journal = j-TWO-YEAR-COLL-MATH-J,
volume = "14",
number = "5",
pages = "427--431",
month = nov,
year = "1983",
CODEN = "????",
DOI = "https://doi.org/10.1080/00494925.1983.11972733",
ISSN = "0049-4925 (print), 2325-9116 (electronic)",
ISSN-L = "0049-4925",
bibdate = "Thu Feb 14 09:49:48 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00494925.1983.11972733",
acknowledgement = ack-nhfb,
fjournal = "Two-Year College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
http://www.jstor.org/journals/00494925.html",
keywords = "rational square roots of rational numbers",
onlinedate = "30 Jan 2018",
}
@Article{Xu:1983:HPG,
author = "Xian Yu Xu and Jia Kai Li and Gui Jing Xiong and Guo
Liang Xu and Chun Qing Lu",
title = "High-precision generation of elementary functions.
({Chinese})",
journal = "Appl. Math. Math. Comput.",
volume = "6",
pages = "24--32",
year = "1983",
MRclass = "65D20",
MRnumber = "86e:65031",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1984:EJCb,
author = "Anonymous",
title = "Errata: {J. Comput. Appl. Math. {\bf 9}: H. E. Salzer,
Note on the Do{\v{c}}ev--Grosswald asymptotic series
for generalized Bessel polynomials, (1983) 131--135}",
journal = j-J-COMPUT-APPL-MATH,
volume = "10",
number = "1",
pages = "133--133",
month = feb,
year = "1984",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:53 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
note = "See \cite{Salzer:1983:NDG}.",
URL = "http://www.sciencedirect.com/science/article/pii/0377042784900773",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Ardill:1984:ABF,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "Accurate {Bessel} functions {$ J_n(z) $}, {$ Y_n(z)
$}, {$ H_n^{(1)}(z) $} and {$ H_n^{(2)}(z) $} of
integer order and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-559--C-559",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82734-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:33 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584827344",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Ardill:1984:BFC,
author = "W. B. Ardill and K. J. M. Moriarty",
title = "The {Bessel} functions {$ J_0 $} and {$ J_1 $} of
complex argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
pages = "C-409--C-409",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82619-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Ardill:1984:SBF,
author = "R. W. B. Ardill and K. J. M. Moriarty",
title = "Spherical {Bessel} functions $ j_n $ and $ y_n $ of
integer order and real argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
pages = "C-466--C-466",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82666-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "No code shown, but uses formulas from
\cite{Abramowitz:1964:HMF} for evaluations. Function
name is {\tt sphbes}.",
}
@Article{Bardin:1984:CFE,
author = "C. Bardin and Y. Dandeu and L. Gauthier and J.
Guillermin and T. Lena and J.-M. Pernet and H. H.
Wolter and T. Tamura",
title = "{Coulomb} functions in entire $ (\eta, \pi) $-plane",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-125--C-126",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82382-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:06 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584823826",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Barnett:1984:CCB,
author = "A. R. Barnett",
title = "{Coulfg}: {Coulomb} and {Bessel} functions and their
derivatives, for real arguments, by {Steed}'s method",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-812--C-813",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82930-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584829306",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Barnett:1984:CWF,
author = "A. R. Barnett and D. H. Feng and J. W. Steed and L. J.
B. Goldfarb",
title = "{Coulomb} wave functions for all real $ \eta $ and $
\rho $",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-285",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82515-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:15 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584825151",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Barnett:1984:KCF,
author = "A. R. Barnett",
title = "{Klein}: {Coulomb} functions for real $ \lambda $ and
positive energy to high accuracy",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-753",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82884-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828842",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Barnett:1984:RMR,
author = "A. R. Barnett",
title = "{RCWFF} --- a modification of the real {Coulomb}
wavefunction program {RCWFN}",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-370",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82585-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:24 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584825850",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Bell:1984:CFN,
author = "K. L. Bell and N. S. Scott",
title = "{Coulomb} functions (negative energies)",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-648",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82808-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:41 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828088",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InCollection{Berges:1984:AFE,
author = "J. C. Berges",
booktitle = "Space mathematics",
title = "Arithm{\'e}tique et fonctions {\'e}l{\'e}mentaires sur
mini-micro calculateurs. ({French}) [Arithmetic and
elementary functions on mini-micro computers]",
publisher = "C{\'e}padu{\`e}s",
address = "Toulouse, France",
pages = "193--229",
year = "1984",
MRclass = "65-01 (65-04)",
MRnumber = "849 200",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Berndt:1984:APA,
author = "Bruce C. Berndt and Larry A. Goldberg",
title = "Analytic properties of arithmetic sums arising in the
theory of the classical theta functions",
journal = j-SIAM-J-MATH-ANA,
volume = "15",
number = "1",
pages = "143--150",
month = jan,
year = "1984",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "11A15 (11A25 11F27)",
MRnumber = "85d:11008",
MRreviewer = "T. M. Apostol",
bibdate = "Sun Nov 28 19:23:19 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/15/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Black:1984:NIS,
author = "Cheryl M. Black and Robert P. Burton and Thomas H.
Miller",
title = "The Need for an Industry Standard of Accuracy for
Elementary-Function Programs",
journal = j-TOMS,
volume = "10",
number = "4",
pages = "361--366",
month = dec,
year = "1984",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20",
MRnumber = "792 000",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; G.1.2; G.4",
CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.4 Efficiency",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, MATHEMATICAL
SOFTWARE, Efficiency",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
genterm = "theory; algorithms; reliability; standardization",
guideno = "02897",
journal-URL = "https://dl.acm.org/loi/toms",
jrldate = "Dec. 1984",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE",
}
@Article{Borwein:1984:AGM,
author = "J. M. Borwein and P. B. Borwein",
title = "The Arithmetic-Geometric Mean and Fast Computation of
Elementary Functions",
journal = j-SIAM-REVIEW,
volume = "26",
number = "3",
pages = "351--366",
month = jul,
year = "1984",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1026073",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D20 (26A09)",
MRnumber = "86d:65029",
MRreviewer = "S. Conde",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
abstract = "We produce a self contained account of the
relationship between the Gaussian arithmetic-geometric
mean iteration and the fast computation of elementary
functions. A particularly pleasant algorithm for pi is
one of the by-products.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
classification = "723; 921",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "AGM (Arithmetic-Geometric Mean); arithmetic-geometric
mean; calculation of pi; computational methods;
elliptic functions; Iterative Methods; mathematical
techniques; numerical mathematics",
}
@Article{Braess:1984:RAE,
author = "Dietrich Braess",
title = "On rational approximation of the exponential and the
square root function",
journal = j-LECT-NOTES-MATH,
volume = "1105",
pages = "89--99",
year = "1984",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0072401",
ISBN = "3-540-13899-4 (print), 3-540-39113-4 (e-book)",
ISBN-13 = "978-3-540-13899-0 (print), 978-3-540-39113-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "41A20 (41A25 65D15)",
MRnumber = "783263 (86g:41025)",
MRreviewer = "G. Meinardus",
bibdate = "Fri May 9 19:07:44 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0072401/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0072395",
book-URL = "http://www.springerlink.com/content/978-3-540-39113-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Campbell:1984:BFRa,
author = "J. B. Campbell",
title = "{Bessel} Functions {$ J_\nu (x) $} of real order and
real argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-583--C-583",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82756-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:33 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584827563",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Campbell:1984:BFZ,
author = "J. B. Campbell",
title = "{Bessel} functions {$ I_\nu (z) $} and {$ K_\nu (z) $}
of real order and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-747--C-748",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82880-5",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828805",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Coleman:1984:FSB,
author = "J. P. Coleman",
title = "A {Fortran} subroutine for the {Bessel} function {$
J_n(x) $} of order $0$ to $ 10 $",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-654--C-654",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82814-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:41 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828143",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "No code shown, but sums two separate Chebyshev series,
one for $x$ in $ [0, 8] $, and a second for $x$ in $
(8, \infty) $. Function name is {\tt realjn}.",
}
@Article{Delic:1984:CSS,
author = "G. Delic",
title = "{Chebyshev} series for the spherical {Bessel} function
$ j_l(r) $",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-577--C-577",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82751-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:33 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584827514",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Demsky:1984:MMC,
author = "J. Demsky and M. Schlesinger and R. D. Kent",
title = "Micro/mini computer program for calculating the square
root of rationals at arbitrary precision",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-877",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82981-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:58 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584829811",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Dhanoa:1984:BPE,
author = "M. S. Dhanoa and J. France",
title = "A {BASIC} program for the evaluation of the gamma
functions",
journal = j-J-APPL-STAT,
volume = "11",
number = "2",
pages = "225--228",
year = "1984",
CODEN = "????",
DOI = "https://doi.org/10.1080/02664768400000021",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:15:50 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "24 May 2006",
}
@TechReport{DiDonato:1984:IGF,
author = "Armido R. DiDonato",
title = "The incomplete gamma function ratios using {Temme}'s
asymptotic expansions",
type = "Report",
number = "NSWC TR 84-79",
institution = "Naval Surface Weapons Center",
address = "Dahlgren, VA, USA",
year = "1984",
bibdate = "Mon Jun 03 12:24:32 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Dutka:1984:EHH,
author = "Jacques Dutka",
title = "The early history of the hypergeometric function",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "31",
number = "1",
pages = "15--34",
month = mar,
year = "1984",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/BF00330241",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A50 (33-03)",
MRnumber = "769538 (86d:01010)",
MRreviewer = "Willard Parker",
bibdate = "Fri Feb 4 21:50:21 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=31&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=31&issue=1&spage=15",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
MRtitle = "The early history of the hypergeometric function",
}
@Article{Fransen:1984:CMM,
author = "Arne Frans{\'e}n and Staffan Wrigge",
title = "Calculation of the moments and the moment generating
function for the reciprocal gamma distribution",
journal = j-MATH-COMPUT,
volume = "42",
number = "166",
pages = "601--616",
month = apr,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (60E10 62E15 65U05)",
MRnumber = "86f:65042a",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C1210B (Reliability theory); C4130 (Interpolation and
function approximation)",
corpsource = "Nat. Defence Res. Inst., Stockholm, Sweden",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "kurtosis; moment generating function; moments;
polynomials; reciprocal gamma distribution; reliability
theory; skewness; variance",
treatment = "T Theoretical or Mathematical",
}
@Article{Glaeske:1984:LTS,
author = "H.-J. Glaeske and O. I. Mari{\v{c}}ev",
title = "The {Laguerre} transform of some elementary
functions",
journal = j-Z-ANAL-ANWEND,
volume = "3",
number = "3",
pages = "237--244",
year = "1984",
ISSN = "0232-2064 (print), 1661-4534 (electronic)",
ISSN-L = "0232-2064",
MRclass = "44A15 (34A10)",
MRnumber = "86a:44005",
MRreviewer = "Ram Kishore Saxena",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Analysis und ihre Anwendungen}",
}
@Article{Grodd:1984:REN,
author = "Laurence W. Grodd and Charles M. Patton",
title = "{ROM} extends numerical function set of handheld
computer",
journal = j-HEWLETT-PACKARD-J,
volume = "35",
number = "7",
pages = "25--36",
month = jul,
year = "1984",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Tue Mar 25 14:12:15 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1984-07.pdf",
abstract = "The plug-in math PAC for HP's new HP-71B Handheld
Computer further extends the HP-71B's comprehensive
standard numerical function set to provide a
mathematical tool of unprecedented capability and power
in a personal machine. Full use of complex variables,
integration, matrix algebra, and polynomial root
finding are some of the capabilities provided by this
plug-in module.",
acknowledgement = ack-nhfb,
affiliation = "Hewlett--Packard Co, Corvallis, OR, USA",
affiliationaddress = "Hewlett--Packard Co, Corvallis, OR, USA",
classcodes = "C7310 (Mathematics computing)",
classification = "723",
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
journalabr = "Hewlett Packard J",
keywords = "complex; complex variables; computers, miniature; data
storage, digital --- Fixed; data type; extended I/O
functions; fast Fourier transform; handheld computer;
HP-71B hand-held computer; matrix operations; numerical
analysis; numerical function set; polynomial; read-only
storage; ROM; root finder",
remark = "The paper notes: ``Completely support provisions of
the proposed IEEE floating-point mathematics standard.
\ldots{} an HP-71B REAL variable --- a 12-digit
mantissa and a three-digit exponent in the range from $
- 499 $ to $ 499 $. Each part of a COMPLEX SHORT
variable or array element has the same precision as an
HP-71B SHORT variable --- a five-digit mantissa and a
three-digit exponent in the range from $ - 499 $ to $
499 $. Of course, denormalized numbers, Inf (infinity),
and NaNs (not-a-numbers) are also permitted.''",
treatment = "P Practical; X Experimental",
}
@Article{Gustafson:1984:SCC,
author = "Sven-{\AA}ke Gustafson",
title = "On the stability of a class of convergence
acceleration methods for power series",
journal = j-BIT,
volume = "24",
number = "4",
pages = "510--519",
month = dec,
year = "1984",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934909",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65B10",
MRnumber = "764823 (86c:65006)",
MRreviewer = "D. Levin",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=24&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=24&issue=4&spage=510",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "convergence acceleration",
}
@Article{Karp:1984:ELS,
author = "A. H. Karp",
title = "Exponential and Logarithm by Sequential Squaring",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "5",
pages = "462--464",
month = may,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676464",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:52 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676464",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kolbig:1984:PCL,
author = "K. S. K{\"o}lbig",
title = "Programs for computing the logarithm of the gamma
function, and the digamma function, for complex
argument",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-152",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82404-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:06 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584824042",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Laforgia:1984:FIG,
author = "Andrea Laforgia",
title = "Further Inequalities for the Gamma Function",
journal = j-MATH-COMPUT,
volume = "42",
number = "166",
pages = "597--600",
month = apr,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A15",
MRnumber = "85i:33001",
MRreviewer = "H. E. Fettis",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Math., Univ. of Torino, Torino, Italy",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "gamma function; inequalities; polynomials",
treatment = "T Theoretical or Mathematical",
}
@Article{McCurley:1984:EE,
author = "Kevin S. McCurley",
title = "Explicit Estimates for $ \theta (x; 3, l) $ and $ \psi
(x; 3, l) $",
journal = j-MATH-COMPUT,
volume = "42",
number = "165",
pages = "287--296",
month = jan,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11N56",
MRnumber = "85g:11085",
MRreviewer = "G. J. Rieger",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Maths., Michigan State Univ., East Lansing,
MI, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "arithmetic progressions; Chebyshev approximation;
Chebyshev functions; Dirichlet L-; explicit estimates;
functions; prime number; theorem; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Moon:1984:AFC,
author = "Wooil Moon",
title = "{Airy} function with complex arguments",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-692",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82842-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:41 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828428",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@TechReport{Morris:1984:NLM,
author = "A. H. Morris",
title = "{NSWC} library of mathematics subroutines",
type = "Report",
number = "NSWC TR 84-143",
institution = "Naval Surface Weapons Center",
address = "Dahlgren, VA, USA",
year = "1984",
bibdate = "Mon Jun 03 12:24:32 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Nesbet:1984:ARI,
author = "R. K. Nesbet",
title = "Algorithms for regular and irregular {Coulomb} and
{Bessel} functions",
journal = j-COMP-PHYS-COMM,
volume = "32",
number = "4",
pages = "341--347",
month = jul,
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(84)90051-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465584900511",
abstract = "Algorithms for computing Coulomb--Bessel functions are
considered, with emphasis on obtaining accurate values
when the argument $x$ is inside the classical turning
point $ x \lambda $. Algorithms of Barnett et al. for
the generalized Coulomb functions and their derivatives
are discussed in the context of the phase integral
formalism. Modified or alternative algorithms are
considered that are designed to be valid for all values
of argument $x$ and index $ \lambda $ for the functions
$ F_\lambda (x) $, $ G_\lambda (x) $. An algorithm for
accelerating convergence of a power series by
conversion to a continued fraction is presented, and is
applied to the evaluation of spherical Bessel
functions. An explicit formula for the integrand of the
phase integral is presented for spherical Bessel
functions. The methods considered need to be augmented
by an efficient algorithm for computing the logarithmic
derivative of $ G_0 + i F_0 $ for Coulomb functions
when $x$ is smaller than the charge parameter $ \eta
$.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Newman:1984:ABS,
author = "J. N. Newman",
title = "Approximations for the {Bessel} and {Struve}
functions",
journal = j-MATH-COMPUT,
volume = "43",
number = "168",
pages = "551--556",
month = oct,
year = "1984",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1984-0758202-X",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33A40)",
MRnumber = "86c:65021",
MRreviewer = "S. Conde",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C1120 (Mathematical analysis); C4130 (Interpolation and
function approximation)",
corpsource = "Dept. of Ocean Eng., MIT, Cambridge, MA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "accuracy; Bessel functions; function approximation;
functions; IBM PC computer; minimax; polynomial
approximations; polynomials; rational-fraction
approximations; single-precision computations; Struve",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Ng:1984:DAA,
author = "K. C. Ng",
title = "Contributions to the computation of the matrix
exponential",
type = "Report",
number = "PAM-212",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = feb,
year = "1984",
bibdate = "Fri Nov 11 09:06:19 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Based on the author's Ph.D. thesis.",
acknowledgement = ack-nhfb,
keywords = "$\exp(Bt)$",
}
@Article{Nishimoto:1984:TFD,
author = "Katsuyuki Nishimoto",
title = "Tables of fractional differintegrations of elementary
functions",
journal = "J. College Engrg. Nihon Univ. Ser. B",
volume = "25",
pages = "41--46",
year = "1984",
ISSN = "0285-6182",
MRclass = "30E20 (26A33)",
MRnumber = "85f:30065",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Noble:1984:CPE,
author = "C. J. Noble and I. J. Thompson",
title = "{COULN}, a program for evaluating negative energy
{Coulomb} functions",
journal = j-COMP-PHYS-COMM,
volume = "33",
number = "4",
pages = "413--419",
month = oct,
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(84)90146-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Feb 24 13:39:14 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465584901462",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Piessens:1984:ACB,
author = "R. Piessens",
title = "Automatic computation of {Bessel} function integrals",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-791",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82915-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S001046558482915X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Piessens:1984:CBF,
author = "Robert Piessens",
title = "The computation of {Bessel} functions on a small
computer",
journal = j-COMPUT-MATH-APPL,
volume = "10",
number = "2",
pages = "161--166",
month = "????",
year = "1984",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:00:50 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122184900452",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Piessens:1984:CSA,
author = "R. Piessens",
title = "{Chebyshev} series approximations for the zeros of the
{Bessel} functions",
journal = j-J-COMPUT-PHYS,
volume = "53",
number = "1",
pages = "188--192",
month = jan,
year = "1984",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(84)90060-3",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:18 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999184900603",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Piessens:1984:SEF,
author = "R. Piessens",
title = "A Series Expansion for the First Positive Zero of the
{Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "42",
number = "165",
pages = "195--197",
month = jan,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A40 (65D20)",
MRnumber = "84m:33014",
MRreviewer = "M. E. Muldoon",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database; Theory/Comp.Alg.1.bib",
acknowledgement = ack-nhfb,
annote = "Gives explicit series for first positive zero for 4
terms, using REDUCE.",
classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical
analysis)",
corpsource = "Dept. of Computer Sci., Univ. of Leuven, Heverlee,
Belgium",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; poles and zeros; positive zero;
Reduce; series (mathematics); series expansion",
treatment = "T Theoretical or Mathematical",
}
@Article{Schmidt:1984:TAI,
author = "J. W. Schmidt",
title = "Two-Sided Approximations of Inverses, Square Roots and
{Cholesky} Factors",
journal = "Comput. Math., Banach Center Publ.",
volume = "13",
pages = "483--497",
year = "1984",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-jr,
}
@Article{Seaton:1984:CFA,
author = "M. J. Seaton",
title = "{Coulomb} functions analytic in the energy",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-771",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82899-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584828994",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Takemasa:1984:CFC,
author = "T. Takemasa and T. Tamura and H. H. Wolter",
title = "{Coulomb} functions with complex angular momenta",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-562",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82737-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:33 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S001046558482737X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Talman:1984:LSC,
author = "James D. Talman",
title = "{LSFBTR}: a subroutine for calculating spherical
{Bessel} transforms",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-903",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)83002-7",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:58 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584830027",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Tamura:1984:CFC,
author = "Taro Tamura and Frank Rybicki",
title = "{Coulomb} functions for complex energies",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-5",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82276-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:55:58 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584822766",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Trojan:1984:LBF,
author = "George M. Trojan",
title = "Lower Bounds and Fast Algorithms for Sequence
Acceleration",
journal = j-J-ACM,
volume = "31",
number = "2",
pages = "329--335",
month = apr,
year = "1984",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Tight upper and lower bounds are obtained for sequence
accelerating. The lower bounds follow from a powerful
asymptotic adversary principle. Algorithms are
presented and shown to be almost optimal.",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Western Ontario, Dep of Physics, London,
Ont, Can",
ajournal = "J. Assoc. Comput. Mach.",
classification = "723",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
keywords = "Algorithms; computer programming; convergence
acceleration; lower bounds; sequence acceleration;
upper bounds",
}
@Book{vanderLaan:1984:CSF,
author = "C. G. van der Laan and N. M. Temme",
title = "Calculation of special functions: the gamma function,
the exponential integrals and error-like functions",
volume = "10",
publisher = "Centre for Mathematics and Computer Science",
address = "Amsterdam, The Netherlands",
pages = "iv + 231",
year = "1984",
ISBN = "90-6196-277-3",
ISBN-13 = "978-90-6196-277-9",
LCCN = "QA1 M4591 no. 10",
bibdate = "Sat Oct 30 18:43:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "CWI tract / Centrum voor Wiskunde en Informatica",
acknowledgement = ack-nhfb,
}
@Article{vonGudenberg:1984:BMG,
author = "J. Wolff {von Gudenberg}",
title = "{Berechnung maximal genauer Standardfunktionen mit
einfacher Mantissenl{\"a}nge} \toenglish {Computation
of Maximally Accurate Elementary Functions Using Simple
Mantissa Length} \endtoenglish",
journal = j-ELEK-RECHENANLAGEN,
volume = "26",
number = "5",
pages = "230--238",
month = oct,
year = "1984",
CODEN = "ELRAA4",
ISSN = "0013-5720",
bibdate = "Sun Oct 25 10:29:27 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
fjournal = "Elektronische Rechenanlagen",
}
@Article{Walmsley:1984:EEM,
author = "John L. Walmsley",
title = "On the efficient evaluation of modified {Bessel}
functions of zeroth and first orders for arguments of
the form $ x \exp (i \pi / 4) $",
journal = j-J-COMPUT-PHYS,
volume = "56",
number = "2",
pages = "349--355",
month = nov,
year = "1984",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(84)90100-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:21 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999184901001",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Book{Wawrzynczyk:1984:GRS,
author = "Antoni Wawrzy{\'n}czyk and Aleksander Strasburger",
title = "Group representations and special functions",
volume = "8",
publisher = pub-REIDEL,
address = pub-REIDEL:adr,
pages = "xvi + 688",
year = "1984",
ISBN = "90-277-1269-7",
ISBN-13 = "978-90-277-1269-1",
LCCN = "QA171 .W3513 1984; QA1 M4281 v. 8",
bibdate = "Sat Oct 30 18:29:38 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematics and its applications. East European
series",
acknowledgement = ack-nhfb,
remark = "Translation of Polish title Wsp{\'o}\pm{}czesna teoria
funkcji specjalnych.",
subject = "Representations of groups; Functions, Special",
}
@Article{Wrigge:1984:NMG,
author = "Staffan Wrigge",
title = "A note on the moment generating function for the
reciprocal gamma distribution",
journal = j-MATH-COMPUT,
volume = "42",
number = "166",
pages = "617--621",
month = apr,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (60E10 62E15 65U05)",
MRnumber = "86f:65042b",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Nat. Defence Res. Inst., Stockholm, Sweden",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Euler--Maclaurin expansion; moment generating
function; polynomials; reciprocal gamma distribution",
treatment = "T Theoretical or Mathematical",
}
@Article{Akrivis:1985:ENC,
author = "G. Akrivis",
title = "The error norm of certain {Gaussian} quadrature
formulae",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "513--519",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D32",
MRnumber = "87a:65051",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
corpsource = "Math. Inst., Munchen Univ., West Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "error analysis; error functional; error norm; function
approximation; Gaussian quadrature formulae;
integration; weight functions; wide class",
treatment = "T Theoretical or Mathematical",
}
@Book{Arfken:1985:MMP,
author = "George B. (George Brown) Arfken",
title = "Mathematical methods for physicists",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
edition = "Third",
pages = "xxii + 985",
year = "1985",
ISBN = "0-12-059820-5",
ISBN-13 = "978-0-12-059820-5",
LCCN = "QA37.2 .A74 1985",
bibdate = "Wed Mar 15 06:50:49 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/book/9780120598205",
abstract = "Mathematical Methods for Physicists, Third Edition
provides an advanced undergraduate and beginning
graduate study in physical science, focusing on the
mathematics of theoretical physics. This edition
includes sections on the non-Cartesian tensors,
dispersion theory, first-order differential equations,
numerical application of Chebyshev polynomials, the
fast Fourier transform, and transfer functions. Many of
the physical examples provided in this book, which are
used to illustrate the applications of mathematics, are
taken from the fields of electromagnetic theory and
quantum mechanics. The Hermitian operators, Hilbert
space, and concept of completeness are also
deliberated. This book is beneficial to students
studying graduate level physics, particularly
theoretical physics.",
acknowledgement = ack-nhfb,
author-dates = "1922--",
subject = "Mathematics; Mathematical physics; Math{\'e}matiques;
Physique math{\'e}matique; Mathematical physics.;
Mathematics.; Wiskundige methoden.; Reactoren.;
Groepentheorie.; Kwantummechanica.; Elektromechanica.;
Vectoren (wiskunde); Elektrodynamica.;
Math{\'e}matiques.; Physique math{\'e}matique.;
Math{\'e}matiques de l'ing{\'e}nieur.",
tableofcontents = "Vector Analysis \\
Rotation of the Coordinate Axes \\
Scalar or Dot Product \\
Vector or Cross Product \\
Triple Scalar Product, Triple Vector Product \\
Gradient, [down triangle, open] \\
Divergence, [down triangle, open] \\
Curl, [down triangle, open] x \\
Successive Applications of [down triangle, open] \\
Vector Integration \\
Gauss's Theorem \\
Stokes's Theorem \\
Potential Theory \\
Gauss's Law, Poisson's Equation \\
Dirac Delta Function \\
Helmholtz's Theorem \\
Curved Coordinates, Tensors \\
Orthogonal Coordinates \\
Differential Vector Operators \\
Special Coordinate Systems: Introduction \\
Circular Cylindrical Coordinates \\
Spherical Polar Coordinates \\
Tensor Analysis \\
Contraction, Direct Product \\
Quotient Rule \\
Pseudotensors, Dual Tensors \\
Non-Cartesian Tensors \\
Tensor Derivative Operators \\
Determinants and Matrices \\
Determinants \\
Matrices \\
Orthogonal Matrices \\
Hermitian Matrices, Unitary Matrices \\
Diagonalization of Matrices \\
Normal Matrices \\
Group Theory \\
Introduction to Group Theory \\
Generators of Continuous Groups \\
Orbital Angular Momentum \\
Angular Momentum Coupling \\
Homogeneous Lorentz Group \\
Lorentz Covariance of Maxwell's Equations \\
Discrete Groups \\
Infinite Series \\
Convergence Tests \\
Alternating Series \\
Algebra of Series \\
Series of Functions \\
Taylor's Expansion \\
Power Series \\
Elliptic Integrals \\
Bernoulli Numbers, Euler-Maclaurin Formula \\
Asymptotic Series \\
Infinite Products \\
Functions of a Complex Variable I \\
Complex Algebra",
}
@Article{Bank:1985:SEM,
author = "Randolph E. Bank and Craig C. Douglas",
title = "Sharp estimates for multigrid rates of convergence
with general smoothing and acceleration",
journal = j-SIAM-J-NUMER-ANAL,
volume = "22",
number = "4",
pages = "617--633",
month = aug,
year = "1985",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F10 (65N20)",
MRnumber = "86j:65037",
MRreviewer = "L. W. Ehrlich",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "convergence acceleration",
}
@InProceedings{Bannur:1985:VIS,
author = "J. Bannur and A. Varma",
title = "The {VLSI} Implementation of a Square Root Algorithm",
crossref = "Hwang:1985:PSC",
pages = "159--165",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bannur_Varma.pdf",
abstract = "VLSI implementation of a square root algorithm is
studied. Two possible implementations of the basic
nonrestoring algorithm are presented --- the second is
more area-efficient and modular than the first. The
implementations are simple and easy to control, but, at
the same time, are more area-time efficient than many
existing designs. A hardware algorithm suited to
microprogram implementation is also given. Extension of
the algorithms to achieve $ 1 / 2 $-bit precision is
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Borodin:1985:DND,
author = "Allan Borodin and Ronald Fagin and John E. Hopcroft
and Martin Tompa",
title = "Decreasing the Nesting Depth of Expressions Involving
Square Roots",
journal = j-J-SYMBOLIC-COMP,
volume = "1",
number = "2",
pages = "169--188",
month = jun,
year = "1985",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "68Q40 (12F05)",
MRnumber = "87a:68087",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "Simplification",
}
@Article{Brezinski:1985:CAM,
author = "Claude Brezinski",
title = "Convergence acceleration methods: the past decade",
journal = j-J-COMPUT-APPL-MATH,
volume = "12--13",
number = "??",
pages = "19--36",
month = may,
year = "1985",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(85)90005-6",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65Bxx (65J05)",
MRnumber = "793942 (86f:65019)",
bibdate = "Thu Dec 01 10:11:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "convergence acceleration",
remark = "Proceedings of the international conference on
computational and applied mathematics (Leuven, 1984).",
}
@Article{Carlson:1985:AEF,
author = "B. C. Carlson and John L. Gustafson",
title = "Asymptotic expansion of the first elliptic integral",
journal = j-SIAM-J-MATH-ANA,
volume = "16",
number = "5",
pages = "1072--1092",
month = sep,
year = "1985",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A25 (41A60)",
MRnumber = "87d:33002",
MRreviewer = "Kusum Soni",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Cathey:1985:ISR,
author = "James Cathey",
title = "68000 Integer square root routine in {16BST}",
journal = j-DDJ,
volume = "10",
number = "5",
pages = "118--??",
month = may,
year = "1985",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Conover:1985:AHS,
author = "B. Conover and D. L. Gustafson",
title = "An Algorithm for High Speed Square Roots",
crossref = "IEEE:1985:ERC",
pages = "19--21",
year = "1985",
bibdate = "Fri Jun 11 18:04:41 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Frenzen:1985:NAE,
author = "C. L. Frenzen and R. Wong",
title = "A note on asymptotic evaluation of some {Hankel}
transforms",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "537--548",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "41A60 (44A15 65R10)",
MRnumber = "87c:41024",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0230 (Integral transforms); B0290Z (Other numerical
methods)C1130 (Integral transforms); C4190 (Other
numerical methods)",
corpsource = "Dept. of Math., British Columbia Univ., Vancouver, BC,
Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic expansion; Bessel function; Bessel
functions; growth condition; Hankel transforms;
meromorphic function; transforms",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Gal:1985:CEF,
author = "Shmuel Gal",
title = "Computing Elementary Functions: a New Approach for
Achieving High Accuracy and Good Performance",
crossref = "Miranker:1985:ASC",
pages = "1--16",
year = "1985",
DOI = "https://doi.org/10.1007/3-540-16798-6_1",
bibdate = "Thu Sep 01 12:27:23 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Gustafson:1985:SCA,
author = "Sven-{\AA}ke Gustafson",
title = "Stable convergence acceleration using {Laplace}
transforms",
journal = j-NUM-MATH,
volume = "47",
number = "3",
pages = "387--394",
month = nov,
year = "1985",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65B10 (65D30)",
MRnumber = "86m:65009",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "B0230 (Integral transforms); C1130 (Integral
transforms)",
corpsource = "Dept. of Numerical Anal. and Comput. Sci., R. Inst. of
Technol., Stockholm, Sweden",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration; Laplace transforms; power
series; quadrature schemes; series (mathematics);
stable convergence acceleration",
treatment = "T Theoretical or Mathematical",
}
@Article{Hill:1985:RCS,
author = "I. D. Hill and M. C. Pike",
title = "Remark on ``{Algorithm 299: Chi-Squared Integral}''",
journal = j-TOMS,
volume = "11",
number = "2",
pages = "185--185",
month = jun,
year = "1985",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Feb 06 05:28:22 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Hill:1967:ACS,elLozy:1976:RAC,elLozy:1979:RAS}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Hull:1985:PRV,
author = "T. E. Hull and A. Abrham",
title = "Properly Rounded Variable Precision Square Root",
journal = j-TOMS,
volume = "11",
number = "3",
pages = "229--237",
month = sep,
year = "1985",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/214408.214413",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15 (65G05)",
MRnumber = "87a:65041",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/;
http://www.acm.org/pubs/toc/Abstracts/toms/214413.html",
abstract = "The square root function presented here returns a
properly rounded approximation to the square root of
its argument, or it raises an error condition if the
argument is negative. {\em Properly rounded} means
rounded to the nearest, or to nearest even in case of a
tie. It is {\em variable precision} in that it is
designed to return a $p$-digit approximation to a
$p$-digit argument, for any $ p > 0 $. (Precision $p$
means $p$ decimal digits.) The program and the analysis
are valid for all $ p > 0 $, but current
implementations place some restrictions on $p$.",
acknowledgement = ack-nhfb,
catcode = "G.4; G.4; G.1.0; G.1.2; G.4; G.1.0",
CRclass = "G.4 Algorithm analysis; G.4 Verification; G.1.0
General; G.1.0 Numerical algorithms; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.4 Certification and testing; G.1.0 General; G.1.0
Error analysis",
descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis; Mathematics of Computing,
MATHEMATICAL SOFTWARE, Verification; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Error
analysis",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
genterm = "algorithms; verification",
guideno = "02789",
journal-URL = "https://dl.acm.org/loi/toms",
jrldate = "Sept. 1985",
keywords = "algorithms; decimal floating-point arithmetic;
verification",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
General, Error analysis. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
}
@Article{Humblet:1985:BFE,
author = "J. Humblet",
title = "{Bessel} function expansions of {Coulomb} wave
functions",
journal = j-J-MATH-PHYS,
volume = "26",
number = "4",
pages = "656--659",
month = apr,
year = "1985",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.526602",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "81C05 (33A40 81G45)",
MRnumber = "87c:81034",
bibdate = "Mon Oct 31 11:57:19 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v26/i4/p656_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "4",
}
@Article{Jones:1985:CIG,
author = "William B. Jones and W. J. Thron",
title = "On the computation of incomplete gamma functions in
the complex domain",
journal = j-J-COMPUT-APPL-MATH,
volume = "12--13",
number = "??",
pages = "401--417",
month = may,
year = "1985",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:27:12 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042785900342",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Kravchuk:1985:ACE,
author = "V. R. Kravchuk",
title = "Approximation of certain elementary functions by
rational functions of order $ (n, 2) $. ({Russian})",
journal = "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
volume = "18",
pages = "7--40",
year = "1985",
MRclass = "41A25 (41A10)",
MRnumber = "87b:41017",
MRreviewer = "R. Smarzewski",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Kravchuk:1985:EAE,
author = "V. R. Kravchuk",
title = "Effective approximation of elementary functions by
rational polynomials of order $ (n, 1) $. ({Russian})",
journal = j-UKR-MAT-Z,
volume = "37",
number = "2",
pages = "175--180, 270",
year = "1985",
CODEN = "UMZHAA",
ISSN = "0041-6053",
MRclass = "41A20 (41A25)",
MRnumber = "86h:41013",
MRreviewer = "Miguel A. Jim{\'e}nez Pozo",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Ukrainskii matematicheskii zhurnal",
language = "Russian",
}
@Article{Lazard:1985:PFD,
author = "Daniel Lazard",
title = "Primitives des fonctions {\'e}l{\'e}mentaires
(d'apr{\`e}s {Risch} et {Davenport}). ({French})
[Primitives of elementary functions (following {Risch}
and {Davenport})] {Seminar Bourbaki, Vol. 1983/84, No.
121-122}",
journal = "Ast{\'e}risque",
volume = "121--122",
pages = "295--308",
year = "1985",
MRclass = "12H05 (12-04)",
MRnumber = "86k:12010",
MRreviewer = "J. H. Davenport",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Lewanowicz:1985:RRH,
author = "Stanis{\l}aw Lewanowicz",
title = "Recurrence relations for hypergeometric functions of
unit argument",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "521--535",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A35 (65Q05)",
MRnumber = "86m:33004",
MRreviewer = "S. Conde",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290 (Numerical analysis); C4100 (Numerical
analysis)",
corpsource = "Inst. of Comput. Sci., Wroclaw Univ., Poland",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "(mathematics); convergence of numerical methods;
hypergeometric function; numerical analysis; recurrence
relation; series; unit argument",
treatment = "T Theoretical or Mathematical",
}
@Article{Lo:1985:GPB,
author = "Hao-Yung Lo and Y. Aoki",
title = "Generation of a Precise Binary Logarithm with
Difference Grouping Programmable Logic Array",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "681--691",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676614",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676614",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Majerski:1985:SRA,
author = "S. Majerski",
title = "Square-Rooting Algorithms for High-Speed Digital
Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "724--733",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676618",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Martin:1985:FAB,
author = "Pablo Mart{\'\i}n and Antonio L. Guerrero",
title = "Fractional approximations to the {Bessel} function {$
J_0 (x) $}",
journal = j-J-MATH-PHYS,
volume = "26",
number = "4",
pages = "705--707",
month = apr,
year = "1985",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.526610",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "41A21 (33A40)",
MRnumber = "86g:41031",
MRreviewer = "Hans-J{\"u}rgen Albrand",
bibdate = "Mon Oct 31 11:57:19 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v26/i4/p705_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "3",
}
@Article{Milgram:1985:GIE,
author = "M. S. Milgram",
title = "The Generalized Integro-Exponential Function",
journal = j-MATH-COMPUT,
volume = "44",
number = "170",
pages = "443--458",
month = apr,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A70 (65D15)",
MRnumber = "86c:33024",
MRreviewer = "S. Conde",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); B0290F (Interpolation
and function approximation); C4120 (Functional
analysis); C4130 (Interpolation and function
approximation)",
corpsource = "AECL, Chalk River, Ont., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "exponential function; exponential integral;
first-order functions; function; function
approximation; function evaluation; generalized
integro-; incomplete gamma; minimax; rational minimax
approximations; techniques",
treatment = "T Theoretical or Mathematical",
}
@Article{Muller:1985:DBC,
author = "Jean-Michel Muller",
title = "Discrete basis and computation of elementary
functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "9",
pages = "857--862",
month = sep,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676643",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65D20 (65V05)",
MRnumber = "87e:65016",
MRreviewer = "D. Zwick",
bibdate = "Sun Jul 10 08:33:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643",
abstract = "We give necessary and sufficient conditions in order
that the infinite product or sum of the terms of a
positive decreasing sequence generates the reals in a
given interval.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InCollection{Muller:1985:RNR,
author = "Jean-Michel Muller",
booktitle = "Seminar on number theory, 1984--1985 (Talence,
1984/1985)",
title = "Repr{\'e}sentation des nombres r{\'e}els et calcul des
fonctions {\'e}l{\'e}mentaires. ({French})
[Representation of real numbers and calculation of
elementary functions]",
volume = "12",
publisher = "Univ. Bordeaux {I}",
address = "Talence, France",
pages = "22",
year = "1985",
MRclass = "26-04 (11B13 11B34 26A09)",
MRnumber = "87k:26001",
MRreviewer = "S. L. Segal",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "French",
remark = "From the MRreview: ``About one third of the paper is
devoted to algorithms for calculating quantities like
square root, exponential, logarithm, or trigonometric
funtions, using discrete bases. Indeed, the major
motivation for the present paper is obtaining simple
algorithms which can easily be realized by
hardware.''",
}
@TechReport{Parlett:1985:DAA,
author = "Beresford N. Parlett and K. C. Ng",
title = "Development of an accurate algorithm for {$ \exp (B t)
$}",
type = "Technical Report",
number = "PAM-294",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = aug,
year = "1985",
bibdate = "Fri Nov 11 09:06:19 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Peralta:1985:TRN,
author = "Rene Caupolican Peralta",
title = "Three results in number theory and cryptography: a new
algorithm to compute square roots modulo a prime
number; On the bit complexity of the discrete
logarithm; a framework for the study of
cryptoprotocols",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "52",
month = dec,
year = "1985",
LCCN = "????",
bibdate = "Sat Oct 17 16:25:07 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "dissertations; dissertations, academic --- UCB ---
computer science --- 1981--1990; University of
California, Berkeley. computer science division --",
}
@Article{Pereira:1985:ECF,
author = "N. Costa Pereira",
title = "Estimates for the {Chebyshev} function $ \psi (x) -
\theta (x) $",
journal = j-MATH-COMPUT,
volume = "44",
number = "169",
pages = "211--221",
month = jan,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11A25 (11N45 11Y35 33A70)",
MRnumber = "86k:11005",
bibdate = "Thu Jun 15 07:26:46 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
note = "See corrigendum \cite{Pereira:1987:CEC}.",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Chebyshev approximation; Chebyshev function",
treatment = "T Theoretical or Mathematical",
}
@Article{Schoof:1985:ECF,
author = "Ren{\'e} Schoof",
title = "Elliptic Curves Over Finite Fields and the Computation
of Square Roots $ \operatorname {mod} p $",
journal = j-MATH-COMPUT,
volume = "44",
number = "170",
pages = "483--494",
month = apr,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y16 (11G20 14G15)",
MRnumber = "86e:11122",
MRreviewer = "Karl Rubin",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0250 (Combinatorial mathematics); B0290D (Functional
analysis); C1160 (Combinatorial mathematics); C4120
(Functional analysis); C4240 (Programming and algorithm
theory)",
corpsource = "Amsterdam Univ., Netherlands",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computational complexity; deterministic algorithm;
elliptic curve; F/sub q/-points; finite fields;
function evaluation; number theory; square roots mod p;
Weierstrass equation",
treatment = "T Theoretical or Mathematical",
}
@Article{Shah:1985:SAA,
author = "Arvind K. Shah",
title = "A Simpler Approximation for Areas Under the Standard
Normal Curve",
journal = j-AMER-STAT,
volume = "39",
number = "1",
pages = "80--80",
month = feb,
year = "1985",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 12:40:28 MST 2012",
bibsource = "http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326426;
https://www.math.utah.edu/pub/tex/bib/amstat1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2683918",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Spijker:1985:SRS,
author = "M. N. Spijker",
title = "Stepsize restrictions for stability of one-step
methods in the numerical solution of initial value
problems",
journal = j-MATH-COMPUT,
volume = "45",
number = "172",
pages = "377--392",
month = oct,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65L20 (65M10)",
MRnumber = "86j:65106",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "A0260 (Numerical approximation and analysis); A0560
(Transport processes: theory); B0290F (Interpolation
and function approximation); B0290P (Differential
equations); C4130 (Interpolation and function
approximation); C4170 (Differential equations); C7320
(Physics and chemistry computing)",
corpsource = "Inst. of Appl. Math. and Comput. Sci., Leiden Univ.,
Netherlands",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "convection; convergence of numerical methods;
differential equations; diffusion;
diffusion-convection; error growth; initial value
problems; iterative methods; numerical solution;
partial; problem; stability of one-step methods;
stepsize restrictions",
treatment = "T Theoretical or Mathematical",
}
@Article{Sreedharan:1985:ASS,
author = "J. Sreedharan and A. Dhurkadas",
title = "8086 algorithm solves square roots",
journal = j-EDN,
volume = "30",
number = "7",
pages = "272",
month = apr,
year = "1985",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Temme:1985:LTI,
author = "N. M. Temme",
title = "{Laplace} type integrals: transformation to standard
form and uniform asymptotic expansions",
journal = j-QUART-APPL-MATH,
volume = "43",
number = "1",
pages = "103--123",
year = "1985",
CODEN = "QAMAAY",
DOI = "https://doi.org/10.1090/qam/782260",
ISSN = "0033-569x (print), 1552-4485 (electronic)",
ISSN-L = "0033-569X",
MRclass = "44A10 (41A60)",
MRnumber = "782260",
MRreviewer = "I. Feny{\H{o}}",
bibdate = "Tue Feb 6 11:42:02 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Quarterly of Applied Mathematics",
journal-URL = "http://dl.acm.org/citation.cfm?id=J641;
http://www.ams.org/journals/qam",
}
@Article{Agarwal:1986:NSV,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "New Scalar and Vector Elementary Functions for the
{IBM System\slash 370}",
journal = j-IBM-JRD,
volume = "30",
number = "2",
pages = "126--144",
month = mar,
year = "1986",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.302.0126",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "76W05",
MRnumber = "840 341",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
note = "See clarification \cite{Agarwal:1987:CNS}.",
abstract = "Algorithms have been developed to compute short-and
long-precision elementary functions: SIN, COS, TAN,
COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
ATAN2, and CABS, in scalar (28 functions) and vector
(22 functions) mode. They have been implemented as part
of the new VS FORTRAN library recently announced along
with the IBM 3090 Vector Facility. These algorithms are
essentially table-based algorithms. An important
feature of these algorithms is that they produce
bitwise-identical results on scalar and vector
System\slash 370 machines. Of these, for five functions
the computed value result is always the correctly
rounded value of the infinite-precision result. For the
rest of the functions, the value returned is one of the
two floating-point neighbors bordering the
infinite-precision result, which implies exact results
if they are machine-representable. For the five
correctly rounded elementary functions, scalar and
vector algorithms are designed independently to
optimize performance in each case.",
accepted = "2 December 1985",
acknowledgement = ack-nhfb,
ajournal = "IBM J. Res. Develop.",
classcodes = "C6140D (High level languages); C7310 (Mathematics
computing)",
classification = "723",
corpsource = "IBM Res. Div., Yorktown Heights, NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
journalabr = "IBM J Res Dev",
keywords = "ACOS; Algorithms; algorithms; ASIN; ATAN; ATAN2;
bitwise-identical results; CABS; computer metatheory;
computer programming; computer programming languages
--- fortran; COS; COTAN; design; elementary functions;
EXP; FORTRAN; fortran library; functions; IBM
computers; IBM System/370; infinite-precision result;
LOG; LOG10; mainframes; measurement; performance;
POWER; scalar elementary functions; SIN; SQRT;
subroutines; table-based algorithms; TAN; vector
elementary; VS FORTRAN library",
received = "5 November 1985",
remark-1 = "Numerous figures show errors in ulps, in either linear
or logarithmic scales, as dot plots over a range of
arguments, an idea that the authors credit to a
suggestion by Cleve Moler, then consulting with IBM
Palo Alto labs; such plots are used extensively in
\cite{Beebe:2017:MFC}.",
remark-2 = "From pages 128--129: ``A great deal of satisfaction
was obtained from the fact that five of the intrinsic
functions reported here always deliver correctly
rounded results; these are SQRT, DSQRT, CABS, CDABS,
and EXP. One important aspect of this is that correctly
rounded results were obtained with surprisingly little
sacrifice in performance.''",
remark-3 = "From page 132: ``Our CABS and CDABS functions satisfy
$\e/u < 0.5$ (this can also be called a half-ulp
criterion). They have best-possible rounding, except
that unavoidably there are cases when $| e/u | = 0.5$,
in which case it would be equally correct to round
downward or upward; we choose to round upward. This is
consistent with the System/370 definition of
rounding.''",
remark-4 = "From pages 134--135: ``Tuckerman's condition is of
historic significance, as its use allowed us to produce
IBM's first elementary function that delivered
correctly rounded results for all arguments.''",
remark-5 = "From page 137: ``X**2.0 usually produces a correctly
rounded value, while X*X always produces the truncated
value of $X^2$ .''",
remark-6 = "From page 139: ``Generating precise times is
difficult, since seemingly inconsequential changes in
the timing procedure may have a noticeable effect on
the measured times. For example, on the 3081KX the
performance of the STM [store multiple] and LM [load
multiple] instructions is severely degraded near page
boundaries. This means that in the rare event that the
save area of a subroutine is near a page boundary, the
speed of execution of the subroutine will be
substantially decreased.''",
subject = "C.4 Computer Systems Organization, PERFORMANCE OF
SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms \\ F.3.3 Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
of Program Constructs, Functional constructs \\ C.1.2
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Array and vector processors",
treatment = "N New Development; P Practical",
}
@Article{Amos:1986:APP,
author = "D. E. Amos",
title = "{Algorithm 644}: a Portable Package for {Bessel}
Functions of a Complex Argument and Nonnegative Order",
journal = j-TOMS,
volume = "12",
number = "3",
pages = "265--273",
month = sep,
year = "1986",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/7921.214331",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20",
MRnumber = "889 069",
bibdate = "Tue Mar 09 10:26:27 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See also
\cite{Amos:1990:RPP,Amos:1995:RAP,Kodama:2007:RA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p265-amos/",
abstract = "This algorithm is a package of subroutines for
Computing Bessel functions $ H_v^{(1)}(z) $, $
H_v^{(2)}(z) $, $ I_v(z) $, $ J_v(z) $, $ K_v(z) $, $
Y_v(z) $ and Airy functions $ \mbox {Ai}(z) $, $ \mbox
{Ai}'(z) $, $ \mbox {Bi}(z) $, $ \mbox {Bi}'(z) $ for
orders $ v \geq 0 $ and complex $z$ in $ - \pi < \mbox
{arg} z \leq \pi $. Eight callable subroutines and
their double-precision counterparts are provided.
Exponential scaling and sequence generation are
auxiliary options.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.m}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Miscellaneous. {\bf G.m}: Mathematics of Computing,
MISCELLANEOUS.",
}
@Article{Andrews:1986:SCA,
author = "George E. Andrews and Ian P. Goulden and David M.
Jackson",
title = "{Shanks}' convergence acceleration transform,
{Pad{\'e}} approximants and partitions",
journal = j-J-COMB-THEORY-A,
volume = "43",
number = "1",
pages = "70--84",
year = "1986",
CODEN = "JCBTA7",
DOI = "https://doi.org/10.1016/0097-3165(86)90024-5",
ISSN = "0097-3165 (print), 1096-0899 (electronic)",
ISSN-L = "0097-3165",
MRclass = "65B99 (11N99 11Y35)",
MRnumber = "859298 (88c:65005)",
MRreviewer = "Kenneth A. Jukes",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory (Series A)",
journal-URL = "http://www.sciencedirect.com/science/journal/00973165",
keywords = "convergence acceleration",
}
@Article{Bustoz:1986:GFI,
author = "Joaquin Bustoz and Mourad E. H. Ismail",
title = "On Gamma Function Inequalities",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "659--667",
month = oct,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A15 (26D20)",
MRnumber = "87m:33002",
MRreviewer = "G. Gasper",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1130 (Integral transforms); C1140Z (Other and
miscellaneous)",
corpsource = "Dept. of Math., Arizona State Univ., Tempe, AZ, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "gamma function inequalities; infinite divisibility;
Laplace; Laplace transforms; monotonic functions;
probability; probability distributions; quotients;
transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Campbell:1986:NSR,
author = "R. A. Campbell",
title = "{NS32000} Square Roots",
journal = j-DDJ,
volume = "11",
number = "3",
pages = "122--123, 106",
month = mar,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Fri Dec 08 13:05:56 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Cathey:1986:LEI,
author = "J. Cathey",
title = "Letter to the editor [Integer Square Root]",
journal = j-DDJ,
volume = "11",
number = "8",
pages = "14, 82--85",
month = aug,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 08 07:59:25 1994",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Clenshaw:1986:GEL,
author = "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
and P. R. Turner",
title = "Generalized Exponential and Logarithmic Functions",
journal = j-COMPUT-MATH-APPL,
volume = "12",
number = "5--6",
pages = "1091--1101",
month = sep # "\slash " # dec,
year = "1986",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(86)90233-6",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "33A70 (39B10 65G05)",
MRnumber = "MR0871348 (88a:33027)",
bibdate = "Fri Jul 09 06:27:26 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Generalizations of the exponential and logarithmic
functions are defined and an investigation is made of
two possible versions of these functions. Some
applications are described, including computer
arithmetic, properties of very large and very small
numbers, and the determination of functional roots.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Clenshaw:1986:UAR,
author = "C. W. Clenshaw and F. W. J. Olver",
title = "Unrestricted algorithms for reciprocals and square
roots",
journal = j-BIT,
volume = "26",
number = "4",
pages = "475--492",
month = dec,
year = "1986",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01935054",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D20",
MRnumber = "87k:65019",
MRreviewer = "Luciano Biasini",
bibdate = "Wed Jan 4 18:52:19 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
xxpages = "476--492??",
}
@Article{DiDonato:1986:CIG,
author = "Armido R. DiDonato and Alfred H. {Morris, Jr.}",
title = "Computation of the Incomplete Gamma Function Ratios
and Their Inverse",
journal = j-TOMS,
volume = "12",
number = "4",
pages = "377--393",
month = dec,
year = "1986",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/22721.23109",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 21:31:03 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p377-didonato/",
abstract = "An algorithm is given for computing the incomplete
gamma function ratios $ P(a, x) $ and $ Q(a, x) $ for $
a \geq 0 $, $ x \geq 0 $, $ a + x \neq 0 $. Temme's
uniform asymptotic expansions are used. The algorithm
is robust; results accurate to 14 significant digits
can be obtained. An extensive set of coefficients for
the Temme expansions is included.\par
An algorithm, employing third-order Schr{\"o}der
iteration supported by Newton-Raphson iteration, is
provided for computing $x$ when $a$, $ P(a, x) $, and $
Q(a, x) $ are given. Three iterations at most are
required to obtain 10 significant digit accuracy for
$x$.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
review = "ACM CR 8709-0775",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation.",
}
@Article{DiMarzio:1986:IPA,
author = "F. {Di Marzio}",
title = "An improved procedure for the accurate evaluation of
polygamma functions with integer and half-integer
argument",
journal = j-COMP-PHYS-COMM,
volume = "39",
number = "3",
pages = "343--345",
month = apr,
year = "1986",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(86)90095-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:13 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465586900950",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Dutka:1986:SRT,
author = "Jacques Dutka",
title = "On square roots and their representations",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "36",
number = "1",
pages = "21--39",
month = mar,
year = "1986",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/BF00357439",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A05 (11-03 11A63)",
MRnumber = "863340 (87m:01003)",
MRreviewer = "Donald Cook",
bibdate = "Fri Feb 4 21:50:24 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1;
https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
MRtitle = "On square roots and their representations",
}
@Article{Evans:1986:RIU,
author = "D. J. Evans and G. M. Megson",
title = "{Romberg} integration using systolic arrays",
journal = j-PARALLEL-COMPUTING,
volume = "3",
number = "4",
pages = "289--304",
month = oct,
year = "1986",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "11019",
catcode = "G.1.1; G.1.2",
CRclass = "G.1.1 Interpolation; G.1.1 Extrapolation; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Extrapolation; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Parallel Computing",
genterm = "theory; design; algorithms",
guideno = "1986-10554",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
journalabbrev = "Parallel Comput.",
jrldate = "Oct. 1986",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{FernandezVelicia:1986:HPA,
author = "F. J. {Fern{\'a}ndez Velicia}",
title = "High-precision analytic approximations for the
{Fermi--Dirac} functions by means of elementary
functions",
journal = j-PHYS-REV-A-3,
volume = "34",
number = "5",
pages = "4387--4395",
year = "1986",
CODEN = "PLRAAN",
ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
MRclass = "33A70 (82A05)",
MRnumber = "MR869021 (88b:33024)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review. A. Third Series",
journal-URL = "http://pra.aps.org/browse",
}
@Article{Froman:1986:PIF,
author = "Per Olof Fr{\"o}man and Finn Karlsson and Staffan
Yngve",
title = "Phase-integral formulas for {Bessel} functions and
their relation to already existing asymptotic
formulas",
journal = j-J-MATH-PHYS,
volume = "27",
number = "11",
pages = "2738--2747",
month = nov,
year = "1986",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.527296",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "41A60 (33A40 81C12)",
MRnumber = "87j:41073",
bibdate = "Mon Oct 31 11:57:50 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v27/i11/p2738_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "10",
}
@InProceedings{Gal:1986:CEF,
author = "Shmuel Gal",
title = "Computing elementary functions: a new approach for
achieving high accuracy and good performance",
crossref = "Miranker:1986:ASC",
pages = "1--16",
year = "1986",
MRclass = "65D20",
MRnumber = "868 283",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gustavson:1986:FEF,
author = "F. G. Gustavson",
title = "Fast Elementary Function Algorithms for 370 Machines",
crossref = "Miranker:1986:ASC",
pages = "17--17",
year = "1986",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Misc/MPG/lncs235.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Hochstadt:1986:FMP,
author = "Harry Hochstadt",
title = "The Functions of Mathematical Physics",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xi + 322",
year = "1986",
ISBN = "0-486-65214-9 (paperback), 0-486-16878-6 (e-book)",
ISBN-13 = "978-0-486-65214-6 (paperback), 978-0-486-16878-4
(e-book)",
LCCN = "QA351 .H68 1986",
bibdate = "Tue Dec 5 10:51:16 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1: Orthogonal Polynomials \\
1 Linear Spaces / 1 \\
2 Orthogonal Polynomials / 6 \\
3 The Recurrence Formula / 8 \\
4 The Christoffel--Darboux Formula / 9 \\
5 The Weierstrass Approximation Theorem / 11 \\
6 The Zeros of the Orthogonal Polynomials / 14 \\
7 Approximation Theory / 16 \\
8 More about the Zeros of the Orthonormal Polynomials /
23 \\
9 The completeness of the Orthonormal Polynomials in
the Space of Square-Integrable Functions / 27 \\
10 Generalizations and an Application to Conformal
Mappings / 32 \\
\\
2: The Classical Orthogonal Polynomials 1 Rodrigues'
Formula and the Classical Orthogonal Polynomials / 39
\\
2 The Differential Equations Satisfied by the Classical
Orthogonal Polynomials / 43 \\
3 On the Zeros of the Jacobi Polynomials / 45 \\
4 An Alternative Approach to the Tchebicheff
Polynomials / 46 \\
5 An Application of the Hermite Polynomials to Quantum
Mechanics / 49 \\
6 The Completeness of the Hermite and Laguerre
Polynomials / 53 \\
7 Generating Functions / 57 \\
\\
3: The Gamma Function 1 Definitions and Basic
Properties / 61 \\
2 Analytic Continuation and Integral Representations /
65 \\
3 Asymptotic Expansions / 69 \\
4 Beta Functions / 75 \\
5 The Logarithmic Derivative of the Gamma Function / 77
\\
6 Mellin--Barnes Integrals / 78 \\
7 Mellin Transforms / 80 \\
8 Applications to Algebraic Equations / 81 \\
\\
4: Hypergeometric Functions 1 Review of Linear
Differential Equations with Regular Singular Points /
88 \\
2 The Hypergeometric Differential Equation / 90 \\
3 The Hypergeometric Function / 93 \\
4 A General Method for Finding Integral Representations
/ 100 \\
5 Integral Representations for the Hypergeometric
Function / 105 \\
6 The Twenty-four Solutions of the Hypergeometric /
Equation / 106 \\
7 The Schwarz--Christoffel Transformation / 112 \\
8 Mappings of Curvilinear Triangles / 119 \\
9 Group Theoretic Discussion of the Case $ \pi(\alpha_1
+ \alpha_2 + \alpha_3) > \pi$ / 130 \\
10 Nonlinear Transformations of Hypergeometric
Functions / 132 \\
\\
5: The Legendre Functions 1 Laplace's Differential
Equation / 138 \\
2 Maxwell's Theory of Poles / 140 \\
3 Relationship to the Hypergeometric Functions / 141
\\
4 Expansion Formulas / 147 \\
5 The Addition Theorem / 149 \\
6 Green's Functions / 153 \\
7 The Complete Solution of Legendre's Differential
Equation / 156 \\
8 Asymptotic Formulas / 161 \\
\\
6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous
Polynomials / 168 \\
2 Orthogonality of Spherical Harmonics / 171 \\
3 Legendre Polynomials / 175 \\
4 Applications to Boundary Value Problems / 183 \\
\\
7: Confluent Hypergeometric Functions 1 Relationship to
the Hypergeometric Functions / 189 \\
2 Applications of These Functions in Mathematical
Physics / 191 \\
3 Integral Representations / 195 \\
4 Asymptotic Representations / 198 \\
\\
8: Bessel Functions 1 Basic Definitions / 200 \\
2 Integral Representations / 203 \\
3 Relationship to the Legendre Functions / 205 \\
4 The Generating Function of the Bessel Function / 207
\\
5 More Integral Representations / 210 \\
6 Addition Theorems / 216 \\
7 The Complete Solution of Bessel's Equation / 223 \\
8 Asymptotic Expansions for Large Argument / 225 \\
9 Airy Functions / 230 \\
10 Asymptotic Expansions for Large Indices and Large
Arguments / 235 \\
11 Some Applications of Bessel Functions in Physical
Optics / 241 \\
12 The Zeros of Bessel Functions / 249 \\
13 Fourier--Bessel Expansions / 257 \\
14 Applications in Mathematical Physics / 266 \\
15 Discontinuous Integrals / 269 \\
\\
9: Hill's Equation 1 Mathieu's Equation / 281 \\
2 Hill's Equation / 282 \\
3 The Discriminant / 287 \\
4 Expansion Theorems / 299 \\
5 Inverse Problems / 305 \\
6 Hill's Equations with Even Coefficients / 309 \\
7 Mathieu's Equation Revisited / 310 \\
8 Energy Bands in Crystals / 313 \\
Appendix / 314 \\
\\
Bibliography / 318 \\
\\
Index / 321",
}
@Article{Hull:1986:VPE,
author = "T. E. Hull and A. Abrham",
title = "Variable Precision Exponential Function",
journal = j-TOMS,
volume = "12",
number = "2",
pages = "79--91",
month = jun,
year = "1986",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15 (65D20)",
MRnumber = "863 786",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/;
http://www.acm.org/pubs/toc/Abstracts/toms/6498.html",
acknowledgement = ack-nhfb,
bibno = "91",
content = "algorithms; verification; THEORY",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.4 Algorithm analysis; G.4
Certification and testing; G.4 Verification",
CRnumber = "1986-02428",
descriptor = "mathematics of computing, numerical analysis,
approximation, elementary function approximation;
mathematics of computing, mathematical software,
algorithm analysis; mathematics of computing,
mathematical software, certification and testing;
mathematics of computing, mathematical software,
verification",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
fortitle = "ACM Trans. Math. Softw.",
genterm = "June 1986",
guideno = "2",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; theory; verification",
review = "ACM CR 8702-0091",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Verification.",
}
@Article{Jacobsen:1986:FRC,
author = "Lisa Jacobsen and William B. Jones and Haakon
Waadeland",
title = "Further results on the computation of incomplete gamma
functions",
journal = j-LECT-NOTES-MATH,
volume = "1199",
pages = "67--89",
year = "1986",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0075936",
ISBN = "3-540-16768-4 (print), 3-540-38817-6 (e-book)",
ISBN-13 = "978-3-540-16768-6 (print), 978-3-540-38817-3
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "40A15 (33A10 33A15)",
MRnumber = "870245 (88f:40004)",
MRreviewer = "Marietta J. Tretter",
bibdate = "Thu May 15 18:46:23 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1985.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0075936/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0075930",
book-URL = "http://www.springerlink.com/content/978-3-540-38817-3",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Kushner:1986:ECC,
author = "Ed Kushner and Rick Broussard",
title = "Efficient computation of the cylindrical {Bessel}
functions of complex argument",
journal = j-COMP-PHYS-COMM,
volume = "42",
number = "3",
pages = "345--349",
month = nov,
year = "1986",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(86)90004-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:16 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465586900044",
abstract = "An algorithm that generates the cylindrical Bessel
function very accurately for a wide range of complex
arguments has been developed by Mason. The Mason
algorithm consists of four different methods that apply
to different portions of the complex plane. Experience
with the Floating Point Systems FPS-364
minisupercomputer indicates several ways by which these
methods can be made more efficient. Specific
improvements relate to: (1) the method for
determination of the point where backward recursion is
initiated for the Bessel functions of the first kind;
(2) the way that the Bessel functions of the first and
second kind are normalized when $ |y| < 5 $ and $ |x|
\leq 20 $; and (3) the extent that asymptotic
expansions are used when $ |x| > 20 $ and $ |y| < 5 $.
The first and third modifications will result in
increased efficiency for all architectures. The second
modification will be of value for many, but probably
not all, architectures.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Laforgia:1986:IBF,
author = "Andrea Laforgia",
title = "Inequalities for {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "15",
number = "1",
pages = "75--81",
month = may,
year = "1986",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:55 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786902396",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Lavoie:1986:SEG,
author = "J. L. Lavoie",
title = "Some evaluations for the generalized hypergeometric
series",
journal = j-MATH-COMPUT,
volume = "46",
number = "173",
pages = "215--218",
month = jan,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A35 (65D20)",
MRnumber = "87c:33007",
MRreviewer = "S. D. Bajpai",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0200 (Engineering mathematics and mathematical
techniques); B0290Z (Other numerical methods); C1100
(Mathematical techniques); C4190 (Other numerical
methods)",
corpsource = "Laval Univ., Que., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "evaluation formulae; generalized hypergeometric
series; series (mathematics); summation formulae; unit
argument; Whipple's theorem",
treatment = "T Theoretical or Mathematical",
}
@Article{Marsaglia:1986:CIG,
author = "John C. W. Marsaglia",
title = "{C249}. {The} incomplete gamma function and
{Ramanujan}'s rational approximation to $ e^x $",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "24",
number = "2",
pages = "163--168",
year = "1986",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949658608810899",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:11:07 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Muller:1986:MDC,
author = "Jean-Michel Muller",
title = "Une m{\'e}thodologie du calcul hardware des fonctions
{\'e}l{\'e}mentaires. ({French}) [{A} methodology for
the hardware computation of elementary functions]",
journal = j-MATH-MODEL-NUM-ANA,
volume = "20",
number = "4",
pages = "667--695",
year = "1986",
CODEN = "RMMAEV",
ISSN = "0764-583X (print), 1290-3841 (electronic)",
ISSN-L = "0764-583X",
MRclass = "65D20 (41-04)",
MRnumber = "88h:65043",
MRreviewer = "E. W. Cheney",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical modelling and numerical analysis =
Modelisation math{\'e}matique et analyse num{\'e}rique:
$M^2AN$",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=MZA",
language = "Russian",
}
@Article{Petkovic:1986:SIS,
author = "M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}",
title = "On some improvements of square root iteration for
polynomial complex zeros",
journal = j-J-COMPUT-APPL-MATH,
volume = "15",
number = "1",
pages = "13--25",
month = may,
year = "1986",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(86)90235-9",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:55 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786902359",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "polynomial root finding",
}
@Article{Piessens:1986:ATP,
author = "Robert Piessens and Shafique Ahmed",
title = "Approximation for the turning points of {Bessel}
functions",
journal = j-J-COMPUT-PHYS,
volume = "64",
number = "1",
pages = "253--257",
month = may,
year = "1986",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(86)90029-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:29 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199918690029X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Book{Prudnikov:1986:ISE,
author = "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
Oleg I. Mari{\v{c}}ev",
title = "Integrals and series. {Elementary} functions",
volume = "1",
publisher = "Gordon and Breach Science Publishers",
address = "New York, NY, USA",
pages = "798",
year = "1986",
ISBN = "2-88124-089-5",
ISBN-13 = "978-2-88124-089-8",
LCCN = "QA308.P7813 1986",
bibdate = "Thu Nov 2 15:40:35 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "1927--",
remark = "Translated from the Russian by N. M. Queen.",
seriestableofcontents = "v. 1. Elementary functions \\
v. 2. Special functions \\
v. 3. More special functions \\
v. 4. Direct Laplace transforms \\
v. 5. Inverse Laplace transforms",
subject = "Integrals; Series",
}
@Book{Prudnikov:1986:ISS,
author = "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
Oleg I. Mari{\v{c}}ev",
title = "Integrals and series. {Special} functions",
volume = "2",
publisher = "Gordon and Breach Science Publishers",
address = "New York, NY, USA",
pages = "750",
year = "1986",
ISBN = "2-88124-090-9",
ISBN-13 = "978-2-88124-090-4",
LCCN = "QA308.P7813 1986",
MRclass = "26A33, 26A36, 26A39, 26A42, 26B15, 26B20, 26B25",
bibdate = "Thu Nov 2 15:43:13 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Translated from the Russian by N. M. Queen.",
seriestableofcontents = "v. 1. Elementary functions \\
v. 2. Special functions \\
v. 3. More special functions \\
v. 4. Direct Laplace transforms \\
v. 5. Inverse Laplace transforms",
subject = "Integrals; Series",
}
@Article{Reichel:1986:PAU,
author = "L. Reichel",
title = "On polynomial approximation in the uniform norm by the
discrete least squares method",
journal = j-BIT,
volume = "26",
number = "3",
pages = "350--368",
month = jan,
year = "1986",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "12404",
catcode = "G.1.2; G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Least squares
approximation; G.1.2 Approximation; G.1.2 Spline and
piecewise polynomial approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Least squares approximation; Mathematics
of Computing, NUMERICAL ANALYSIS, Approximation, Spline
and piecewise polynomial approximation",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
genterm = "algorithms",
guideno = "1986-03278",
journal-URL = "http://link.springer.com/journal/10543",
jrldate = "Jan. 1986",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Ronning:1986:CTF,
author = "Gerd Ronning",
title = "On the curvature of the trigamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "15",
number = "3",
pages = "397--399",
month = jul,
year = "1986",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:56 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786902311",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{S:1986:CEF,
author = "A. S. Kuz'menko and K. I. Rogozin",
title = "Calculation of elementary functions in a number system
with arbitrary basis on the basis of order-differential
transformations. ({Russian})",
journal = "Prace Nauk. Inst. Cybernet. Tech. Politech.
Wroc{\l}aw. Ser. Konfer.",
volume = "74",
number = "31",
pages = "259--262",
year = "1986",
MRclass = "65G99 (65D20)",
MRnumber = "894 691",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Shore:1986:AID,
author = "Haim Shore",
title = "An approximation for the inverse distribution function
of a combination of random variables, with an
application to operating theatres",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "23",
number = "3",
pages = "157--181",
year = "1986",
CODEN = "JSCSAJ",
ISSN = "0094-9655 (print), 1563-5163 (electronic)",
ISSN-L = "0094-9655",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Ban-llan University, Israel",
bibno = "5358",
catcode = "G.3; G.m; G.1.2; G.2.1; J.3; G.3",
content = "The author worked on a project to predict the
percentage of time that operations are carried out
relative to the time that the operating theater is
available. The numerator of the percentage is a
weighted sum of the times required to carry out
different kinds of operations, where the weights are
the numbers of operations of each kind to be performed.
Since different kinds of operations have different mean
times, this sum has a skewed distribution.\par
Based on the Central Limit Theorem, the normal
distribution is the most widely used approximation to
the distribution of a weighted sum of random variables.
However, this approximation is not very good if the sum
has a skewed distribution.\par
In a separate paper [1], the author derived an
alternative approximation based on the first four
moments of the sum. In the present paper, he applies
this approximation to the operating theater problem by
estimating the moments of the times of the different
kinds of operations. The paper also contains a Monte
Carlo comparison of the normal approximation with the
proposed approximation for four underlying
distributions of the sum.",
CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2
Elementary function approximation; G.2.1 Combinatorics;
G.2.1 Generating functions; J.3 Health; G.3
Probabilistic algorithms (including Monte Carlo)",
CRnumber = "8612-1109",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
MISCELLANEOUS; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Generating functions;
Computer Applications, LIFE AND MEDICAL SCIENCES,
Health; Mathematics of Computing, PROBABILITY AND
STATISTICS, Probabilistic algorithms (including Monte
Carlo)",
fjournal = "Journal of Statistical Computation and Simulation",
genterm = "algorithms; measurement",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
journalabbrev = "J. Stat. Comput. Simul.",
jrldate = "1986",
reviewer = "M. Snyder",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.m
MISCELLANEOUS; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
DISCRETE MATHEMATICS; J. Computer Applications; J.3
LIFE AND MEDICAL SCIENCES; G. Mathematics of Computing;
G.3 PROBABILITY AND STATISTICS",
}
@Article{Skeel:1986:CVS,
author = "Robert D. Skeel",
title = "Construction of Variable-Stepsize Multistep Formulas",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "503--510, S45--S52",
month = oct,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65L05",
MRnumber = "87j:65080",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4110 (Error analysis in numerical methods); C4170
(Differential equations)",
corpsource = "Dept. of Comput. Sci., Illnois Univ., Urbana, IL,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Adams formula; adaptable multistep methods;
backward-differentiation; differential equations; error
analysis; estimation; first Dahlquist barrier; fixed
leading coefficient method; fixed-coefficient methods;
fixed-stepsize; formula; formula changing; initial
value; interpolatory methods; local error; minimum
storage variable-stepsize; multistep formula; Nordsieck
stepsize changing technique; problems; step methods;
variable; variable coefficient methods; variable-order
family of variable-coefficient formulas",
treatment = "T Theoretical or Mathematical",
}
@Article{Skeel:1986:SCV,
author = "Robert D. Skeel",
title = "Supplement to Construction of Variable-Stepsize
Multistep Formulas",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "S45--S52",
month = oct,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Temme:1986:DIC,
author = "N. M. Temme",
title = "A double integral containing the modified {Bessel}
function: asymptotics and computation",
journal = j-MATH-COMPUT,
volume = "47",
number = "176",
pages = "683--691",
month = oct,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A40 (41A60 65D30)",
MRnumber = "87m:33006",
MRreviewer = "S. D. Bajpai",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4110 (Error analysis in numerical methods); C4130
(Interpolation and function approximation); C4160
(Numerical integration and differentiation)",
corpsource = "Centre for Math. and Comput. Sci., Amsterdam,
Netherlands",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "distribution function; double integral; error
analysis; error function; integral; integration;
modified Bessel function; normal; polynomials;
probability; series (mathematics); series expansions;
two-dimensional",
treatment = "T Theoretical or Mathematical",
}
@Article{Thompson:1986:CBF,
author = "I. J. Thompson and A. R. Barnett",
title = "{Coulomb} and {Bessel} functions of complex arguments
and order",
journal = j-J-COMPUT-PHYS,
volume = "64",
number = "2",
pages = "490--509",
month = jun,
year = "1986",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(86)90046-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:30 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199918690046X",
abstract = "The Coulomb wavefunctions, originally constructed for
real $ \varrho > 0 $, real $ \eta $ and integer $
\lambda \geq 0 $ are defined for $ \varrho $, $ \eta $,
and $ \lambda $ all complex. We examine the complex
continuation of a variety of series and
continued-fraction expansions for the Coulomb functions
and their logarithmic derivatives, and then see how
these expansions may be selectively combined to
calculate both the regular and irregular functions and
their derivatives. The resulting algorithm [46] is a
complex generalisation of Steed's method [6, 7] as it
appears in the real procedure COULFG [10]. Complex
Whittaker, confluent hypergeometric and Bessel
functions can also be calculated.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Zaritskaya:1986:ACE,
author = "Z. V. Zaritskaya and A. I. Shva{\u\i} and P. {\=E}.
Antonyuk",
title = "Approximation of certain elementary functions in the
metric $ {L} $. ({Russian})",
journal = "Vestnik L'vov. Politekhn. Inst.",
volume = "202",
pages = "38--40",
year = "1986",
MRclass = "149.41A10 (33A10)",
MRnumber = "87j:41030",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Agarwal:1987:CNS,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "Clarification: {``New scalar and vector elementary
functions for the IBM System/370''} [{IBM J. Res.
Develop. {\bf 30} (1986), no. 2, 126--144}]",
journal = j-IBM-JRD,
volume = "31",
number = "2",
pages = "274--274",
month = mar,
year = "1987",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.312.0274",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "76W05",
MRnumber = "MR894626",
bibdate = "Mon Feb 12 08:07:08 2001",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
note = "See \cite{Agarwal:1986:NSV}.",
acknowledgement = ack-nhfb,
ajournal = "IBM J. Res. Develop.",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@PhdThesis{Braune:1987:HSF,
author = "K. Braune",
title = "{Hochgenaue Standardfunktionen f{\"u}r reelle und
komplexe Punkte und Intervalle in beliebigen
Gleitpunktrastern} \toenglish {High-Accuracy Elementary
Functions for Real and Complex Points and Intervals in
Arbitrary Floating-Point Systems} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1987",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Buhring:1987:BUA,
author = "Wolfgang B{\"u}hring",
title = "The behavior at unit argument of the hypergeometric
function {${}_3 F_2$}",
journal = j-SIAM-J-MATH-ANA,
volume = "18",
number = "5",
pages = "1227--1234",
month = sep,
year = "1987",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A30",
MRnumber = "88j:33004",
MRreviewer = "K. M. Saksena",
bibdate = "Sun Nov 28 19:24:11 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/18/5;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Carlson:1987:TEI,
author = "B. C. Carlson",
title = "A Table of Elliptic Integrals of the Second Kind",
journal = j-MATH-COMPUT,
volume = "49",
number = "180",
pages = "595--606, S13--S17",
month = oct,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05 (33A25 65V05)",
MRnumber = "89b:65013",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4160 (Numerical integration and differentiation);
C7310 (Mathematics)",
corpsource = "Dept. of Math., Iowa State Univ., Ames, IA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "elliptic integrals of the second kind; FORTRAN
listings; integration; mathematics computing; standard
R-functions",
treatment = "P Practical; T Theoretical or Mathematical; X
Experimental",
}
@Article{Crandall:1987:EFE,
author = "R. E. Crandall and J. P. Buhler",
title = "Elementary function expansions for {Madelung}
constants",
journal = j-J-PHYS-A,
volume = "20",
number = "16",
pages = "5497--5510",
year = "1987",
CODEN = "JPHAC5",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "82A60 (82-08)",
MRnumber = "MR924725 (88m:82034)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physics. A. Mathematical and General",
journal-URL = "http://iopscience.iop.org/0305-4470",
}
@Article{DiDonato:1987:AFS,
author = "Armido R. {DiDonato} and Alfred H. {Morris Jr.}",
title = "{Algorithm 654}: {FORTRAN} Subroutines for Computing
the Incomplete Gamma Function Ratios and their
Inverse",
journal = j-TOMS,
volume = "13",
number = "3",
pages = "318--319",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/29380.214348",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 4 21:43:08 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/pdf/10.1145/29380.214348",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation. {\bf G.m}: Mathematics of
Computing, MISCELLANEOUS.",
}
@Article{Dunham:1987:PMAa,
author = "Charles B. Dunham",
title = "Provably monotone approximations",
journal = j-SIGNUM,
volume = "22",
number = "2",
pages = "6--11",
month = apr,
year = "1987",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/24936.24938",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:15 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "theory; verification",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@Article{Dunham:1987:PMAb,
author = "Charles B. Dunham",
title = "Provably monotone approximations, {II}",
journal = j-SIGNUM,
volume = "22",
number = "3",
pages = "30--31",
month = jul,
year = "1987",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/36318.36323",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:15 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@Article{Gervais:1987:RAF,
author = "R. Gervais and Q. I. Rahman and G. Schmeisser",
title = "Representation and approximation of functions via $
(0, 2) $-interpolation",
journal = j-J-APPROX-THEORY,
volume = "50",
number = "2",
pages = "89--110",
month = jun,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30719",
catcode = "G.1.2; G.1.1",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.1 Interpolation; G.1.1 Spline and
piecewise polynomial interpolation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Spline and piecewise polynomial
interpolation",
fjournal = "Journal of Approximation Theory",
genterm = "theory; verification",
guideno = "1987-09238",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "June 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Ifantis:1987:UBF,
author = "E. K. Ifantis and P. D. Siafarikas and C. B. Kouris",
title = "Upper bounds for the first zeros of {Bessel}
functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "17",
number = "3",
pages = "355--358",
month = mar,
year = "1987",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:57 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042787901117",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Johnson:1987:AES,
author = "Kenneth C. Johnson",
title = "{Algorithm 650}: Efficient Square Root Implementation
on the 68000",
journal = j-TOMS,
volume = "13",
number = "2",
pages = "138--151",
month = jun,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/328512.328520",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15",
MRnumber = "898 489",
bibdate = "Sun Sep 4 21:36:32 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See also \cite{Johnson:1987:CES}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Johnson:1987:CES,
author = "Kenneth C. Johnson",
title = "Corrigendum: {``Algorithm 650: efficient square root
implementation on the 68000'' [ACM Trans. Math.
Software {\bf 13} (1987), no. 2, 138--151]}",
journal = j-TOMS,
volume = "13",
number = "3",
pages = "320--320",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/29380.356210",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "320. 65D15",
MRnumber = "918 582",
bibdate = "Thu Aug 08 15:52.08 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Johnson:1987:AES}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Kahan:1987:BCC,
author = "W. Kahan",
title = "Branch Cuts for Complex Elementary Functions or Much
Ado About Nothing's Sign Bit",
crossref = "Iserles:1987:SAN",
volume = "9",
pages = "165--211",
year = "1987",
MRclass = "65E05",
MRnumber = "88k:65027",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Inst. Math. Appl. Conf. Ser. New Ser.",
acknowledgement = ack-nhfb,
}
@Article{Kolbig:1987:BRC,
author = "K. S. K{\"o}lbig",
title = "Book Review: {{\booktitle{Calculation of Special
Functions, the Gamma Function, the Exponential
Integrals and Error-Like Functions}} (C. G. van der
Laan and N. M. Temme)}",
journal = j-SIAM-REVIEW,
volume = "29",
number = "4",
pages = "660--661",
month = "????",
year = "1987",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1029138",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:54:19 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/29/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "December 1987",
}
@PhdThesis{Kramer:1987:ISR,
author = "W. Kr{\"a}mer",
title = "Inverse Standardfunktionen f{\"u}r reelle und komplexe
Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
f{\"u}r beliebige Datenformate \toenglish {Inverse
Elementary Functions for Real and Complex Interval
Arguments with A-Priori Error Estimates for Arbitrary
Data Formats} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1987",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
author-dates = "1952--2014 (WK)",
}
@Article{Lewanowicz:1987:CRR,
author = "Stanis{\l}aw Lewanowicz",
title = "Corrigendum: {``Recurrence relations for
hypergeometric functions of unit argument''} {[Math.
Comp. {\bf 45} (1985), no. 172, 521--535, MR
86m:33004]}",
journal = j-MATH-COMPUT,
volume = "48",
number = "178",
pages = "853--853",
month = apr,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A35 (65Q05)",
MRnumber = "88a:33013",
bibdate = "Wed Jan 15 09:19:34 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@MastersThesis{Liu:1987:BEF,
author = "Z. A. Liu",
title = "{Berkeley} Elementary Function Test Suite",
type = "{M.S.} thesis",
school = "Computer Science Division, Department of Electrical
Engineering and Computer Science, Univerity of
California at Berkeley",
address = "Berkeley, CA, USA",
month = dec,
year = "1987",
bibdate = "Mon Sep 12 23:52:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
}
@Article{Lo:1987:HGA,
author = "Hao-Yung Lo and Jau-Ling Chen",
title = "A Hardwired Generalized Algorithm for Generating the
Logarithm Base-$k$ by Iteration",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "11",
pages = "1363--1367",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009477",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009477",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Mathis:1987:EFP,
author = "Robert F. Mathis",
title = "Elementary Functions Package for {Ada}",
crossref = "ACM:1987:UAA",
pages = "95--100",
month = dec,
year = "1987",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/ada.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Moricz:1987:ACF,
author = "Ferenc Moricz and Xianliang Shi",
title = "Approximation to continuous functions by {Cesaro}
means of double {Fourier} series and conjugate series",
journal = j-J-APPROX-THEORY,
volume = "49",
number = "4",
pages = "346--377",
month = apr,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30744",
catcode = "G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Least squares
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Least squares approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory; verification",
guideno = "1987-09224",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "April 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Musielak:1987:AEG,
author = "J. Musielak",
title = "Approximation of elements of a generalized {Orlicz}
sequence space by nonlinear, singular kernels",
journal = j-J-APPROX-THEORY,
volume = "50",
number = "4",
pages = "366--372",
month = aug,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30716",
catcode = "G.2.1; G.1.5; G.1.2",
CRclass = "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.5
Roots of Nonlinear Equations; G.1.5 Convergence; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Generating functions; Mathematics of
Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
Equations, Convergence; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory; verification",
guideno = "1987-09257",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Aug. 1987",
subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Pereira:1987:CEC,
author = "N. Costa Pereira",
title = "Corrigendum: {``Estimates for the Chebyshev function $
\psi (x) - \theta (x) $''} {[Math. Comp. {\bf 44}
(1985), no. 169, 211--221, MR 86k:11005]}",
journal = j-MATH-COMPUT,
volume = "48",
number = "177",
pages = "447--447",
month = jan,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11A25 (11N45 11Y35 33A70)",
MRnumber = "87k:11006",
bibdate = "Thu Jun 15 07:27:03 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Pereira:1985:ECF}.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Proinov:1987:NIA,
author = "Petko D. Proinov",
title = "Numerical integration and approximation of
differentiable functions, {II}",
journal = j-J-APPROX-THEORY,
volume = "50",
number = "4",
pages = "373--393",
month = aug,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30717",
catcode = "G.1.4; G.1.2",
CRclass = "G.1.4 Quadrature and Numerical Differentiation; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Quadrature and Numerical Differentiation; Mathematics
of Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory; verification",
guideno = "1987-09258",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Aug. 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Rolfe:1987:FIS,
author = "Timothy J. Rolfe",
title = "On a Fast Integer Square Root Algorithm",
journal = j-SIGNUM,
volume = "22",
number = "4",
pages = "6--11",
month = oct,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:16 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "algorithms; performance; theory",
subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations",
}
@Article{Smith:1987:BAM,
author = "P. W. Smith and J. J. Swetits",
title = "Best approximation by monotone functions",
journal = j-J-APPROX-THEORY,
volume = "49",
number = "4",
pages = "398--403",
month = apr,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30747",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory; verification",
guideno = "1987-09227",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "April 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Spanier:1987:AF,
author = "Jerome Spanier and Keith B. Oldham",
title = "An Atlas of Functions",
publisher = pub-HEMISPHERE,
address = pub-HEMISPHERE:adr,
pages = "ix + 700",
year = "1987",
ISBN = "0-89116-573-8, 3-540-17395-1",
ISBN-13 = "978-0-89116-573-6, 978-3-540-17395-3",
LCCN = "QA331 .S685 1987",
bibdate = "Fri Aug 31 16:20:13 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/canjstat.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "See also the second edition \cite{Oldham:2009:AF}.",
acknowledgement = ack-nhfb,
subject = "elementary functions; special functions; cognate
functions; complementary incomplete gamma function;
complementary modulus; complete beta function; complex
argument when; cosecant functions; cotangent functions;
digamma function; economized polynomial; error function
complement; eta numbers; function and its reciprocal;
hypergeometric algorithm; important definite integrals;
incomplete elliptic integrals; inverse gudermannian
function; inverse hyperbolic functions; negative
integer order; other definite integrals; parabolic
cylinder function; polygamma functions; purely
imaginary argument; reciprocal linear function;
reflection formula",
tableofcontents = "Preface / ix \\
0 General Considerations / 1 \\
1 The Constant Function $c$ / 11 \\
2 The Factorial Function $n!$ and Its Reciprocal / 19
\\
3 The Zeta Numbers and Related Functions / 25 \\
4 The Bernoulli Numbers, $B_n$ / 35 \\
5 The Euler Numbers, $E_n$ / 39 \\
6 The Binomial Coefficients $\binom{\nu}{m}$ / 43 \\
7 The Linear Function $b x + c$ and Its Reciprocal / 53
\\
8 The Unit-Step $u(x - a)$ and Related Functions / 63
\\
9 The Integer-Value ${\tt Int}(x)$ and Fractional-Value
${\tt frac}(x)$ Functions / 71 \\
10 The Dirac Delta Function $\delta(x - a)$ / 79 \\
11 The Integer Powers $(bx + c)^n$ and $x^n$ / 83 \\
12 The Square-Root Function $\sqrt{b x + c}$ and Its
Reciprocal / 91 \\
13 The Noninteger Powers $x^\nu$ / 99 \\
14 The $b \sqrt{a^2 - x^2}$ Function and Its Reciprocal
/ 107 \\
15 The $b \sqrt{x^2 + a}$ Function and Its Reciprocal /
115 \\
16 The Quadratic Function $a x^2 + b x + c$ and Its
Reciprocal / 123 \\
17 The Cubic Function $x^3 + a x^2 + b x + c$ and
Higher Polynomials / 131 \\
18 The Pochhammer Polynomials $(x)_n$ / 149 \\
19 The Bernoulli Polynomials $B_n(x)$ / 167 \\
20 The Euler Polynomials $E_n(x)$ / 175 \\
21 The Legendre Polynomials $P_n(x)$ / 183 \\
22 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
193 \\
23 The Laguerre Polynomials $L_n(x)$ / 209 \\
24 The Hermite Polynomials $H_n(x)$ / 217 \\
25 The Logarithmic Function $\ln(x)$ / 225 \\
26 The Exponential Function $\exp(b x + c)$ / 233 \\
27 Exponentials of Powers $\exp(-a x^\nu)$ / 253 \\
28 The Hyperbolic Sine $\sinh(x)$ and Cosine $\cosh(x)$
Functions / 263 \\
29 The Hyperbolic Secant $\sech(x)$ and Cosecant
$\csch(x)$ Functions / 273 \\
30 The Hyperbolic Tangent $\tanh(x)$ and Cotangent
$\coth(x)$ Functions / 279 \\
31 The Inverse Hyperbolic Functions / 285 \\
32 The Sine $\sin(x)$ and Cosine $\cos(x)$ Functions /
295 \\
33 The Secant $\sec(x)$ and Cosecant $\csc(x)$
Functions / 311 \\
34 The Tangent $\tan(x)$ and Cotangent $\cot(x)$
Functions / 319 \\
35 The Inverse Trigonometric Functions / 331 \\
36 Periodic Functions / 343 \\
37 The Exponential Integral $\Ei(x)$ and Related
Functions / 351 \\
38 Sine and Cosine Integrals / 361 \\
39 The Fresnel Integrals $S(x)$ and $C(x)$ / 373 \\
40 The Error Function $\erf(x)$ and Its Complement
$\erfc(x)$ / 385 \\
41 The $\exp(x) \erfc(\sqrt{x})$ and Related Functions
/ 395 \\
42 Dawson's Integral / 405 \\
43 The Gamma Function $\Gamma(x)$ / 411 \\
44 The Digamma Function $\psi(x)$ / 423 \\
45 The Incomplete Gamma $\gamma(\nu,x)$ and Related
Functions / 435 \\
46 The Parabolic Cylinder Function $D_\nu(x)$ / 445 \\
47 The Kummer Function $M(a; c; x)$ / 459 \\
48 The Tricomi Function $U(a; c; x)$ 471 \\
49 The Hyperbolic Bessel Functions $I_0(x)$ and
$I_1(x)$ / 479 \\
50 The General Hyperbolic Bessel Function $I_\nu(x)$ /
489 \\
51 The Basset Function $K_\nu(x)$ / 499 \\
52 The Bessel Coefficients $J_0(x)$ and $J_1(x)$ / 509
\\
53 The Bessel Function $J_\nu(x)$ / 521 \\
54 The Neumann Function $Y_\nu(x)$ / 533 \\
55 The Kelvin Functions / 543 \\
56 The Airy Functions $\Ai(x)$ and $\Bi(x)$ / 555 \\
57 The Struve Function / 563 \\
58 The Incomplete Beta Function $B(\nu; \mu; x)$ / 573
\\
59 The Legendre Functions $P_\nu(x)$ and $Q_\nu(x)$ /
581 \\
60 The Gauss Function $F(a, b; c; x)$ / 599 \\
61 The Complete Elliptic Integrals $K(p)$ and $E(p)$ /
609 \\
62 The Incomplete Elliptic Integrals $F(p; \phi)$ and
$E(p; \phi)$ / 621 \\
63 The Jacobian Elliptic Functions / 635 \\
64 The Hurwitz Function $\zeta(\nu; u)$ / 653 \\
Appendix A Utility Algorithms / 665 \\
Appendix B Some Useful Data / 673 \\
References and Bibliography / 679 \\
Subject Index / 681 \\
Symbol Index / 691",
}
@Article{Stoyanov:1987:AE,
author = "Basil J. Stoyanov and Richard A. Farrell",
title = "On the Asymptotic Evaluation of $ \int^{\pi / 2}_0
{J}^2_0 (\gamma \sin x) d x $",
journal = j-MATH-COMPUT,
volume = "49",
number = "179",
pages = "275--279",
month = jul,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "41A60 (65D30)",
MRnumber = "88e:41067",
MRreviewer = "Roderick Wong",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1120 (Analysis); C4180 (Integral equations)",
corpsource = "Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "analytical expression; asymptotic behavior; asymptotic
evaluation; Bessel functions; first kind; integral;
integral equations; order Bessel function; positive
parameter; zeroth-",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Tanese:1987:PGA,
author = "Reiko Tanese",
editor = "John J. Grefenstette",
booktitle = "Genetic algorithms and their applications: proceedings
of the second International Conference on Genetic
Algorithms: July 28--31, 1987 at the Massachusetts
Institute of Technology, Cambridge, {MA}",
title = "Parallel genetic algorithms for a hypercube",
publisher = pub-ERLBAUM,
address = pub-ERLBAUM:adr,
bookpages = "260",
pages = "177--183",
year = "1987",
ISBN = "0-8058-0158-8, 0-8058-0159-6 (paperback)",
ISBN-13 = "978-0-8058-0158-3, 978-0-8058-0159-0 (paperback)",
LCCN = "Q334 .I5561 1987",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$39.95",
acknowledgement = ack-nhfb,
bibno = "42536",
catcode = "I.2.6; G.1.0; G.1.2; C.1.2",
CRclass = "I.2.6 Learning; I.2.6 Analogies; G.1.0 General; G.1.0
Parallel algorithms; G.1.2 Approximation; G.1.2
Elementary function approximation; C.1.2 Multiple Data
Stream Architectures (Multiprocessors); C.1.2 Parallel
processors",
descriptor = "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Learning, Analogies; Mathematics of Computing,
NUMERICAL ANALYSIS, General, Parallel algorithms;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Parallel processors",
genterm = "algorithms; performance; experimentation",
guideno = "1988-16888",
procdate = "Sponsored by Amer. Assoc. for AI, Naval Res. Lab. and
Bolt Beranek & Newman, July 28-31, 1987",
procloc = "Cambridge, MA",
subject = "I. Computing Methodologies; I.2 ARTIFICIAL
INTELLIGENCE; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; C. Computer Systems Organization;
C.1 PROCESSOR ARCHITECTURES",
}
@InCollection{Temme:1987:CIG,
author = "N. M. Temme",
title = "On the computation of the incomplete gamma functions
for large values of the parameters",
crossref = "Mason:1987:AAB",
pages = "479--489",
year = "1987",
bibdate = "Fri Oct 18 16:42:44 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Thompson:1987:IEF,
author = "Peter Thompson",
title = "Implementing an Elementary Function Library",
journal = j-SIGNUM,
volume = "22",
number = "2",
pages = "2--5",
month = apr,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
bibno = "24937",
catcode = "G.m; D.3.2",
CRclass = "D.3.2 Language Classifications; D.3.2 OCCAM",
descriptor = "Mathematics of Computing, MISCELLANEOUS; Software,
PROGRAMMING LANGUAGES, Language Classifications,
OCCAM",
fjournal = "ACM SIGNUM Newsletter",
genterm = "theory; languages",
guideno = "1987-03363",
journal-URL = "https://dl.acm.org/loi/signum",
journalabbrev = "SIGNUM Newsl.",
jrldate = "April 1987",
subject = "G. Mathematics of Computing; G.m MISCELLANEOUS; D.
Software; D.3 PROGRAMMING LANGUAGES",
}
@Article{Thompson:1987:MBF,
author = "I. J. Thompson and A. R. Barnett",
title = "Modified {Bessel} functions {$ I_\nu (z) $} and {$
K_\nu (z) $} of real order and complex argument, to
selected accuracy",
journal = j-COMP-PHYS-COMM,
volume = "47",
number = "2--3",
pages = "245--257",
month = nov # "\slash " # dec,
year = "1987",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(87)90111-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:21 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See erratum \cite{Thompson:2004:EBB}.",
URL = "http://www.sciencedirect.com/science/article/pii/0010465587901111",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Timan:1987:DFP,
author = "A. F. Timan",
title = "Distribution of fractional parts and approximation of
functions with singularities by {Bernstein}
polynomials",
journal = j-J-APPROX-THEORY,
volume = "50",
number = "2",
pages = "167--174",
month = jun,
year = "1987",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "30725",
catcode = "G.1.5; G.1.2",
CRclass = "G.1.5 Roots of Nonlinear Equations; G.1.5 Polynomials,
methods for; G.1.2 Approximation; G.1.2 Elementary
function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Polynomials, methods for;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory; verification",
guideno = "1987-09244",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "June 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Visentin:1987:FAE,
author = "Kley Visentin and Pablo Mart{\'\i}n",
title = "Fractional approximation to elliptic functions",
journal = j-J-MATH-PHYS,
volume = "28",
number = "2",
pages = "330--333",
month = feb,
year = "1987",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.527661",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "41A10 (33A65)",
MRnumber = "87m:41009",
bibdate = "Mon Oct 31 11:57:55 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v28/i2/p330_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "4",
}
@Article{Zurawski:1987:DHS,
author = "J. H. P. Zurawski and J. B. Gosling",
title = "Design of a High-Speed Square Root Multiply and Divide
Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "1",
pages = "13--23",
month = jan,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009445",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Zwick:1987:BAC,
author = "D. Zwick",
title = "Best approximation by convex functions",
journal = j-AMER-MATH-MONTHLY,
volume = "94",
number = "6",
pages = "528--534",
month = jul,
year = "1987",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "University of Vermont, Vermont, NY",
bibno = "43727",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "American Mathematical Monthly",
genterm = "theory; verification",
guideno = "1988-04405",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
journalabbrev = "Am. Math. Monthly",
jrldate = "June/July 1987",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Aberth:1988:PNA,
author = "Oliver Aberth",
title = "Precise Numerical Analysis",
publisher = pub-WCB,
address = pub-WCB:adr,
pages = "x + 225",
year = "1988",
ISBN = "0-697-06760-2",
ISBN-13 = "978-0-697-06760-9",
LCCN = "QA297 .A28 1988",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "file://sunrise/u/sy/beebe/tex/bib/all_brec.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Aberth addresses elementary issues of precise floating
point computations using variable precision range
arithmetic. Numbers are represented as a variable
precision number $ \pm $ a range. Rational arithmetic
is also considered. Chapters are devoted to
\begin{enumerate} \item rootfinding, \item polynomial
rootfinding, \item numerical linear algebra, \item
differentiation and integration, and \item ordinary
differential equations.\end{enumerate} Differentiation
is handled by a codelist approach like [Rall81a], and
applications to Taylor series are given. Interval
techniques for ordinary differential equations are
based on using an {\it a priori\/} bound to capture
remainder terms. Several methods are illustrated,
including Taylor series methods.",
acknowledgement = ack-nj,
comment = "Text for a one semester, junior level course in
numerical analysis. Includes PC disk with software
written in PBASIC. Sound introductory level discussion
of code lists and error capture techniques.",
keywords = "differentiation; differentiation arithmetic; general
numerical analysis; integration; interval techniques;
linear algebra; ordinary differential equations.;
variable precision arithmetic",
}
@Article{Alonso:1988:SCN,
author = "Javier Alonso and Carlos Benitez",
title = "Some characteristic and non-characteristic properties
of inner product spaces",
journal = j-J-APPROX-THEORY,
volume = "55",
number = "3",
pages = "318--325",
month = dec,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56052",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "theory; verification",
guideno = "1988-10198",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Bailey:1988:CDD,
author = "David H. Bailey",
title = "The computation of $ \pi $ to $ 29, 360, 000 $ decimal
digits using {Borweins}' quartically convergent
algorithm",
journal = j-MATH-COMPUT,
volume = "50",
number = "181",
pages = "283--296",
month = jan,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y60 (11-04 11K16 65-04)",
MRnumber = "88m:11114",
MRreviewer = "A. J. van der Poorten",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C1140Z (Other and miscellaneous); C1160 (Combinatorial
mathematics); C4130 (Interpolation and function
approximation); C5470 (Performance evaluation and
testing); C7310 (Mathematics)",
corpsource = "NASA Ames Res. Centre, Moffet Field, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Borwein quartically convergent algorithm; computation
of pi; computer testing; Cray 2 computer test; decimal
expansion; elliptic integrals; iterative methods;
mathematics computing; multiprecision arithmetic;
number theory; prime modulus; series (mathematics);
statistical analyses; statistical analysis; transform",
treatment = "X Experimental",
}
@Article{Bloom:1988:LCL,
author = "Thomas Bloom",
title = "The {Lebesgue} constant for {Lagrange} interpolation
in the simplex",
journal = j-J-APPROX-THEORY,
volume = "54",
number = "3",
pages = "338--353",
month = sep,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56887",
catcode = "G.1.1; G.1.2; G.1.2; G.1.7; G.1.7",
CRclass = "G.1.1 Interpolation; G.1.1 Interpolation formulas;
G.1.2 Approximation; G.1.2 Minimax approximation and
algorithms; G.1.2 Approximation; G.1.2 Elementary
function approximation; G.1.7 Ordinary Differential
Equations; G.1.7 Convergence and stability; G.1.7
Ordinary Differential Equations; G.1.7 Boundary value
problems",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Interpolation formulas; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Minimax
approximation and algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations, Convergence
and stability; Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations, Boundary
value problems",
fjournal = "Journal of Approximation Theory",
guideno = "1988-10170",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Sept. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Borwein:1988:CFF,
author = "J. M. Borwein and P. B. Borwein",
title = "On the Complexity of Familiar Functions and Numbers",
journal = j-SIAM-REVIEW,
volume = "30",
number = "4",
pages = "589--601",
month = dec,
year = "1988",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1030134",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "68Q25 (03D15 11Y16)",
MRnumber = "967961; 89k:68061",
MRreviewer = "Klaus W. Wagner",
bibdate = "Sat Mar 29 09:54:29 MDT 2014",
bibsource = "ACM Computing Archive CD-ROM database (1991);
Compendex database;
http://epubs.siam.org/toc/siread/30/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
abstract = "This paper examines low-complexity approximations to
familiar functions and numbers. The intent is to
suggest that it is possible to base a taxonomy of such
functions and numbers on their computational
complexity. A central theme is that traditional methods
of approximation are often very far from optimal, while
good or optimal methods are often very far from
obvious. For most functions, provably optimal methods
are not known; however the gap between what is known
and what is possible is often small. A considerable
number of open problems are posed and a number of
related examples are presented.",
acknowledgement = ack-nhfb,
affiliationaddress = "Halifax, NS, Can",
bibno = "58008",
catcode = "G.1.2; F.2.1; F.1.3",
classification = "921",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; F.2.1 Numerical Algorithms and Problems;
F.1.3 Complexity Classes",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Classes",
fjournal = "SIAM Review",
genterm = "algorithms; theory; performance",
guideno = "1988-13907",
journal-URL = "http://epubs.siam.org/sirev",
journalabbrev = "SIAM Rev.",
journalabr = "SIAM Rev",
jrldate = "Dec. 1988",
keywords = "Algebraic Approximation; Approximation Theory;
Computation of Digits; Familiar Functions; Low
Complexity Approximation; Mathematical Techniques;
Rational Approximation; Reduced Complexity
Approximation",
onlinedate = "December 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1
COMPUTATION BY ABSTRACT DEVICES",
}
@Article{Borwein:1988:PAE,
author = "Peter B. Borwein",
title = "{Pad{\'e}} approximants for the $q$-elementary
functions",
journal = j-CONST-APPROX,
volume = "4",
number = "4",
pages = "391--402",
year = "1988",
ISSN = "0176-4276 (print), 1432-0940 (electronic)",
ISSN-L = "0176-4276",
MRclass = "41A21 (33A10 41A20)",
MRnumber = "89f:41022",
MRreviewer = "Annie A. M. Cuyt",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Constructive Approximation",
journal-URL = "http://link.springer.com/journal/365",
}
@InCollection{Brezinski:1988:NAC,
author = "Claude Brezinski",
booktitle = "{Nonlinear numerical methods and rational
approximation (Wilrijk, 1987)}",
title = "A new approach to convergence acceleration methods",
volume = "43",
publisher = "Reidel",
address = "Dordrecht",
pages = "373--405",
year = "1988",
MRclass = "65Bxx (40A25)",
MRnumber = "1005369 (90m:65010)",
MRreviewer = "John P. Coleman",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Math. Appl.",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Carlson:1988:TEI,
author = "B. C. Carlson",
title = "A Table of Elliptic Integrals of the Third Kind",
journal = j-MATH-COMPUT,
volume = "51",
number = "183",
pages = "267--280, S1--S5",
month = jul,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33A25 (65A05)",
MRnumber = "89k:33003",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290R (Integral equations); B0220 (Analysis); B0290D
(Functional analysis); B0290M (Numerical integration
and differentiation); C4180 (Integral equations); C1120
(Analysis); C4120 (Functional analysis); C4160
(Numerical integration and differentiation)",
corpsource = "Iowa State Univ., Ames, IA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Cauchy principal values; elliptic integrals; FORTRAN
listings; function evaluation; integral equations;
integration; points; real singular; recurrence
relations; standard R-functions",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Cartwright:1988:JTC,
author = "Donald I. Cartwright and Krzysztof Kucharski",
title = "{Jackson's Theorem} for compact connect {Lie} groups",
journal = j-J-APPROX-THEORY,
volume = "55",
number = "3",
pages = "352--359",
month = dec,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56056",
catcode = "G.2.m; G.1.2",
CRclass = "G.2.m Miscellaneous; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Journal of Approximation Theory",
genterm = "verification; theory",
guideno = "1988-10202",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Chellali:1988:ACN,
author = "Mustapha Chellali",
title = "Acc{\'e}l{\'e}ration de calcul de nombres de
{Bernoulli}. ({French}) [{Bernoulli} number calculation
acceleration]",
journal = j-J-NUMBER-THEORY,
volume = "28",
number = "3",
pages = "347--362",
month = mar,
year = "1988",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/0022-314X(88)90047-9",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:46:57 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0022314X88900479",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
language = "French",
}
@Article{Chiccoli:1988:EGE,
author = "C. Chiccoli and S. Lorenzutta and G. Maino",
title = "On the evaluation of generalized exponential integrals
{$ E_\nu (x) $}",
journal = j-J-COMPUT-PHYS,
volume = "78",
number = "2",
pages = "278--287",
month = oct,
year = "1988",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(88)90050-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:42 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999188900502",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Cover:1988:DII,
author = "Thomas M. Cover and Joy A. Thomas",
title = "Determinant inequalities via information theory",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "9",
number = "3",
pages = "384--392",
month = jul,
year = "1988",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "58040",
catcode = "H.1.1; G.1.3; F.2.1; G.1.2",
CRclass = "H.1.1 Systems and Information Theory; H.1.1
Information theory; G.1.3 Numerical Linear Algebra;
G.1.3 Determinants; F.2.1 Numerical Algorithms and
Problems; F.2.1 Computations on matrices; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Information Systems, MODELS AND PRINCIPLES, Systems
and Information Theory, Information theory; Mathematics
of Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Determinants; Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
genterm = "algorithms; theory; performance",
guideno = "1988-13777",
journal-URL = "http://epubs.siam.org/simax",
journalabbrev = "SIAM J. Matrix Anal. Appl.",
jrldate = "July 1988",
subject = "H. Information Systems; H.1 MODELS AND PRINCIPLES; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@InProceedings{Davenport:1988:ICF,
author = "J. H. Davenport",
editor = "N. M. Stephens and M. P. Thorne",
booktitle = "Computers in mathematical research: based on the
proceedings of a conference organized by the Institute
of Mathematics and its Applications on computers in
mathematical research, held at University College,
Cardiff in September 1986",
title = "Integration in closed form",
volume = "14",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
bookpages = "235",
year = "1988",
ISBN = "0-19-853620-8",
ISBN-13 = "978-0-19-853620-8",
LCCN = "QA11.A1 C618 1986",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$57.50",
series = "Institute of Mathematics and its applications
conference series, new series",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Bath",
bibno = "52474",
catcode = "J.2; F.2.1; G.1.2; G.1.2; I.2.9; F.2.1",
CRclass = "J.2 Mathematics and statistics; F.2.1 Numerical
Algorithms and Problems; F.2.1 Number-theoretic
computations; G.1.2 Approximation; G.1.2 Rational
approximation; G.1.2 Approximation; G.1.2 Elementary
function approximation; I.2.9 Robotics; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computations in finite
fields",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Mathematics and statistics; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Rational
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Robotics; Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations in finite
fields",
genterm = "algorithms; theory",
guideno = "1988-16247",
page = "119--134",
procdate = "Sept. 1986",
procloc = "Cardiff, Wales",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; I. Computing
Methodologies; I.2 ARTIFICIAL INTELLIGENCE; F. Theory
of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY",
waffil = "Univ. College, Cardiff, Wales; Univ. College, Cardiff,
Wales",
}
@TechReport{DiDonato:1988:SDC,
author = "Armido I. DiDonato and Alfred H. {Morris, Jr.}",
title = "Significant Digit Computation of the Incomplete Beta
Function Ratios",
type = "Technical Report",
number = "NSWC TR 88-365",
institution = "Naval Surface Warfare Center (K33)",
address = "Dahlgren, VA 22448-5000, USA",
month = nov,
year = "1988",
bibdate = "Sat Nov 15 10:30:20 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.dtic.mil/dtic/tr/fulltext/u2/a210118.pdf",
abstract = "An algorithm is given for evaluating the incomplete
beta function ratio $ I_x(a, b) $ and its complement $
1 - I_x(a, b) $. Two new procedures are used with
classical results. A listing of a transportable Fortran
subroutine using this algorithm is given. The
subroutine is accurate to 14 significant digits when
the precision is not restricted by inherent error.",
acknowledgement = ack-nhfb,
keywords = "bratio; continued fraction; expm1; gamma; incomplete
gamma function; ln; log1p; r1mach; spmpar",
}
@Article{Dunham:1988:PMA,
author = "Charles B. Dunham",
title = "Provably monotone approximations, {III}",
journal = j-SIGNUM,
volume = "23",
number = "1",
pages = "10--10",
month = jan,
year = "1988",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/43931.43934",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:16 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@TechReport{Duprat:1988:EPE,
author = "J. Duprat and J. M. Muller",
title = "Evaluation of Polynomials and elementary Functions by
integrated Circuits",
number = "RR698-I",
institution = "IMAG",
address = "Grenoble, France",
month = jan,
year = "1988",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/eureca.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Duprat:1988:HPE,
author = "Jean Duprat and Jean-Michel Muller",
title = "Hardwired polynomial evaluation",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "291--309",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "CNRS, Grenoble, Fr",
classification = "721; 722; 723; 921; C4130 (Interpolation and
function approximation); C5230 (Digital arithmetic
methods)",
corpsource = "Inst. Nat. Polytech. de Grenoble, France",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "computer architecture; computers, digital ---
Circuits; digital arithmetic; elementary functions;
hardwired polynomial evaluation; mathematical
functions; mathematical techniques; Polynomials;
polynomials; special-purpose circuits; VLSI
implementation",
treatment = "P Practical",
}
@Article{Feng:1988:AIN,
author = "Y. Y. Feng and J. Kozak",
title = "An approach to the interpolation of nonuniformly
spaced data",
journal = j-J-COMPUT-APPL-MATH,
volume = "23",
number = "2",
pages = "169--178",
month = aug,
year = "1988",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56475",
catcode = "G.1.1; G.1.2; G.1.7; G.1.1; G.1.4",
CRclass = "G.1.1 Interpolation; G.1.1 Spline and piecewise
polynomial interpolation; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.7 Ordinary
Differential Equations; G.1.7 Boundary value problems;
G.1.1 Interpolation; G.1.1 Smoothing; G.1.4 Quadrature
and Numerical Differentiation; G.1.4 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Spline and piecewise polynomial
interpolation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations, Boundary
value problems; Mathematics of Computing, NUMERICAL
ANALYSIS, Interpolation, Smoothing; Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Error analysis",
fjournal = "Journal of Computational and Applied Mathematics",
genterm = "algorithms; theory",
guideno = "1988-10490",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
journalabbrev = "J. Comput. Appl. Math.",
jrldate = "August 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Gawronski:1988:ZLT,
author = "Wolfgang Gawronski and Ulrich Stadtm{\"u}ller",
title = "On the zeros of {Lerch}'s transcendental function of
real parameters",
journal = j-J-APPROX-THEORY,
volume = "53",
number = "3",
pages = "354--364",
month = jun,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Trier, Trier, FRG; Univ. of Ulm, Ulm, FRG",
bibno = "49727",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "verification; theory",
guideno = "1988-10146",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "June 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Gillman:1988:ARG,
author = "E. Gillman and H. R. Fiebig",
title = "Accurate recursive generation of spherical {Bessel}
and {Neumann} functions for a large range of indices",
journal = j-COMPUT-PHYS,
volume = "2",
number = "1",
pages = "62--??",
month = jan,
year = "1988",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.168296",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:10 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.168296",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Guerrero:1988:HOT,
author = "Antonio L. Guerrero and Pablo Martin",
title = "Higher order two-point quasi-fractional approximations
to the {Bessel} functions {$ J_0 (x) $} and {$ J_1 (x)
$}",
journal = j-J-COMPUT-PHYS,
volume = "77",
number = "1",
pages = "276--281",
month = jul,
year = "1988",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(88)90168-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:41 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999188901684",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
remark = "This work produces only 3D approximations.",
}
@Article{Hautot:1988:CAC,
author = "A. Hautot",
title = "Convergence acceleration of continued fractions of
{Poincar{\'e}} type",
journal = j-APPL-NUM-MATH,
volume = "4",
number = "2--4",
pages = "309--322",
month = jun,
year = "1988",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65B05 (40A15)",
MRnumber = "90b:65005",
MRreviewer = "Gh. Adam",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@Article{Heilmann:1988:SSM,
author = "Margareta Heilmann",
title = "{$ L_p $}-saturation of some modified {Bernstein}
operators",
journal = j-J-APPROX-THEORY,
volume = "54",
number = "3",
pages = "260--273",
month = sep,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56880",
catcode = "G.1.2; G.1.9; G.1.7; G.1.7",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.9 Integral Equations; G.1.9
Integro-differential equations; G.1.7 Ordinary
Differential Equations; G.1.7 Boundary value problems;
G.1.7 Ordinary Differential Equations; G.1.7
Convergence and stability",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Integral
Equations, Integro-differential equations; Mathematics
of Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations, Boundary value problems; Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations, Convergence and stability",
fjournal = "Journal of Approximation Theory",
genterm = "algorithms; theory",
guideno = "1988-10163",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Sept. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Horwitz:1988:TPF,
author = "Alan L. Horwitz and Lee A. Rubel",
title = "Totally positive functions and totally bounded
functions on $ [ - 1, 1] $",
journal = j-J-APPROX-THEORY,
volume = "52",
number = "2",
pages = "204--216",
month = feb,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Pennsylvania State Univ., University Park; Univ. of
Illinois, Urbana",
bibno = "49653",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "verification; theory",
guideno = "1988-10106",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "February 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Ifantis:1988:BFP,
author = "E. K. Ifantis and P. D. Siafarikas",
title = "Bounds for the first positive zero of a mixed {Bessel}
function",
journal = j-J-COMPUT-APPL-MATH,
volume = "21",
number = "2",
pages = "245--249",
month = feb,
year = "1988",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:38 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042788902737",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Jacobsen:1988:CAL,
author = "Lisa Jacobsen and Haakon Waadeland",
title = "Convergence acceleration of limit periodic continued
fractions under asymptotic side conditions",
journal = j-NUM-MATH,
volume = "53",
number = "3",
pages = "285--298",
month = jul,
year = "1988",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65B99 (30B70 40A15)",
MRnumber = "89h:65010",
MRreviewer = "Claude Brezinski",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "B0290 (Numerical analysis); C4100 (Numerical
analysis)",
corpsource = "Dept. of Math. and Stat., Trondheim Univ., Dragvoll,
Norway",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "asymptotic side conditions; convergence acceleration;
convergence of numerical methods; hypergeometric
functions; limit periodic continued fractions; regular
C-fraction expansions",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Johnsson:1988:DPP,
author = "S. L. Johnsson",
editor = "J. R. Rice",
booktitle = "Mathematical aspects of scientific software",
title = "Data parallel programming and basic linear algebra
subroutines",
volume = "14",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "vi + 208",
pages = "183--196",
year = "1988",
ISBN = "0-387-96706-0",
ISBN-13 = "978-0-387-96706-6",
LCCN = "QA76.76.D47 M366 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "The IMS volumes in mathematics and its applications",
acknowledgement = ack-nhfb,
bibno = "42725",
catcode = "G.1.2; D.1.m; G.4",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; D.1.m Miscellaneous",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Software, PROGRAMMING TECHNIQUES, Miscellaneous;
Mathematics of Computing, MATHEMATICAL SOFTWARE",
genterm = "theory; algorithms; design; languages",
guideno = "1988-02324",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
D. Software; D.1 PROGRAMMING TECHNIQUES; G. Mathematics
of Computing; G.4 MATHEMATICAL SOFTWARE",
waffil = "Purdue Univ., West Lafayette, IN",
}
@Article{Kirby:1988:ELA,
author = "James C. Kirby",
title = "An Efficient Logarithm Algorithm for Calculators",
journal = j-COLLEGE-MATH-J,
volume = "19",
number = "3",
pages = "257--260",
month = may,
year = "1988",
CODEN = "????",
DOI = "https://doi.org/10.1080/07468342.1988.11973125",
ISSN = "0746-8342 (print), 1931-1346 (electronic)",
ISSN-L = "0746-8342",
bibdate = "Thu Feb 14 09:50:43 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/07468342.1988.11973125",
acknowledgement = ack-nhfb,
fjournal = "College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
https://www.jstor.org/journal/collmathj",
onlinedate = "30 Jan 2018",
}
@Article{Kowalski:1988:ASP,
author = "Marek Kowalski and Waldemar Sielski",
title = "Approximation of smooth periodic functions in several
variables",
journal = j-J-COMPLEXITY,
volume = "4",
number = "4",
pages = "356--372",
month = dec,
year = "1988",
CODEN = "JOCOEH",
ISSN = "0885-064X (print), 1090-2708 (electronic)",
ISSN-L = "0885-064X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56811",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of complexity",
genterm = "algorithms; verification; theory",
guideno = "1988-10411",
journal-URL = "http://www.sciencedirect.com/science/journal/0885064X",
journalabbrev = "J. Complexity",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Kramer:1988:ISF,
author = "W. Kr{\"a}mer",
title = "Inverse standard functions for real and complex point
and interval arguments with dynamic accuracy",
journal = j-COMPUTING-SUPPLEMENTUM,
pages = "185--212",
year = "1988",
CODEN = "COSPDM",
ISSN = "0344-8029",
bibdate = "Thu Dec 14 17:19:38 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Computer Arithmetic and Scientific Computation.",
abstract = "Algorithms to compute inverse standard functions to
arbitrary accuracy with safe error bounds are given.
Not only approximation errors but also all possible
rounding errors are considered. The desired accuracy of
the function as well as the base of the number system
used are parameters of the error formula. For
implementation it is only assumed that the four
elementary arithmetic operations are performed with a
certain number of correct digits of the function value.
The interval routines are constructed out of the point
routines considering the monotonicity behaviour of the
functions. The ambiguity of the complex functions is
briefly discussed.",
acknowledgement = ack-nhfb,
affiliation = "Karlsruhe Univ., West Germany",
author-dates = "1952--2014 (WK)",
classification = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
confdate = "30 Sept.-2 Oct. 1987",
conflocation = "Karlsruhe, West Germany",
confsponsor = "Karlsruhe Univ.; GAMM Committee",
fjournal = "Computing. Supplementum",
issue = "no.6 p. 185-212",
keywords = "Approximation errors; Dynamic accuracy; Error formula;
Interval arguments; Inverse standard functions;
Monotonicity behaviour; Rounding errors",
pubcountry = "Austria",
thesaurus = "Error analysis; Function approximation",
}
@Article{Laforgia:1988:MRI,
author = "Andrea Laforgia and Silvana Sismondi",
title = "Monotonicity results and inequalities for the gamma
and error functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "23",
number = "1",
pages = "25--33",
month = jul,
year = "1988",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:39 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042788903287",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Lembarki:1988:CAL,
author = "Alami Lembarki",
title = "Convergence acceleration of limit $k$-periodic
continued fractions",
journal = j-APPL-NUM-MATH,
volume = "4",
number = "2--4",
pages = "337--349",
month = jun,
year = "1988",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65B05 (40A15)",
MRnumber = "89j:65012",
MRreviewer = "Thomas A. Atchison",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@InCollection{Levrie:1988:CAM,
author = "Paul Levrie and Robert Piessens",
booktitle = "{Nonlinear numerical methods and rational
approximation (Wilrijk, 1987)}",
title = "Convergence acceleration for {Miller}'s algorithm",
volume = "43",
publisher = "Reidel",
address = "Dordrecht, The Netherlands",
pages = "349--370",
year = "1988",
MRclass = "65B10 (26C15 39A10)",
MRnumber = "1005368 (90m:65012)",
MRreviewer = "Pierre Hillion",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Math. Appl.",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Lou:1988:ETR,
author = "Lou van den Dries",
title = "On the elementary theory of restricted elementary
functions",
journal = j-J-SYMBOLIC-LOGIC,
volume = "53",
number = "3",
pages = "796--808",
year = "1988",
CODEN = "JSYLA6",
ISSN = "0022-4812 (print), 1943-5886 (electronic)",
ISSN-L = "0022-4812",
MRclass = "03C65 (03C40 03C68 12L12)",
MRnumber = "89i:03074",
MRreviewer = "M. Yasuhara",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Logic",
journal-URL = "http://projecteuclid.org/euclid.jsl;
http://www.jstor.org/journal/jsymboliclogic",
}
@PhdThesis{Marsaglia:1988:CES,
author = "John Christopher Winston Marsaglia",
title = "Computer Evaluation of the special functions of
probability and statistics",
type = "{Ph.D.} Dissertation",
school = "Department of Computer Science, Washington State
University",
address = "Pullman, WA, USA",
pages = "vii + 79",
month = aug,
year = "1988",
bibdate = "Wed Jun 22 07:17:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "$\exp(x)$; $\Phi(x)$; Bernoulli numbers; chi-square
distribution; continued fraction; continuous Poisson
distribution; Erlang distribution; exponential
distribution; Gamma function; incomplete Gamma
function; normal distribution; normal probability
distribution; Poisson distribution; Stirling's
approximation",
}
@Article{Milone:1988:EDF,
author = "L. A. Milone and A. A. E. Milone",
title = "Evaluation of {Dawson}'s function",
journal = j-ASTROPHYS-SPACE-SCI,
volume = "147",
number = "1",
pages = "189--191",
year = "1988",
CODEN = "APSSBE",
DOI = "https://doi.org/10.1007/bf00656618",
ISSN = "0004-640X (print), 1572-946X (electronic)",
ISSN-L = "0004-640X",
bibdate = "Sat Feb 17 11:54:06 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "Astrophys. Space Sci.",
fjournal = "Astrophysics and Space Science",
journal-URL = "http://link.springer.com/journal/10509",
}
@Article{Mimachi:1988:PRI,
author = "Katsuhisa Mimachi",
title = "A proof of {Ramanujan}'s identity by use of loop
integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "19",
number = "6",
pages = "1490--1493",
month = nov,
year = "1988",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "58904",
catcode = "G.1.9; G.1.2; F.2.2",
CRclass = "G.1.9 Integral Equations; G.1.9 Integro-differential
equations; G.1.2 Approximation; G.1.2 Elementary
function approximation; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Geometrical problems and
computations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Integral
Equations, Integro-differential equations; Mathematics
of Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations",
fjournal = "SIAM Journal on Mathematical Analysis",
genterm = "algorithms; theory",
guideno = "1988-13744",
journal-URL = "http://epubs.siam.org/sima",
journalabbrev = "SIAM J. Math. Anal.",
jrldate = "Nov. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY",
}
@Article{Muroi:1988:ECR,
author = "Kazuo Muroi",
title = "Extraction of Cube Roots in {Babylonian} Mathematics",
journal = j-CENTAURUS,
volume = "31",
number = "3",
pages = "181--188",
month = oct,
year = "1988",
CODEN = "CENTA4",
DOI = "https://doi.org/10.1111/j.1600-0498.1988.tb00736.x",
ISSN = "0008-8994 (print), 1600-0498 (electronic)",
ISSN-L = "0008-8994",
bibdate = "Sat Jul 27 18:43:36 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/centaurus.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Centaurus: An International Journal of the History of
Science and its Cultural Aspects",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1600-0498/",
onlinedate = "26 Jul 2007",
}
@Book{Nikiforov:1988:SFM,
author = "Arnol'd F. Nikiforov and Vasilij B. Uvarov",
title = "Special functions of mathematical physics: a unified
introduction with applications",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xviii + 427",
year = "1988",
ISBN = "3-7643-3183-6, 0-8176-3183-6",
ISBN-13 = "978-3-7643-3183-2, 978-0-8176-3183-3",
LCCN = "QC20.7.F87 N692e",
bibdate = "Sat Oct 30 18:34:41 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.gbv.de:20011/gvk",
note = "Translated from the Russian by Ralph P. Boas.",
URL = "http://www.gbv.de/dms/hbz/toc/ht002696178",
acknowledgement = ack-nhfb,
}
@Article{Olver:1988:EBL,
author = "F. W. J. Olver",
title = "Error Bounds for Linear Recurrence Relations",
journal = j-MATH-COMPUT,
volume = "50",
number = "182",
pages = "481--499",
month = apr,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65Q05 (39A10 65G05)",
MRnumber = "89e:65146",
MRreviewer = "B. Choczewski",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Maryland Univ., College Park, MD, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "a posteriori methods; analysis; Bessel function;
bounds; computational complexity; difference equations;
error; homogeneous second order; Legendre function;
linear recurrence relations; monotonic systems;
numerical examples; O(r) arithmetic operations;
oscillatory systems; realistic error; relations;
rounded interval arithmetic",
treatment = "T Theoretical or Mathematical",
}
@Article{Polyak:1988:SOM,
author = "R. A. Polyak",
title = "Smooth optimization methods for minimax problems",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "26",
number = "6",
pages = "1274--1286",
month = nov,
year = "1988",
CODEN = "SJCODC",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "57989",
catcode = "G.1.6; G.1.2; F.2.1; G.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Nonlinear programming; G.1.2
Approximation; G.1.2 Minimax approximation and
algorithms; F.2.1 Numerical Algorithms and Problems;
F.2.1 Computation of transforms; G.1.2 Approximation;
G.1.2 Elementary function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Nonlinear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Minimax
approximation and algorithms; Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computation of
transforms; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "SIAM Journal on Control and Optimization",
genterm = "algorithms; theory; performance",
guideno = "1988-13621",
journal-URL = "http://epubs.siam.org/sicon",
journalabbrev = "SIAM J. Control Optim.",
jrldate = "Nov. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@InCollection{Powell:1988:RBF,
author = "J. D. Powell",
editor = "D. F. (David Francis) Griffiths and G. A. Watson",
booktitle = "Numerical analysis 1987",
title = "Radial basis function approximations to polynomials",
volume = "170",
publisher = "Longman, Inc.",
address = "New York, NY, USA",
bookpages = "300",
pages = "223--241",
year = "1988",
ISBN = "0-582-02157-X",
ISBN-13 = "978-0-582-02157-0",
LCCN = "QA297.N828 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$54.95",
series = "Pitman research notes in mathematics series",
acknowledgement = ack-nhfb,
bibno = "54996",
catcode = "G.1.2; G.1.2; G.1.9; G.1.1; G.3; G.1.7",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Spline and
piecewise polynomial approximation; G.1.9 Integral
Equations; G.1.9 Integro-differential equations; G.1.1
Interpolation; G.1.1 Spline and piecewise polynomial
interpolation; G.3 Statistical computing; G.1.7
Ordinary Differential Equations; G.1.7 Convergence and
stability",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Spline and piecewise polynomial
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Integral Equations, Integro-differential
equations; Mathematics of Computing, NUMERICAL
ANALYSIS, Interpolation, Spline and piecewise
polynomial interpolation; Mathematics of Computing,
PROBABILITY AND STATISTICS, Statistical computing;
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Convergence and stability",
genterm = "algorithms; performance",
guideno = "1988-01246",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G.3 PROBABILITY AND STATISTICS",
waffil = "Univ. of Dundee; Univ. of Dundee",
}
@Article{Proinov:1988:ISF,
author = "Petko D. Proinov",
title = "Integration of smooth functions and $ \phi
$-discrepancy",
journal = j-J-APPROX-THEORY,
volume = "52",
number = "3",
pages = "284--292",
month = mar,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Plovdiv, Plovdiv, Bulgaria",
bibno = "49659",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "verification; theory",
guideno = "1988-10111",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "March 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Puoskari:1988:MCB,
author = "M. Puoskari",
title = "A method for computing {Bessel} function integrals",
journal = j-J-COMPUT-PHYS,
volume = "75",
number = "2",
pages = "334--344",
month = apr,
year = "1988",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(88)90116-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:40 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999188901167",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Richardson:1988:NMT,
author = "Daniel Richardson",
title = "Nonstandard models of the theory of elementary
functions of a real variable",
journal = j-Z-MATH-LOGIK-GRUNDL-MATH,
volume = "34",
number = "4",
pages = "355--372",
year = "1988",
CODEN = "ZMLGAQ",
ISBN = "0044-3050",
ISBN-13 = "0044-3050",
ISSN = "0044-3050",
MRclass = "03B30 (03C62 03H15 26E35)",
MRnumber = "90a:03009",
MRreviewer = "Reuven H. Gurevi{\v{c}}",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r mathematische Logik und
Grundlagen der Mathematik}",
}
@Article{Ruscheweyh:1988:EST,
author = "Stephan Ruscheweyh",
title = "Extension of {Szeg{\H{o}}}'s theorem on the sections
of univalent functions",
journal = j-SIAM-J-MATH-ANA,
volume = "19",
number = "6",
pages = "1442--1449",
month = nov,
year = "1988",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "58899",
catcode = "G.1.2; G.1.9; F.2.2; F.2.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.9 Integral Equations; G.1.9
Integro-differential equations; F.2.2 Nonnumerical
Algorithms and Problems; F.2.2 Computations on discrete
structures; F.2.2 Nonnumerical Algorithms and Problems;
F.2.2 Geometrical problems and computations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Integral
Equations, Integro-differential equations; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations",
fjournal = "SIAM Journal on Mathematical Analysis",
genterm = "algorithms; theory",
guideno = "1988-13739",
journal-URL = "http://epubs.siam.org/sima",
journalabbrev = "SIAM J. Math. Anal.",
jrldate = "Nov. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}
@Article{Schappacher:1988:EIG,
author = "Norbert Schappacher",
title = "Elliptic integrals and the gamma function",
journal = j-LECT-NOTES-MATH,
volume = "1301",
pages = "117--127",
year = "1988",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0082098",
ISBN = "3-540-18915-7 (print), 3-540-38842-7 (e-book)",
ISBN-13 = "978-3-540-18915-2 (print), 978-3-540-38842-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Fri May 9 19:07:24 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1985.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0082098/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0082094",
book-URL = "http://www.springerlink.com/content/978-3-540-38842-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@InProceedings{Schwarz:1988:CLI,
author = "Jerry Schwarz",
title = "A {C++} Library for Infinite Precision Floating
Point",
crossref = "USENIX:1988:UPC",
bookpages = "362",
pages = "271--281",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "ftp://ftp.uu.net/library/bibliography;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The Real library supports infinite precision floating
point computation in C++. Arbitrary precision rational
arithmetic and transcendental functions are
supported.",
acknowledgement = ack-nhfb,
affiliation = "AT\&T Bell Laboratories, Murray Hill",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
confdate = "17--21 Oct. 1988",
conflocation = "Denver, CO, USA",
keywords = "C++ library; Infinite precision floating point;
Rational arithmetic; Real library; Transcendental
functions",
pubcountry = "USA",
thesaurus = "C language; Digital arithmetic; Object-oriented
programming; Subroutines",
}
@InProceedings{Sobczyk:1988:SMA,
author = "Kazimierz Sobczyk",
editor = "W. Schiehlen and W. Wedig",
booktitle = "Analysis and estimation of stochastic mechanical
systems",
title = "Stochastic modelling and analysis of fatigue",
volume = "303",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "350",
pages = "269--313",
year = "1988",
ISBN = "0-387-82058-2",
ISBN-13 = "978-0-387-82058-3",
LCCN = "TA350.3.I5 no.303; TJ173 .A531 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Courses and lectures",
acknowledgement = ack-nhfb,
bibno = "58064",
catcode = "J.2; I.6.3; G.1.8; G.3; G.1.2; G.1.9",
CRclass = "J.2 Engineering; I.6.3 Applications; G.1.8 Partial
Differential Equations; G.1.8 Difference methods; G.3
Probabilistic algorithms (including Monte Carlo); G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.9 Integral Equations; G.1.9 Integro-differential
equations",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Engineering; Computing Methodologies,
SIMULATION AND MODELING, Applications; Mathematics of
Computing, NUMERICAL ANALYSIS, Partial Differential
Equations, Difference methods; Mathematics of
Computing, PROBABILITY AND STATISTICS, Probabilistic
algorithms (including Monte Carlo); Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Integral Equations,
Integro-differential equations",
genterm = "algorithms; theory; design; measurement; reliability",
guideno = "1988-17476",
procdate = "1987",
procloc = "International Centre for Mechanical Sciences in
Udine",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; I. Computing Methodologies; I.6 SIMULATION
AND MODELING; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3
PROBABILITY AND STATISTICS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS",
waffil = "Univ. of Stuttgart; Univ. of Karlsruhe",
}
@Article{Stephens:1988:SCR,
author = "A. J. Stephens and H. C. Williams",
title = "Some computational results on a problem concerning
powerful numbers",
journal = j-MATH-COMPUT,
volume = "50",
number = "182",
pages = "619--632",
month = apr,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11R11 (11A51 11R27 11Y16 11Y40)",
MRnumber = "89d:11091",
MRreviewer = "H. J. Godwin",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0210 (Algebra); B0250 (Combinatorial mathematics);
C1110 (Algebra); C1160 (Combinatorial mathematics)",
corpsource = "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computational complexity; continued; fractions; free
integer; fundamental unit; number theory; positive
square-; real quadratic number fields; regulator
algorithm Amdahl 5850; step algorithm; time complexity
$O(D^{1/4+\epsilon})$",
treatment = "T Theoretical or Mathematical; X Experimental",
}
@InProceedings{Stillinger:1988:CPS,
author = "Frank H. Stillinger",
editor = "Donald G. Truhlar",
booktitle = "Mathematical frontiers in computational chemical
physics",
title = "Collective phenomena in statistical mechanics and the
geometry of potential energy hypersurfaces",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xii + 349",
pages = "157--173",
year = "1988",
ISBN = "0-387-96782-6",
ISBN-13 = "978-0-387-96782-0",
LCCN = "QD455.3.M3 M38 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the Workshop on Atomic and Molecular
Structure and Dynamics, held June 15--July 24, 1987, at
the Institute for Mathematics and Its Applications,
University of Minnesota.",
price = "US\$36.80",
series = "The IMA volumes in mathematics and its applications",
acknowledgement = ack-nhfb,
bibno = "58051",
catcode = "J.2; J.2; J.2; F.2.2; G.3; G.1.2",
CRclass = "J.2 Physics; J.2 Chemistry; J.2 Engineering; F.2.2
Nonnumerical Algorithms and Problems; F.2.2 Geometrical
problems and computations; G.3 Statistical computing;
G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics; Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Chemistry; Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Engineering; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations; Mathematics of Computing, PROBABILITY AND
STATISTICS, Statistical computing; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
genterm = "algorithms; theory",
guideno = "1988-17776",
procdate = "1982",
procloc = "Univ. of Minnesota, Minneapolis",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; J. Computer Applications; J.2 PHYSICAL
SCIENCES AND ENGINEERING; J. Computer Applications; J.2
PHYSICAL SCIENCES AND ENGINEERING; F. Theory of
Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY; G. Mathematics of Computing; G.3
PROBABILITY AND STATISTICS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS",
waffil = "Univ. of Minnesota, Minneapolis",
}
@Article{Sun:1988:SAF,
author = "Xiehua Sun",
title = "On the simultaneous approximation of functions and
their derivatives by the {Szasz--Mirakyan} operator",
journal = j-J-APPROX-THEORY,
volume = "55",
number = "3",
pages = "279--288",
month = dec,
year = "1988",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "56048",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "verification; theory",
guideno = "1988-10194",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Dec. 1988",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@TechReport{Tang:1988:PIG,
author = "Ping Tak Peter Tang",
title = "Portable Implementation of a Generic Exponential
Function",
type = "Technical report",
number = "ANL-88-3",
institution = inst-ANL,
address = inst-ANL:adr,
year = "1988",
bibdate = "Fri Dec 28 11:27:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{vanRijckevorsek:1988:CCA,
editor = "Jan L. A. van Rijckevorsek and Jan de Leeus",
title = "Component and correspondence analysis: dimension
reduction by functional approximation",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 146",
year = "1988",
ISBN = "0-471-91847-4",
ISBN-13 = "978-0-471-91847-9",
LCCN = "QA278.5 .C6571 1988",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$40",
series = "Wiley series in probability and mathematical
statistics",
acknowledgement = ack-nhfb,
bibno = "59092",
catcode = "G.1.2; G.3",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.3 Statistical computing",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing",
genterm = "theory; algorithms",
guideno = "1988-03042",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS",
}
@Book{Vilenkin:1988:SFT,
author = "N. Ja. (Naum Jakovlevich) Vilenkin",
title = "Special functions and the theory of group
representations",
volume = "22",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "x + 613",
year = "1988",
ISBN = "0-8218-1572-5",
ISBN-13 = "978-0-8218-1572-4",
LCCN = "QA3 .A5 v.22 1988",
bibdate = "Sat Oct 30 17:01:56 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Reprint of 1968 edition.",
series = "Translations of mathematical monographs",
acknowledgement = ack-nhfb,
subject = "Representations of groups; Functions, Special",
}
@Article{Wong:1988:AE,
author = "R. Wong",
title = "Asymptotic Expansion of $ \int^{\pi / 2}_0 {J}^2_\nu
(\lambda \cos \theta) d \theta $",
journal = j-MATH-COMPUT,
volume = "50",
number = "181",
pages = "229--234",
month = jan,
year = "1988",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "41A60 (33A40)",
MRnumber = "89g:41022",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "A0260 (Numerical approximation and analysis); A0270
(Computational techniques); C4130 (Interpolation and
function approximation); C4160 (Numerical integration
and differentiation)",
corpsource = "Dept. of Appl. Math., Manitoba Univ., Winnipeg, Man.,
Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic expansion; Bessel function; Bessel
functions; crystallography; diffraction theory;
function approximation; integral; integration",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Ahmed:1989:EEF,
author = "H. M. Ahmed",
title = "Efficient Elementary Function Generation with
Multipliers",
crossref = "Ercegovac:1989:PSC",
pages = "52--59",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
}
@Article{Armbruster:1989:KSD,
author = "Dieter Armbruster and John Guckenheimer and Philip
Holmes",
title = "{Kuramoto--Sivashinsky} dynamics on the
center-unstable manifold",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "676--691",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY;
Cornell Univ., Ithaca, NY",
bibno = "64938",
catcode = "G.1.7; G.1.7; G.1.0; J.2; G.1.2; G.1.8",
CRclass = "G.1.7 Ordinary Differential Equations; G.1.7
Convergence and stability; G.1.7 Ordinary Differential
Equations; G.1.7 Boundary value problems; G.1.0
General; G.1.0 Numerical algorithms; J.2 Physics; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.8 Partial Differential Equations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Convergence and stability;
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Boundary value problems;
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms; Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Physics; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Partial Differential
Equations",
fjournal = "SIAM Journal on Applied Mathematics",
genterm = "algorithms; theory; experimentation",
guideno = "1989-09707",
journal-URL = "http://epubs.siam.org/siap",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Avellaneda:1989:OBE,
author = "Marco Avellaneda and Graeme W. Milton",
title = "Optimal bounds on the effective bulk modulus of
polycrystals",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "824--837",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64947",
catcode = "G.1.8; J.2; G.1.2; G.1.6",
CRclass = "G.1.8 Partial Differential Equations; G.1.8 Difference
methods; J.2 Physics; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.6 Optimization;
G.1.6 Constrained optimization",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations, Difference methods; Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Physics; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Constrained optimization",
fjournal = "SIAM Journal on Applied Mathematics",
genterm = "algorithms; theory; experimentation",
guideno = "1989-09716",
journal-URL = "http://epubs.siam.org/siap",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Bauer:1989:BKR,
author = "Friedrich L. Bauer",
title = "{Eine Bemerkung zu Koechers Reihen f{\"u}r die
Eulersche Konstante}. ({German}) [{A} remark on
{Koecher}'s series for the {Euler}'s constant]",
journal = "Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber.",
pages = "27--33 (1990)",
year = "1989",
ISSN = "0340-7586",
MRclass = "11Y60 (65D20) 26A06 11Y60 65D20",
MRnumber = "1086008",
MRreviewer = "F. Beukers",
bibdate = "Thu Aug 20 18:22:34 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMID = "00005959",
ZMnumber = "0777.26004",
acknowledgement = ack-nhfb,
author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
March 2015)",
fjournal = "Bayerische Akademie der Wissenschaften.
Mathematisch-Naturwissenschaftliche Klasse.
Sitzungsberichte",
keywords = "asymptotic expansion; Euler's constant; series
representation",
language = "German",
}
@Article{Belaga:1989:TMM,
author = "E. G. Belaga",
title = "Through the mincing machine with a {Boolean} layer
cake: nonstandard computations over {Boolean} circuits
in the lower-bounds-to-circuit-size complexity
proving",
journal = j-ACTA-INFO,
volume = "26",
number = "4",
pages = "381--407",
month = feb,
year = "1989",
CODEN = "AINFA2",
ISSN = "0001-5903 (print), 1432-0525 (electronic)",
ISSN-L = "0001-5903",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. Louis Pasteur, Strasbourg Cedex, France and
Univ. su Pisa, Pisa, Italy",
bibno = "69310",
catcode = "F.4.1; B.6.1; F.1.1; F.1.3; F.2.2; F.1.2; G.1.2;
F.2.2",
CRclass = "F.4.1 Mathematical Logic; F.4.1 Computational logic;
B.6.1 Design Styles; B.6.1 Combinational logic; F.1.1
Models of Computation; F.1.1 Unbounded-action devices;
F.1.3 Complexity Classes; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Complexity of proof procedures;
F.1.2 Modes of Computation; F.1.2 Alternation and
nondeterminism; G.1.2 Approximation; G.1.2 Elementary
function approximation; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Computations on discrete
structures",
descriptor = "Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic, Computational logic;
Hardware, LOGIC DESIGN, Design Styles, Combinational
logic; Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Models of Computation, Unbounded-action
devices; Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Complexity Classes; Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Complexity of
proof procedures; Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Alternation and
nondeterminism; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures",
fjournal = "Acta Informatica",
genterm = "algorithms; theory",
guideno = "1989-03239",
journal-URL = "http://www.springerlink.com/content/0001-5903",
journalabbrev = "Acta Inf.",
jrldate = "Feb. 1989",
subject = "F. Theory of Computation; F.4 MATHEMATICAL LOGIC AND
FORMAL LANGUAGES; B. Hardware; B.6 LOGIC DESIGN; F.
Theory of Computation; F.1 COMPUTATION BY ABSTRACT
DEVICES; F. Theory of Computation; F.1 COMPUTATION BY
ABSTRACT DEVICES; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
Theory of Computation; F.1 COMPUTATION BY ABSTRACT
DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY",
}
@Article{Birge:1989:SUB,
author = "John R. Birge and Roger J. Wets",
title = "Sublinear upper bounds for stochastic programs with
recourse",
journal = j-MATH-PROG,
volume = "43",
number = "2",
pages = "131--149",
month = feb,
year = "1989",
CODEN = "MHPGA4",
ISSN = "0025-5610",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Michigan, Ann Arbor; Univ. of California,
Davis",
bibno = "65226",
catcode = "G.1.6; G.1.7; G.3; G.1.6; G.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.7
Ordinary Differential Equations; G.1.7 Convergence and
stability; G.3 Probabilistic algorithms (including
Monte Carlo); G.1.6 Optimization; G.1.6 Gradient
methods; G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations, Convergence and stability; Mathematics of
Computing, PROBABILITY AND STATISTICS, Probabilistic
algorithms (including Monte Carlo); Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization, Gradient
methods; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Mathematical Programming",
genterm = "algorithms; theory; performance",
guideno = "1989-09042",
journal-URL = "http://link.springer.com/journal/10107",
journalabbrev = "Math. Program.",
jrldate = "February 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Borwein:1989:MI,
author = "J. M. Borwein and P. B. Borwein",
title = "On the Mean Iteration $ (a, b) \leftarrow \big (\frac
{a + 3b}{4}, \frac {\sqrt {ab} + b}{2} \big) $",
journal = j-MATH-COMPUT,
volume = "53",
number = "187",
pages = "311--326",
month = jul,
year = "1989",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008364",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "30D05 (33A25)",
MRnumber = "968148, 90a:30075",
MRreviewer = "Carl C. Cowen",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
URL = "http://docserver.carma.newcastle.edu.au/1586/",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Math. Stat. and Comput. Sci., Dalhousie
Univ., Halifax, NS, Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computation; convergence of numerical methods;
converging process; iterative methods; iterative
process; limit; mean iteration; nontrivial
identifications; quadratically; symbolic; uniformizing
parameters",
treatment = "T Theoretical or Mathematical",
}
@Article{Borwein:1989:RME,
author = "J. M. Borwein and P. B. Borwein and D. H. Bailey",
title = "{Ramanujan}, modular equations, and approximations to
$ \pi $ or how to compute one billion digits of $ \pi
$",
journal = j-AMER-MATH-MONTHLY,
volume = "96",
number = "3",
pages = "201--219",
month = mar,
year = "1989",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Dalhousie Univ., Halifax; Dalhousie Univ., Halifax",
bibno = "65243",
catcode = "I.1.2; G.1.2; G.1.8; G.1.4; I.1.3; F.2.1; F.2.1",
CRclass = "I.1.2 Algorithms; I.1.2 Algebraic algorithms; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.8 Partial Differential Equations; G.1.8 Elliptic
equations; G.1.4 Quadrature and Numerical
Differentiation; G.1.4 Multiple quadrature; I.1.3
Languages and Systems; F.2.1 Numerical Algorithms and
Problems; F.2.1 Computation of transforms; F.2.1
Numerical Algorithms and Problems; F.2.1
Number-theoretic computations",
descriptor = "Computing Methodologies, ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Partial Differential
Equations, Elliptic equations; Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Multiple quadrature; Computing
Methodologies, ALGEBRAIC MANIPULATION, Languages and
Systems; Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computation of transforms; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations",
fjournal = "American Mathematical Monthly",
genterm = "algorithms; theory",
guideno = "1989-03459",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
journalabbrev = "Am. Math. Monthly",
jrldate = "March 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
}
@Article{Bos:1989:CPR,
author = "L. Bos",
title = "A characteristic of points in {$ R^2 $} having
{Lebesgue} function of polynomial growth",
journal = j-J-APPROX-THEORY,
volume = "56",
number = "3",
pages = "316--329",
month = mar,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72254",
catcode = "F.2.1; G.1.1; G.1.2; F.2.2; G.1.2; G.1.3",
CRclass = "F.2.1 Numerical Algorithms and Problems; F.2.1
Computations on matrices; G.1.1 Interpolation; G.1.1
Interpolation formulas; G.1.2 Approximation; G.1.2
Elementary function approximation; F.2.2 Nonnumerical
Algorithms and Problems; F.2.2 Geometrical problems and
computations; G.1.2 Approximation; G.1.2 Chebyshev
approximation and theory; G.1.3 Numerical Linear
Algebra; G.1.3 Sparse and very large systems",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices; Mathematics of Computing,
NUMERICAL ANALYSIS, Interpolation, Interpolation
formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Chebyshev approximation and theory;
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Sparse and very large systems",
fjournal = "Journal of Approximation Theory",
genterm = "algorithms; theory",
guideno = "1989-07812",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Mar. 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Boyd:1989:CFS,
author = "John Philip Boyd",
title = "{Chebyshev} and {Fourier} spectral methods",
volume = "49",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 798",
year = "1989",
ISBN = "0-387-51487-2, 3-540-51487-2",
ISBN-13 = "978-0-387-51487-1, 978-3-540-51487-9",
LCCN = "QA404.5 .B69 1989",
bibdate = "Sat Feb 17 14:00:30 MST 2024",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture notes in engineering",
acknowledgement = ack-nhfb,
subject = "Chebyshev polynomials; Fourier analysis; Spectral
theory (Mathematics); Polyn{\'y}omes de Tchebychev;
Analyse de Fourier; Spectre (Math{\'y}ematiques);
Chebyshev polynomials; Fourier analysis; Spectral
theory (Mathematics)",
}
@Article{Bronstein:1989:AIE,
author = "Manuel Bronstein",
title = "An algorithm for the integration of elementary
functions",
journal = j-LECT-NOTES-COMP-SCI,
volume = "378",
pages = "491--497",
year = "1989",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRclass = "65D30",
MRnumber = "91a:65050",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "EUROCAL '87 (Leipzig, 1987).",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Bronstein:1989:SRE,
author = "M. Bronstein",
title = "Simplification of real elementary functions",
crossref = "ACM:1989:PAI",
pages = "207--211",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author describes an algorithm, based on Risch's
real structure theorem, that determines explicitly all
the algebraic relations among a given set of real
elementary functions. He provides examples from its
implementation in the Scratchpad computer algebra
system that illustrate the advantages over the use of
complex logarithms and exponentials.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., T. J. Watson Res. Center, Yorktown
Heights, NY, USA",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Computer algebra system; Real elementary functions;
Real structure theorem; Scratchpad",
thesaurus = "Functions; Mathematics computing; Symbol
manipulation",
}
@Article{Cao:1989:ABS,
author = "J.-D. Cao and H. H. Gonska",
title = "Approximation by {Boolean} sums of positive linear
operators. {II}. {Gopengauz}-type estimates",
journal = j-J-APPROX-THEORY,
volume = "57",
number = "1",
pages = "77--89",
month = apr,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72266",
catcode = "G.1.2; G.1.2; G.3; G.2.1",
CRclass = "G.1.2 Approximation; G.1.2 Nonlinear approximation;
G.1.2 Approximation; G.1.2 Elementary function
approximation; G.3 Statistical computing; G.2.1
Combinatorics; G.2.1 Generating functions",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Nonlinear approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, PROBABILITY AND STATISTICS, Statistical
computing; Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Generating functions",
fjournal = "Journal of Approximation Theory",
genterm = "algorithms; theory; measurement",
guideno = "1989-07823",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "April 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.2 DISCRETE
MATHEMATICS",
}
@Article{Carlson:1989:TEI,
author = "B. C. Carlson",
title = "A Table of Elliptic Integrals: Cubic Cases",
journal = j-MATH-COMPUT,
volume = "53",
number = "187",
pages = "327--333",
month = jul,
year = "1989",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65A05 (33A25 65D20)",
MRnumber = "89m:65009",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4180 (Integral equations); C1120 (Analysis)",
corpsource = "Dept. of Math., Iowa State Univ., Ames, IA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "cubic polynomial; elliptic; elliptic integral; first
kind; Fortran codes; functions; integral equations;
integrals; integration interval; R-; rational
integrands; real zeros; second kind; square root;
table; third kind",
treatment = "T Theoretical or Mathematical",
}
@Article{Chen:1989:EMB,
author = "X. R. Chen and P. R. Krishnaiah and W. W. Liang",
title = "Estimation of multivariate binary density using
orthogonal functions",
journal = j-J-MULTIVAR-ANAL,
volume = "31",
number = "2",
pages = "178--186",
month = nov,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259x (print), 1095-7243 (electronic)",
ISSN-L = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Pittsburgh, Pittsburgh, PA; Univ. of
Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh,
Pittsburgh, PA",
bibno = "69313",
catcode = "D.3.3; G.3; G.1.3; G.1.2",
CRclass = "D.3.3 Language Constructs; D.3.3 Procedures,
functions, and subroutines; G.3 Statistical computing;
G.1.3 Numerical Linear Algebra; G.1.3 Linear systems
(direct and iterative methods); G.1.2 Approximation;
G.1.2 Elementary function approximation",
descriptor = "Software, PROGRAMMING LANGUAGES, Language Constructs,
Procedures, functions, and subroutines; Mathematics of
Computing, PROBABILITY AND STATISTICS, Statistical
computing; Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Linear systems
(direct and iterative methods); Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
fjournal = "Journal of Multivariate Analysis",
genterm = "algorithms; theory; verification",
guideno = "1989-08483",
journalabbrev = "J. Multivariate Anal.",
jrldate = "Nov. 1989",
subject = "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
of Computing; G.3 PROBABILITY AND STATISTICS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Chen:1989:FCR,
author = "S.-G. Chen and P. Y. Hsieh",
title = "Fast computation of the $ {N} $ th root",
journal = j-COMPUT-MATH-APPL,
volume = "17",
number = "10",
pages = "1423--1427",
month = "????",
year = "1989",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(89)90024-2",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Dec 29 08:01:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122189900242",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From the abstract: ``A new class of iterative methods
for computing a differentiable function is proposed,
which is based on Pad{\'e} approximation to Taylor's
series of the function. It leads to a faster algorithm
than Newton's method for $ x^{1 / N} $ and a different
interpretation of Newton's method.''",
}
@Article{Chen:1989:FCTa,
author = "S.-G. Chen and P. Y. Hsieh",
title = "Fast computation of the {$N$}-th root",
journal = j-COMPUT-MATH-APPL,
volume = "17",
number = "10",
pages = "1423--1427",
month = "????",
year = "1989",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(89)90024-2",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:01:11 MST 2017",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122189900242",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From the abstract: ``A new class of iterative methods
for computing a differentiable function is proposed,
which is based on Pad{\'e} approximation to Taylor's
series of the function. It leads to a faster algorithm
than Newton's method for $ x^{1 / N} $ and a different
interpretation of Newton's method.''",
}
@Article{Corliss:1989:IIV,
author = "George Corliss and Gary Krenz",
editor = "L. Gatteschi",
title = "Indefinite Integration with Validation",
journal = j-TOMS,
volume = "15",
number = "4",
pages = "375--393",
month = dec,
year = "1989",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D30 (65-04)",
MRnumber = "1 062 497",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/;
http://www.acm.org/pubs/toc/Abstracts/toms/76915.html",
acknowledgement = ack-nhfb,
bibno = "393",
content = "ALGORITHMS; THEORY",
CRclass = "G.1.4 Quadrature and Numerical Differentiation; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.2 Approximation; G.1.2 Chebyshev approximation and
theory",
CRnumber = "1989-03199",
descriptor = "mathematics of computing, numerical analysis,
quadrature and numerical differentiation; mathematics
of computing, numerical analysis, approximation,
elementary function approximation; mathematics of
computing, numerical analysis, approximation, Chebyshev
approximation and theory",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
fortitle = "ACM Trans. Math. Softw.",
guideno = "4",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; theory",
review = "ACM CR 9007-0598",
subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation.
{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.1.2}: Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Chebyshev
approximation and theory.",
waffil = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Critchfield:1989:CEF,
author = "Charles L. Critchfield",
title = "Computation of elliptic functions",
journal = j-J-MATH-PHYS,
volume = "30",
number = "2",
pages = "295--297",
month = feb,
year = "1989",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.528444",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33A25 (65D20)",
MRnumber = "89k:33004",
MRreviewer = "H. Hochstadt",
bibdate = "Mon Oct 31 11:58:32 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v30/i2/p295_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "3",
}
@Misc{Darley:1989:FPI,
author = "H. M. Darley and others",
title = "Floating Point\slash Integer Processor with Divide and
Square Root Functions",
year = "1989",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 4,878,190.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Dehling:1989:FLI,
author = "Herold Dehling",
title = "The functional law of the iterated logarithm for {von
Mises} functionals and multiple {Wiener} integrals",
journal = j-J-MULTIVAR-ANAL,
volume = "28",
number = "2",
pages = "177--189",
month = feb,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259x (print), 1095-7243 (electronic)",
ISSN-L = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of G{\"o}ttingen, G{\"o}ttingen, FRG",
bibno = "64336",
catcode = "G.3; G.1.9; G.1.2",
CRclass = "G.3 Statistical computing; G.1.9 Integral Equations;
G.1.9 Integro-differential equations; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Integral Equations,
Integro-differential equations; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation",
fjournal = "Journal of Multivariate Analysis",
genterm = "algorithms; theory; measurement",
guideno = "1989-08462",
journalabbrev = "J. Multivariate Anal.",
jrldate = "February 1989",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Demirbas:1989:MSE,
author = "K. Demirbas",
title = "Multidimensional state estimation using stacks for
dynamic systems with interference",
journal = j-AUTOMATICA,
volume = "25",
number = "4",
pages = "617--621",
month = jul,
year = "1989",
CODEN = "ATCAA9",
ISSN = "0005-1098 (print), 1873-2836 (electronic)",
ISSN-L = "0005-1098",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72661",
catcode = "G.1.2; G.1.2; G.1.3; G.1.5; H.1.1",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Linear
approximation; G.1.3 Numerical Linear Algebra; G.1.3
Linear systems (direct and iterative methods); G.1.5
Roots of Nonlinear Equations; H.1.1 Systems and
Information Theory; H.1.1 Information theory",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Linear approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative methods);
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations; Information Systems, MODELS AND
PRINCIPLES, Systems and Information Theory, Information
theory",
fjournal = "Automatica: the journal of IFAC, the International
Federation of Automatic Control",
genterm = "algorithms; theory",
guideno = "1989-03952",
jrldate = "July 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; H.
Information Systems; H.1 MODELS AND PRINCIPLES",
}
@TechReport{Dritz:1989:RPS,
author = "K. W. Dritz",
title = "Rationale for the Proposed Standard for a Generic
Package of Elementary Functions for {Ada}",
type = "Report",
number = "ANL-89/2 Rev. 1",
institution = "Argonne National Laboratory, Mathematics and Computer
Science Division",
address = "Argonne, IL, USA",
pages = "????",
month = oct,
year = "1989",
bibdate = "Thu Sep 01 12:08:24 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@InProceedings{Duprat:1989:SRA,
author = "J. Duprat and Y. Herreros and J.-M. Muller",
title = "Some results about on-line computation of functions",
crossref = "Ercegovac:1989:PSC",
pages = "112--118",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Dyn:1989:PEB,
author = "N. Dyn and A. Ron",
title = "Periodic exponential box splines on a three direction
mesh",
journal = j-J-APPROX-THEORY,
volume = "56",
number = "3",
pages = "287--296",
month = mar,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72251",
catcode = "G.1.2; F.2.2; G.1.2; G.1.2; G.1.2; G.2.1; G.3",
CRclass = "G.1.2 Approximation; G.1.2 Spline and piecewise
polynomial approximation; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Geometrical problems and
computations; G.1.2 Approximation; G.1.2 Chebyshev
approximation and theory; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.2 Approximation;
G.1.2 Linear approximation; G.2.1 Combinatorics; G.2.1
Recurrences and difference equations; G.3 Statistical
computing",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Spline and piecewise polynomial
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Chebyshev approximation and
theory; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Linear approximation; Mathematics of
Computing, DISCRETE MATHEMATICS, Combinatorics,
Recurrences and difference equations; Mathematics of
Computing, PROBABILITY AND STATISTICS, Statistical
computing",
fjournal = "Journal of Approximation Theory",
genterm = "algorithms; theory; design",
guideno = "1989-07809",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Mar. 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3
PROBABILITY AND STATISTICS",
}
@Article{Eberlein:1989:SAC,
author = "E. Eberlein",
title = "Strong approximation of continuous time stochastic
processes",
journal = j-J-MULTIVAR-ANAL,
volume = "31",
number = "2",
pages = "220--235",
month = nov,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259x (print), 1095-7243 (electronic)",
ISSN-L = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. Freiburg, Freiburg, W. Germany",
bibno = "69316",
catcode = "D.4.8; F.1.2; G.1.2",
CRclass = "D.4.8 Performance; D.4.8 Stochastic analysis; F.1.2
Modes of Computation; F.1.2 Probabilistic computation;
G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Software, OPERATING SYSTEMS, Performance, Stochastic
analysis; Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Probabilistic
computation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Journal of Multivariate Analysis",
genterm = "algorithms; performance; theory",
guideno = "1989-08486",
journalabbrev = "J. Multivariate Anal.",
jrldate = "Nov. 1989",
subject = "D. Software; D.4 OPERATING SYSTEMS; F. Theory of
Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Egger:1989:PAC,
author = "A. Egger and R. Huotari",
title = "The {Polya} algorithm on convex sets",
journal = j-J-APPROX-THEORY,
volume = "56",
number = "2",
pages = "212--216",
month = feb,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72242",
catcode = "F.2.2; F.2.2; G.1.2; G.1.2; G.1.5",
CRclass = "F.2.2 Nonnumerical Algorithms and Problems; F.2.2
Geometrical problems and computations; F.2.2
Nonnumerical Algorithms and Problems; F.2.2
Computations on discrete structures; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.2 Approximation; G.1.2 Minimax approximation and
algorithms; G.1.5 Roots of Nonlinear Equations; G.1.5
Convergence",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations; Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Minimax
approximation and algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
Convergence",
fjournal = "Journal of Approximation Theory",
genterm = "algorithms; theory",
guideno = "1989-07801",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Feb. 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS",
}
@Article{Ehrenmark:1989:ONF,
author = "Ulf T. Ehrenmark",
title = "Overconvergence of the near-field expansion for
linearized waves normally incident on a sloping beach",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "799--815",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64945",
catcode = "G.1.7; G.1.2; F.2.1; G.1.2; F.2.2",
CRclass = "G.1.7 Ordinary Differential Equations; G.1.7
Convergence and stability; G.1.2 Approximation; G.1.2
Minimax approximation and algorithms; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computation of
transforms; G.1.2 Approximation; G.1.2 Elementary
function approximation; F.2.2 Nonnumerical Algorithms
and Problems; F.2.2 Geometrical problems and
computations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Convergence and stability;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Minimax approximation and algorithms;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computation of transforms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations",
fjournal = "SIAM Journal on Applied Mathematics",
genterm = "algorithms; theory; experimentation",
guideno = "1989-09714",
journal-URL = "http://epubs.siam.org/siap",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}
@Article{Einmahl:1989:ERK,
author = "U. Einmahl",
title = "Extensions of results of {Komlos}, {Major}, and
{Tusnady} to the multivariate case",
journal = j-J-MULTIVAR-ANAL,
volume = "28",
number = "1",
pages = "20--68",
month = jan,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259x (print), 1095-7243 (electronic)",
ISSN-L = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. zu Koln, West Germany",
bibno = "66700",
catcode = "G.3; G.1.2; F.2.1",
CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2
Elementary function approximation; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computation of
transforms",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computation of transforms",
fjournal = "Journal of Multivariate Analysis",
genterm = "algorithms; theory",
guideno = "1989-08456",
journalabbrev = "J. Multivariate Anal.",
jrldate = "Jan. 1989",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY",
}
@Article{Epperson:1989:UIM,
author = "J. F. Epperson",
title = "On the use of iteration methods for approximating the
natural logarithm",
journal = j-AMER-MATH-MONTHLY,
volume = "96",
number = "9",
pages = "831--835",
month = nov,
year = "1989",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "26A06 (26A09)",
MRnumber = "91a:26002",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "71703",
catcode = "G.1.2; G.1.2; K.3.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Spline and
piecewise polynomial approximation; K.3.2 Computer and
Information Science Education",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Spline and piecewise polynomial
approximation; Computing Milieux, COMPUTERS AND
EDUCATION, Computer and Information Science Education",
fjournal = "American Mathematical Monthly",
genterm = "algorithms; theory",
guideno = "1989-03518",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
journalabbrev = "Am. Math. Monthly",
jrldate = "Nov. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K.
Computing Milieux; K.3 COMPUTERS AND EDUCATION",
}
@InProceedings{Ercegovac:1989:FRD,
author = "M. D. Ercegovac and T. Lang",
title = "On-the-fly rounding for division and square root",
crossref = "Ercegovac:1989:PSC",
pages = "169--173",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "In division and square root implementation based on
digit-recurrence algorithms, the result is obtained in
digit-serial form, from most significant digit to least
significant. To reduce the complexity of the
result-digit selection and to allow the \ldots{}",
}
@InProceedings{Ercegovac:1989:IMC,
author = "M. D. Ercegovac and T. Lang",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Implementation of module combining multiplication,
division, and square root",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "150--153",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The implementation of a module that performs radix-$2$
multiplication, division, and square root is presented.
The module is compact because most of the components
are shared by all three operations, the complexity
being similar to that of a radix-$2$ \ldots{}",
}
@InProceedings{Ercegovac:1989:RSR,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "Radix-4 square root without initial {PLA}",
crossref = "Ercegovac:1989:PSC",
pages = "162--168",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_radix4.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "A systematic derivation of a radix-$4$ square root
algorithm using redundance in the partial residuals and
the result is presented. Unlike other similar schemes,
the algorithm does not use a table-lookup or
programmable logic array (PLA) for the \ldots{}",
}
@InProceedings{Fandrianto:1989:AHS,
author = "Jan Fandrianto",
title = "Algorithms for high-speed shared radix 8 division and
radix 8 square root",
crossref = "Ercegovac:1989:PSC",
pages = "68--75",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fandrianto.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-9",
summary = "An algorithm for performing radix-$8$ division and
square root in a shared hardware is described. To
achieve short iteration cycle time, it utilizes an
optimized `next quotient/root prediction PLA' generally
used in a radix-$4$ SRT division with minimal
\ldots{}",
}
@Article{Ge:1989:OCL,
author = "Renpu Ge",
title = "Optimal choice of linear interval extension",
journal = j-APPL-MATH-COMP,
volume = "30",
number = "2",
pages = "165--189",
month = mar,
year = "1989",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64710",
catcode = "G.1.6; G.1.2; G.1.2; G.2.1; F.2.2; G.1.2; G.1.1;
G.1.0",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
Approximation; G.1.2 Linear approximation; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.2.1 Combinatorics; G.2.1 Combinatorial algorithms;
F.2.2 Nonnumerical Algorithms and Problems; F.2.2
Computations on discrete structures; G.1.2
Approximation; G.1.2 Minimax approximation and
algorithms; G.1.1 Interpolation; G.1.1 Difference
formulas; G.1.0 General; G.1.0 Numerical algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Linear
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Combinatorial algorithms;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Minimax approximation and algorithms;
Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Difference formulas; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms",
fjournal = "Applied Mathematics and Computation",
genterm = "algorithms; theory; measurement",
guideno = "1989-03670",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
journalabbrev = "Appl. Math. Comput.",
jrldate = "March 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS",
}
@Article{Gersch:1989:SPT,
author = "W. Gersch and G. Kitagawa",
title = "Smoothness priors transfer function estimation",
journal = j-AUTOMATICA,
volume = "25",
number = "4",
pages = "603--608",
month = jul,
year = "1989",
CODEN = "ATCAA9",
ISSN = "0005-1098 (print), 1873-2836 (electronic)",
ISSN-L = "0005-1098",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72658",
catcode = "G.1.1; G.1.2; G.1.6",
CRclass = "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.6 Optimization; G.1.6 Gradient methods",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Smoothing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Optimization, Gradient methods",
fjournal = "Automatica: the journal of IFAC, the International
Federation of Automatic Control",
genterm = "algorithms; theory",
guideno = "1989-03949",
jrldate = "July 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InCollection{Glover:1989:THN,
author = "Keith Glover",
editor = "Jan C. Willems",
booktitle = "From data to model",
title = "A tutorial on {Hankel}-norm approximation",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "246",
pages = "26--48",
year = "1989",
ISBN = "0-387-51571-2",
ISBN-13 = "978-0-387-51571-7",
LCCN = "QA279 .F76 1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "70545",
catcode = "G.1.2; F.2.1; F.2.1",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; F.2.1 Numerical Algorithms and Problems;
F.2.1 Computations on matrices; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computation of
transforms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices; Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computation of
transforms",
genterm = "algorithms; theory",
guideno = "1989-01692",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
waffil = "Univ. of Groningen, Groningen, The Netherlands",
}
@InProceedings{Glynn:1989:OSS,
author = "P. W. Glynn",
editor = "Edward A. MacNair and Kenneth J. Musselman and Philip
Heidelberger",
booktitle = "1989 Winter Simulation Conference proceedings:
December 4--6, 1989, the Capital Hilton Hotel,
Washington, {DC}",
title = "Optimization of stochastic systems via simulation",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "xx + 1139",
pages = "90--105",
year = "1989",
ISBN = "0-911801-58-8",
ISBN-13 = "978-0-911801-58-3",
LCCN = "QA76.9.C65 W56 1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE order no. 89CH2778-9.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5823",
acknowledgement = ack-nhfb,
bibno = "76750",
catcode = "I.6.3; G.1.6; G.3; G.1.2",
CRclass = "I.6.3 Applications; G.1.6 Optimization; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computing Methodologies, SIMULATION AND MODELING,
Applications; Mathematics of Computing, NUMERICAL
ANALYSIS, Optimization; Mathematics of Computing,
PROBABILITY AND STATISTICS; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; design; performance",
guideno = "1989-12012",
procdate = "December 4-6, 1989",
procloc = "Washington, D. C.",
subject = "I. Computing Methodologies; I.6 SIMULATION AND
MODELING; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY
AND STATISTICS; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Article{Gomes:1989:GGL,
author = "M. I. Gomes",
title = "Generalized {Gumbel} and likelihood ratio test
statistics in the multivariate {GEV} model",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "7",
number = "3",
pages = "259--267",
month = feb,
year = "1989",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "70043",
catcode = "G.3; G.1.7; I.5.1; G.1.6; G.1.2",
CRclass = "G.3 Statistical computing; G.1.7 Ordinary Differential
Equations; G.1.7 Convergence and stability; I.5.1
Models; I.5.1 Statistical; G.1.6 Optimization; G.1.6
Nonlinear programming; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations,
Convergence and stability; Computing Methodologies,
PATTERN RECOGNITION, Models, Statistical; Mathematics
of Computing, NUMERICAL ANALYSIS, Optimization,
Nonlinear programming; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Computational Statistics \& Data Analysis",
genterm = "algorithms; measurement; reliability; theory",
guideno = "1989-04403",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
journalabbrev = "Comput. Stat. Data Anal.",
jrldate = "Feb. 1989",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; I. Computing Methodologies; I.5 PATTERN
RECOGNITION; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@InProceedings{Gonzaga:1989:ASL,
author = "Cl{\'o}vis C. Gonzaga",
title = "An algorithm for solving linear programming programs
in {$ O(n^3 L) $} operations",
crossref = "Megiddo:1989:PMP",
pages = "1--28",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74172",
catcode = "G.1.6; G.1.2; F.2.1; I.1.2; I.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
Approximation; G.1.2 Elementary function approximation;
F.2.1 Numerical Algorithms and Problems; F.2.1
Computations on matrices; I.1.2 Algorithms; I.1.2
Algebraic algorithms; I.1.2 Algorithms; I.1.2 Analysis
of algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices; Computing Methodologies,
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms; Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms",
genterm = "algorithms; theory",
guideno = "1989-12474",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
}
@TechReport{Gragg:1989:FSE,
author = "W. Gragg and B. Neta",
title = "{Fortran} Subroutines for the Evaluation of the
Confluent Hypergeometric Functions",
number = "NPS-MA-89-014",
institution = inst-MATH-NPS,
address = inst-MATH-NPS:adr,
year = "1989",
bibdate = "Fri Nov 11 14:50:24 MST 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/n/neta-beny.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Software available URL http://math.nps.navy.mil",
}
@Article{Guo:1989:RCS,
author = "S.-S. Guo and M. K. Khan",
title = "On the rate of convergence of some operators on
functions of bounded variation",
journal = j-J-APPROX-THEORY,
volume = "58",
number = "1",
pages = "90--101",
month = jul,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "69424",
catcode = "F.2.1; G.1.2",
CRclass = "F.2.1 Numerical Algorithms and Problems; F.2.1
Computations on polynomials; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Journal of Approximation Theory",
genterm = "algorithms; theory",
guideno = "1989-07854",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "July 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS",
}
@Article{Hornik:1989:MFN,
author = "K. Hornik and M. Stinchcombe and H. White",
title = "Multilayer feedforward networks are universal
approximators",
journal = j-NEURAL-NETWORKS,
volume = "2",
number = "5",
pages = "359--366",
year = "1989",
CODEN = "NNETEB",
ISSN = "0893-6080 (print), 1879-2782 (electronic)",
ISSN-L = "0893-6080",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Technisce Univ. Wien, Vienna, Austria; Univ. of
California, San Diego; Univ. of California, San Diego",
bibno = "70408",
catcode = "F.2.1; G.1.2; F.1.1; I.2.4",
CRclass = "F.2.1 Numerical Algorithms and Problems; G.1.2
Approximation; G.1.2 Elementary function approximation;
F.1.1 Models of Computation; F.1.1 Unbounded-action
devices; I.2.4 Knowledge Representation Formalisms and
Methods",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Models of Computation, Unbounded-action devices;
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Knowledge Representation Formalisms and Methods",
fjournal = "Neural Networks",
genterm = "design; performance",
guideno = "1989-09273",
journalabbrev = "Neural Networks",
jrldate = "1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1
COMPUTATION BY ABSTRACT DEVICES; I. Computing
Methodologies; I.2 ARTIFICIAL INTELLIGENCE",
}
@Article{Jamieson:1989:RCI,
author = "M. J. Jamieson",
title = "Rapidly converging iterative formulae for finding
square roots and their computational efficiencies",
journal = j-COMP-J,
volume = "32",
number = "1",
pages = "93--94",
month = feb,
year = "1989",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/32.1.93",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65H05",
MRnumber = "89k:65063",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "This work generalizes the Pythagorean sums in
\cite{Dubrulle:1983:CNM,Moler:1983:RSR}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/93.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/94.tif",
abstract = "A derivation is given of rapidly converging iterative
formulae for finding square roots which include, as
special cases, some recently published examples. Their
computational efficiencies are investigated for
sequential and parallel implementation. It is concluded
that the most efficient method is equivalent to
sequential application of the Newton Raphson formula; a
simple modification is suggested which brings the
advantage of root bracketing at little extra
computational cost.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Glasgow Univ., UK",
affiliationaddress = "Glasgow, Scotl",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
classification = "723; 921; B0290F (Interpolation and function
approximation); C4130 (Interpolation and function
approximation)",
corpsource = "Dept. of Comput. Sci., Glasgow Univ., UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "computational; Computational efficiencies;
Computational Efficiency; Computer Metatheory;
Convergence; convergence of numerical methods;
Converging iterative formulae; converging iterative
formulae; efficiencies; formula; function
approximation; Iterative Methods; iterative methods;
Newton Raphson; Newton Raphson formula, Mathematical
Techniques; Parallel implementation; parallel
implementation; Square Roots; Square roots; square
roots",
thesaurus = "Convergence of numerical methods; Function
approximation; Iterative methods",
treatment = "P Practical",
}
@Article{Jeffries:1989:GFA,
author = "John S. Jeffries and Donald R. Smith",
title = "A {Green} function approach for a singularly perturbed
vector boundary-value problem",
journal = j-ADV-APPL-MATH,
volume = "10",
number = "1",
pages = "1--50",
month = mar,
year = "1989",
CODEN = "????",
ISSN = "0196-8858 (print), 1090-2074 (electronic)",
ISSN-L = "0196-8858",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of California at San Diego, La Jolla; Univ. of
California at San Diego, La Jolla",
bibno = "64833",
catcode = "G.1.7; G.1.7; F.2.1; G.1.2; G.1.3; G.1.2; G.1.3",
CRclass = "G.1.7 Ordinary Differential Equations; G.1.7 Boundary
value problems; G.1.7 Ordinary Differential Equations;
G.1.7 Convergence and stability; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computation of
transforms; G.1.2 Approximation; G.1.2 Nonlinear
approximation; G.1.3 Numerical Linear Algebra; G.1.3
Eigenvalues; G.1.2 Approximation; G.1.2 Elementary
function approximation; G.1.3 Numerical Linear Algebra;
G.1.3 Linear systems (direct and iterative methods)",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Boundary value problems;
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Convergence and stability;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computation of transforms; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Nonlinear
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Eigenvalues;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods)",
fjournal = "Advances in Applied Mathematics",
genterm = "algorithms; theory",
guideno = "1989-03271",
journal-URL = "http://www.sciencedirect.com/science/journal/01968858",
journalabbrev = "Adv. Appl. Math.",
jrldate = "March 1989",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS",
}
@Article{Johnson:1989:IMA,
author = "K. R. Johnson",
title = "An Iterative Method for Approximating Square Roots",
journal = j-MATH-MAG,
volume = "62",
number = "4",
pages = "253--259",
month = oct,
year = "1989",
CODEN = "MAMGA8",
ISSN = "0025-570X",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@Article{Kaishev:1989:SSC,
author = "A. I. Kaishev",
title = "A sharpened scheme for constructing an a posteriori
interval extension of an elementary function.
({Russian})",
journal = "Voprosy Kibernet. (Moscow)",
volume = "149",
pages = "14--18",
year = "1989",
ISBN = "0134-6388",
ISBN-13 = "0134-6388",
MRclass = "65G10",
MRnumber = "91i:65090",
MRreviewer = "I. N. Molchanov",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@InProceedings{Kak:1989:BAS,
author = "S. C. Kak and A. O. Barbir",
booktitle = "Proceedings of the Twenty-First Southeastern Symposium
on System Theory, 26--28 March 1989",
title = "The {Brahmagupta} algorithm for square rooting",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "456--459",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An algorithm for square root evaluation is introduced.
Novel features of the algorithm include suitability for
parallel processing and multi-initial guesses of the
root. An extension of the algorithm to the nth rooting
is provided. A VLSI \ldots{}",
}
@Article{Kogan:1989:GBF,
author = "B. J. Kogan",
title = "General background of functional memory algorithms",
journal = j-TRANS-SOC-COMP-SIM,
volume = "5",
number = "4",
pages = "285--317",
month = oct,
year = "1989",
CODEN = "TSCSEV",
ISSN = "0740-6797",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of California, Los Angeles",
bibno = "69149",
catcode = "C.3; G.1.2; G.1.2; E.4",
CRclass = "C.3 Signal processing systems; G.1.2 Approximation;
G.1.2 Elementary function approximation; G.1.2
Approximation; G.1.2 Linear approximation; E.4 Data
compaction and compression",
descriptor = "Computer Systems Organization, SPECIAL-PURPOSE AND
APPLICATION-BASED SYSTEMS, Signal processing systems;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Linear approximation; Data, CODING AND
INFORMATION THEORY, Data compaction and compression",
fjournal = "Transactions of the Society for Computer Simulation",
genterm = "algorithms; design",
guideno = "1989-10680",
journalabbrev = "Trans. Soc. Comput. Simul.",
jrldate = "Oct. 1989",
subject = "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
AND APPLICATION-BASED SYSTEMS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS; E. Data; E.4 CODING
AND INFORMATION THEORY",
}
@InProceedings{Kojima:1989:PDI,
author = "M. Kojima and S. Mizuno and A. Yoshise",
title = "A primal-dual interior point algorithm for linear
programming",
crossref = "Megiddo:1989:PMP",
bookpages = "x + 158",
pages = "29--47",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74173",
catcode = "G.1.6; F.2.1; G.1.2; F.2.2; F.2.1; I.1.2; I.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; F.2.1
Numerical Algorithms and Problems; G.1.2 Approximation;
G.1.2 Elementary function approximation; F.2.2
Nonnumerical Algorithms and Problems; F.2.2 Geometrical
problems and computations; F.2.1 Numerical Algorithms
and Problems; F.2.1 Computations on matrices; I.1.2
Algorithms; I.1.2 Algebraic algorithms; I.1.2
Algorithms; I.1.2 Analysis of algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations; Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices; Computing Methodologies,
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms; Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms",
genterm = "algorithms; theory",
guideno = "1989-12475",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
}
@Article{Kraaikamp:1989:SEP,
author = "Cor Kraaikamp",
title = "Statistic and ergodic properties of {Minkowski}'s
diagonal continued fraction",
journal = j-THEOR-COMP-SCI,
volume = "65",
number = "2",
pages = "197--212",
day = "28",
month = jun,
year = "1989",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Amsterdam Univ., Amsterdam, The Netherlands and Univ.
de Provence, Marseille, France",
bibno = "70095",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Theoretical Computer Science",
genterm = "algorithms; theory",
guideno = "1989-10594",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
journalabbrev = "Theor. Comput. Sci.",
jrldate = "28 June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Kreider:1989:WSA,
author = "K. L. Kreider",
title = "A wave splitting approach to time dependent inverse
scattering for the stratified cylinder",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "932--943",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64953",
catcode = "G.1.7; G.1.2; J.2; J.2; F.2.2; G.1.3; I.1.1",
CRclass = "G.1.7 Ordinary Differential Equations; G.1.7 Initial
value problems; G.1.2 Approximation; G.1.2 Elementary
function approximation; J.2 Physics; J.2 Electronics;
F.2.2 Nonnumerical Algorithms and Problems; F.2.2
Geometrical problems and computations; G.1.3 Numerical
Linear Algebra; G.1.3 Linear systems (direct and
iterative methods); I.1.1 Expressions and Their
Representation; I.1.1 Simplification of expressions",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations, Initial value problems;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics; Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Electronics; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations; Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative methods);
Computing Methodologies, ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions",
fjournal = "SIAM Journal on Applied Mathematics",
genterm = "algorithms; theory; experimentation; measurement",
guideno = "1989-09722",
journal-URL = "http://epubs.siam.org/siap",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; J. Computer Applications; J.2 PHYSICAL
SCIENCES AND ENGINEERING; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I.
Computing Methodologies; I.1 ALGEBRAIC MANIPULATION",
}
@Article{Lin:1989:ANT,
author = "Jinn Tyan Lin",
title = "Approximating the normal tail probability and its
inverse for use on a pocket calculator",
journal = j-APPL-STAT,
volume = "38",
number = "1",
pages = "69--70",
year = "1989",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
MRclass = "62E15",
MRnumber = "983 303",
bibdate = "Sat Apr 21 10:25:25 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/as1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@PhdThesis{Littlestone:1989:MBL,
author = "N. Littlestone",
title = "Mistake bounds and logarithmic linear-threshold
learning algorithms",
type = "{Ph.D} Thesis",
school = "University of California at Santa Cruz",
address = "Santa Cruz, CA, USA",
pages = "????",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "76493",
catcode = "I.2.6; J.4; H.1.2; G.1.2",
CRclass = "I.2.6 Learning; J.4 Psychology; H.1.2 User/Machine
Systems; H.1.2 Human information processing; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Learning; Computer Applications, SOCIAL AND BEHAVIORAL
SCIENCES, Psychology; Information Systems, MODELS AND
PRINCIPLES, User/Machine Systems, Human information
processing; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; human factors; performance",
guideno = "1989-12934",
source = "UMI Order No: GAX89-26506",
subject = "I. Computing Methodologies; I.2 ARTIFICIAL
INTELLIGENCE; J. Computer Applications; J.4 SOCIAL AND
BEHAVIORAL SCIENCES; H. Information Systems; H.1 MODELS
AND PRINCIPLES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Article{Lo:1989:RBP,
author = "Shaw-Hwa Lo and Jane-Ling Wang",
title = "Representations for the bivariate product limit
estimators and the bootstrap versions",
journal = j-J-MULTIVAR-ANAL,
volume = "28",
number = "2",
pages = "211--226",
month = feb,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259x (print), 1095-7243 (electronic)",
ISSN-L = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of California, Davis; Univ. of California,
Davis",
bibno = "64339",
catcode = "G.3; G.1.2; G.1.4; G.1.7",
CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.4 Quadrature and
Numerical Differentiation; G.1.4 Gaussian quadrature;
G.1.7 Ordinary Differential Equations; G.1.7
Convergence and stability",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation,
Gaussian quadrature; Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations,
Convergence and stability",
fjournal = "Journal of Multivariate Analysis",
genterm = "algorithms; theory; measurement",
guideno = "1989-08465",
journalabbrev = "J. Multivariate Anal.",
jrldate = "February 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G.3 PROBABILITY AND STATISTICS",
}
@Article{Lorentz:1989:NA,
author = "G. G. Lorentz",
title = "Notes on approximation",
journal = j-J-APPROX-THEORY,
volume = "56",
number = "3",
pages = "360--365",
month = mar,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72258",
catcode = "G.1.1; G.1.2; G.1.1",
CRclass = "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.1 Interpolation; G.1.1 Spline and piecewise
polynomial interpolation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Smoothing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Interpolation, Spline and piecewise
polynomial interpolation",
fjournal = "Journal of Approximation Theory",
genterm = "algorithms; theory",
guideno = "1989-07816",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Mar. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InCollection{Lovelace:1989:SAE,
author = "Augusta Ada Lovelace",
title = "Sketch of the {Analytical Engine} (1843)",
crossref = "Campbell-Kelly:1989:WCB-3",
pages = "89--170",
year = "1989",
bibdate = "Tue Jan 22 17:54:41 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "Bernoulli numbers",
}
@InProceedings{Lu:1989:VMI,
author = "P. Y. Lu and K. Dawallu",
title = "A {VLSI} Module for {IEEE} Floating-Point
Multiplication\slash Division\slash Square Root",
crossref = "IEEE:1989:PII",
bookpages = "xvii + 587",
pages = "366--368",
year = "1989",
bibdate = "Wed Nov 06 12:08:38 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The major objective of this VLSI module design is to
determine how to modify a fast floating-point
multiplier so that it can perform division and square
root in accordance with IEEE standards. This has been
achieved by applying the Newton-Ralphson iteration only
on the mantissa and adjusting the iterated result by a
rounding algorithm. Using 1.0- mu m CMOS standard cell
technology, the total area of this module is
approximately 7.0 mm*6.5 mm, which is just 25\% larger
than the floating-point multiplier. The module can
compute multiplication, division, and square root in 3,
31, and 43 cycles, respectively. The cycle time, under
nominal conditions, is expected to be 20 ns. (2
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "LSI Logic Corp., Menlo Park, CA, USA",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C4130 (Interpolation and function
approximation); C5230 (Digital arithmetic methods)",
keywords = "1 Micron; 20 Ns; 7 To 6.5 mm; CMOS standard cell
technology; Cycle time; Fast floating-point multiplier;
Floating point division; Floating point square root;
IEEE standards; Iterated result; Mantissa; Multiplier
modification; Newton-Ralphson iteration; Rounding
algorithm; VLSI module design",
numericalindex = "Time 2.0E-08 s; Size 1.0E-06 m; Size 6.5E-03 to
7.0E-03 m",
thesaurus = "Cellular arrays; CMOS integrated circuits; Digital
arithmetic; Dividing circuits; Iterative methods;
Modules; Multiplying circuits; VLSI",
}
@Article{Macleod:1989:SAA,
author = "Allan J. Macleod",
title = "Statistical Algorithms: {Algorithm AS 245}: a Robust
and Reliable Algorithm for the Logarithm of the Gamma
Function",
journal = j-APPL-STAT,
volume = "38",
number = "2",
pages = "397--402",
month = jun,
year = "1989",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:25:27 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://lib.stat.cmu.edu/apstat/245",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@InProceedings{Mansour:1989:CAS,
author = "Y. Mansour and B. Schieber and P. Tiwari",
booktitle = "30th Annual Symposium on Foundations of Computer
Science, 1989",
title = "The complexity of approximating the square root",
crossref = "IEEE:1989:ASF",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "325--330",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors prove upper and lower bounds for
approximately computing the square root using a given
set of operations. The bounds are extended to hold for
approximating the kth root, for any fixed k. Several
tools from approximation \ldots{}",
}
@Article{Martin:1989:TPQ,
author = "Pablo Martin and Antonio Luis Guerrero",
title = "Two-point quasi-fractional approximations to the
{Bessel} function {$ J_\nu (x) $} of fractional order",
journal = j-J-COMPUT-PHYS,
volume = "85",
number = "2",
pages = "487--492",
month = dec,
year = "1989",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(89)90161-7",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:48 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999189901617",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
remark = "This work produces only 3D approximations.",
}
@InProceedings{Megiddo:1989:POS,
author = "N. Megiddo",
title = "Pathways to the optimal set in linear programming",
crossref = "Megiddo:1989:PMP",
pages = "131--158",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74179",
catcode = "G.1.6; G.1.2; G.2.2; G.1.2; G.1.5; F.2.1; I.1.2; G.4;
G.4",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.2.2 Graph Theory; G.2.2 Path and circuit problems;
G.1.2 Approximation; G.1.2 Spline and piecewise
polynomial approximation; G.1.5 Roots of Nonlinear
Equations; G.1.5 Iterative methods; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computations on
matrices; I.1.2 Algorithms; I.1.2 Analysis of
algorithms; G.4 Algorithm analysis; G.4 Efficiency",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation,
Elementary function approximation; Mathematics of
Computing, DISCRETE MATHEMATICS, Graph Theory, Path and
circuit problems; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Spline and piecewise
polynomial approximation; Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
Iterative methods; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices; Computing
Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
Analysis of algorithms; Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics
of Computing, MATHEMATICAL SOFTWARE, Efficiency",
genterm = "algorithms; performance; theory",
guideno = "1989-12481",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing;
G.4 MATHEMATICAL SOFTWARE",
}
@PhdThesis{Miler:1989:EEM,
author = "T. H. Miler",
title = "Error evaluation of microcomputer intrinsic
functions",
type = "{Ph.D} Thesis",
school = "University of Idaho",
address = "Moscow, ID",
pages = "????",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "76168",
catcode = "G.4; G.1.2; J.2",
CRclass = "G.4 Reliability and robustness; G.1.2 Approximation;
G.1.2 Elementary function approximation; J.2
Mathematics and statistics",
descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Computer Applications, PHYSICAL SCIENCES
AND ENGINEERING, Mathematics and statistics",
genterm = "algorithms; reliability",
guideno = "1989-12941",
source = "UMI order no: GAX89-22813",
subject = "G. Mathematics of Computing; G.4 MATHEMATICAL
SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; J. Computer Applications; J.2 PHYSICAL
SCIENCES AND ENGINEERING",
}
@InProceedings{Montuschi:1989:EIH,
author = "Paolo Montuschi and Luigi Cinimera",
title = "On the efficient implementation of higher radix square
root algorithms",
crossref = "Ercegovac:1989:PSC",
pages = "154--161",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "Square root nonrestoring algorithms operating with a
radix higher than two (but power of 2) are discussed.
Formulas are derived delimiting the feasibility space
of the class of algorithms considered as a function of
the different parameters. This \ldots{}",
}
@Book{Moshier:1989:MPM,
author = "Stephen L. B. Moshier",
title = "Methods and Programs for Mathematical Functions",
publisher = pub-ELLIS-HORWOOD,
address = pub-ELLIS-HORWOOD:adr,
pages = "vii + 415",
year = "1989",
ISBN = "0-7458-0289-3",
ISBN-13 = "978-0-7458-0289-3",
LCCN = "QA331 .M84 1989",
MRclass = "*65D20, 26-04, 33-04, 65-02, 65C99",
bibdate = "Thu Sep 01 10:33:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\pounds 48.00",
URL = "http://www.moshier.net/;
http://www.netlib.org/cephes",
ZMnumber = "0701.65011",
acknowledgement = ack-nj,
shorttableofcontents = "Preface / vii \\
1: Floating Point Arithmetic / 1 \\
2: Approximation Methods / 75 \\
3: Software Notes / 129 \\
4: Elementary Functions / 143 \\
5: Probability Distributions and Related Functions /
201 \\
6: Bessel Functions / 263 \\
7: Other Special Functions / 333 \\
Bibliography / 411 \\
Index / 413",
tableofcontents = "Preface / vii \\
1: Floating Point Arithmetic / 1 \\
1.1 Numeric Data Structures / 1 \\
1.2 Rounding / 5 \\
1.3 Addition and Subtraction / 6 \\
1.4 Multiplication / 7 \\
1.4.1 Long Multiplication in Binary Radix / 8 \\
1.4.2 Multiplication in Word Integer Radix / 8 \\
1.4.3 Fast Multiplication / 9 \\
1.5 Division / 10 \\
1.5.1 Long Division / 10 \\
1.5.2 Division by Taylor Series / 11 \\
1.5.3 Newton--Raphson Division / 11 \\
1.6 C Language / 12 \\
1.7 An Extended Double Arithmetic: ieee.c / 13 \\
1.8 Binary - Decimal Conversion / 46 \\
1.8.1 etoasc.c / 47 \\
1.8.2 asctoe.c / 54 \\
1.9 Analysis of Error / 58 \\
1.9.1 Roundoff and Cancellation / 58 \\
1.9.2 Error Propagation / 60 \\
1.9.3 Error as a Random Variable / 61 \\
1.9.4 Order of Summation / 62 \\
1.10 Complex Arithmetic / 62 \\
1.10.1 cmplx.c / 64 \\
1.10.2 Absolute Value: cabs.c / 67 \\
1.11 Rational Arithmetic / 69 \\
1.11.1 euclid.c / 70 \\
2: Approximation Methods / 75 \\
2.1 Power Series / 75 \\
2.2 Chebyshev Expansions / 76 \\
2.2.1 chbevl.c / 79 \\
2.3 Pad{\'e} Approximations / 80 \\
2.4 Least Maximum Approximations / 82 \\
2.4.1 Best Polynomial Approximations / 82 \\
2.4.2 Best Rational Approximations / 85 \\
2.4.3 Special Rational Forms / 87 \\
2.5 A Program to Find Best Approximations: remes.c / 88
\\
2.6 Forms of Approximation / 111 \\
2.7 Asymptotic Expansions / 113 \\
2.8 Continued Fractions / 114 \\
2.8.1 Continued Fractions from Recurrences / 115 \\
2.8.2 Recurrences from Differential Equations / 116 \\
2.8.3 Computing Continued Fractions / 117 \\
2.9 Polynomials / 117 \\
2.9.1 polevl.c / 118 \\
2.10 Newton--Raphson Iterations / 119 \\
2.10.1 Division / 120 \\
2.10.2 Exponent Separation / 121 \\
2.10.3 Square Root / 122 \\
2.10.4 sqrt.c / 123 \\
2.10.5 Longhand Square Root / 124 \\
2.10.6 esqrt.c / 124 \\
2.10.7 Cube Root / 126 \\
2.10.8 cbrt.c / 127 \\
3: Software Notes / 129 \\
3.1 Design Strategy / 129 \\
3.2 Testing / 131 \\
3.3 System Utilities / 132 \\
3.3.1 mconf.h / 132 \\
3.3.2 mtherr.c / 134 \\
3.3.3 const.c / 136 \\
3.4 Arithmetic Utilities / 137 \\
3.4.1 efloor.c / 138 \\
3.4.2 efrexp.c / 140 \\
3.4.3 eldexp.c / 140 \\
4: Elementary Functions / 143 \\
4.1 $e^x$ / 143 \\
4.1.1 exp.c / 145 \\
4.2 $\ln x$ / 147 \\
4.2.1 log.c / 149 \\
4.3 Argument Transformation for Circular Functions /
152 \\
4.4 Sine and cosine / 153 \\
4.4.1 sin.c / 154 \\
4.4.2 cos.c / 156 \\
4.5 Tangent and Cotangent / 157 \\
4.5.1 tan.c / 158 \\
4.6 Complex Circular Functions / 161 \\
4.7 $\sin^{-1} x $ / 162 \\
4.7.1 asin.c / 163 \\
4.8 $\cos^{-1} x $ / 165 \\
4.8.1 acos.c / 165 \\
4.9 $\tan^{-1} x$ / 166 \\
4.9.1 atan.c / 168 \\
4.9.2 atan2.c / 169 \\
4.10 Complex Inverse Circular Functions / 170 \\
4.11 $\sinh x$ / 170 \\
4.11.1 sinh.c / 171 \\
4.12 $\cosh x$ / 172 \\
4.12.1 cosh.c / 173 \\
4.13 $\tanh x$ / 173 \\
4.13.1 tanh.c / 174 \\
4.14 $\sinh^{-1} x $ / 175 \\
4.14.1 asinh.c / 176 \\
4.15 $\cosh^{-1} x $ / 177 \\
4.15.1 acosh.c / 178 \\
4.16 $\tanh^{-1} x$ / 179 \\
4.16.1 atanh.c / 180 \\
4.17 Power Function / 181 \\
4.17.1 Real Exponent / 182 \\
4.17.2 pow.c / 182 \\
4.17.3 Integer Exponent / 189 \\
4.17.4 powi.c / 190 \\
4.18 Testing / 192 \\
4.19 Single Precision Polynomial Approximations / 193
\\
4.19.1 $\cos x$ / 193 \\
4.19.2 $\cosh^{-1} x $ / 193 \\
4.19.3 $\exp x$ / 196 \\
4.19.4 $\ln x$ / 196 \\
4.19.5 $\sin x$ / 197 \\
4.19.6 $\sin^{-1} x $ / 197 \\
4.19.7 Square Root / 197 \\
4.19.8 $\tan x$ / 198 \\
4.19.9 $\tan^{-1} x$ / 198 \\
4.19.10 $\tanh x$ / 199 \\
4.19.11 $tanh^{-1} x$ / 199 \\
5: Probability Distributions and Related Functions /
201 \\
5.1 $n!$ / 202 \\
5.1.1 fac.c / 204 \\
5.2 $\Gamma(x)$ / 206 \\
5.2.1 gamma.c / 210 \\
5.2.2 lgam.c / 214 \\
5.3 Incomplete Gamma Integral / 217 \\
5.3.1 igamc.c / 218 \\
5.3.2 igam.c / 220 \\
5.3.3 Functional Inverse of Incomplete Gamma Integral /
221 \\
5.3.4 igami.c / 221 \\
5.4 Gamma Distribution / 222 \\
5.4.1 gdtr c / 222 \\
5.4.2 gdtrc.c / 223 \\
5.5 $\chi^2$ Distribution / 223 \\
5.5.1 chdtrc.c / 224 \\
5.5.2 chdtr.c / 224 \\
5.5.3 chdtrl.c / 224 \\
5.6 Poisson Distribution / 225 \\
5.6.1 pdtrc.c / 225 \\
5.6.2 pdtr.c / 226 \\
5.6.3 pdtri.c / 226 \\
5.7 Beta Function / 227 \\
5.7.1 beta.c / 227 \\
5.8 Incomplete Beta Integral / 229 \\
5.8.1 ibet.c / 231 \\
5.8.2 Functional Inverse of Incomplete Beta Integral /
238 \\
5.9 Beta Distribution / 241 \\
5.9.1 btdtr.c / 241 \\
5.10 Binomial Distribution / 241 \\
5.10.1 bdtrc.c / 242 \\
5.10.2 bdtr.c / 243 \\
5.10.3 bdtri.c / 244 \\
5.11 Negative Binomial Distribution / 244 \\
5.11.1 nbdtr.c / 245 \\
5.11.2 nbdtrc.c / 245 \\
5.12 F Distribution / 246 \\
5.12.1 fdtrc.c / 247 \\
5.12.2 fdtr.c / 247 \\
5.12.3 fdtrci.c / 248 \\
5.13 Student's $t$ distribution / 249 \\
5.13.1 stdtr.c / 250 \\
5.14 Gaussian Distribution / 252 \\
5.14.1 ndtr.c / 254 \\
5.14.2 erfc.c / 256 \\
5.14.3 erf.c / 257 \\
5.14.4 Functional Inverse of Gaussian Distribution /
258 \\
5.14.5 ndtri.c / 259 \\
6: Bessel Functions / 263 \\
6.1 $J_0(x)$ / 263 \\
6.1.1 jO.c / 265 \\
6.2 $Y_0(x)$ / 268 \\
6.2.1 yO.c / 269 \\
6.3 Modulus and Phase / 270 \\
6.4 $J_1(x)$ / 271 \\
6.4.1 jl.c / 272 \\
6.5 $Y_1(x)$ / 275 \\
6.5.1 yl.c / 275 \\
6.6 $J_n(x)$ / 276 \\
6.1 $I_0(x)$ / 277 \\
6.7.1 i0.c / 278 \\
6.8 $I_1(x)$ / 281 \\
6.8.1 i1.c / 283 \\
6.9 $I_\nu(x)$ / 285 \\
6.9.1 iv.c / 286 \\
6.10 $K_0(x)$ / 287 \\
6.10.1 kO.c / 287 \\
6.11 $K_1(x)$ / 291 \\
6.11.1 kl.c / 291 \\
6.12 $K_n(x)$ / 294 \\
6.12.1 kn.c / 295 \\
6.13 $J_\nu(x)$ / 299 \\
6.13.1 jv.c / 301 \\
6.14 Airy Functions / 315 \\
6.14.1 airy.c / 322 \\
6.15 $Y_n(x)$ / 328 \\
6.15.1 yn.c / 329 \\
6.16 Testing / 330 \\
7: Other Special Functions / 333 \\
7.1 Hypergeometric Functions / 333 \\
7.1.1 $_2F_1$ / 334 \\
7.1.2 hyp2fi.c / 335 \\
7.1.3 $_1F_1$ / 341 \\
7.1.4 hyplfi.c / 342 \\
7.1.5 $_2F_0$ / 346 \\
7.1.6 hyp2ffi.c / 346 \\
7.2 Struve Functions / 348 \\
7.2.1 hypl1f2.c / 348 \\
7.2.2 hyp3f0.c / 349 \\
7.2.3 yv.c / 351 \\
7.2.4 struve.c / 351 \\
7.3 $\psi(x)$ / 352 \\
7.3.1 psi.c / 354 \\
7.4 Exponential Integral / 355 \\
7.4.1 en.c / 356 \\
7.5 Sine and Cosine Integrals / 360 \\
7.5.1 sici.c / 362 \\
7.5.2 Hyperbolic Sine and Cosine Integrals / 367 \\
7.5.3 shichi.c / 370 \\
7.6 Dilogarithm / 374 \\
7.6.1 spence.c / 375 \\
7.7 Dawson's Integral / 377 \\
7.7.1 dawsn.c / 378 \\
7.8 Fresnel Integrals / 381 \\
7.8.1 fresnl.c / 383 \\
7.9 Elliptic Functions / 387 \\
7.9.1 $K(m)$ / 387 \\
7.9.2 ellpk.c / 388 \\
7.9.3 $F(\phi|m)$ / 389 \\
7.9.4 ellik.c / 390 \\
7.9.5 $E(m)$ / 392 \\
7.9.6 ellpe.c / 392 \\
7.9.7 $E(\phi|m)$ / 393 \\
7.9.8 ellie.c / 394 \\
7.9.9 Jacobian Elliptic Functions / 396 \\
7.9.10 ellpj.c / 398 \\
7.10 Zeta Functions / 400 \\
7.10.1 hurwiz.c / 400 \\
7.10.2 Riemann Zeta Function / 402 \\
7.10.3 zetac.c / 405 \\
Bibliography / 411 \\
Index / 413",
}
@Article{Norton:1989:PCA,
author = "Robert M. Norton",
title = "Pocket-Calculator Approximation for Areas under the
Standard Normal Curve",
journal = j-AMER-STAT,
volume = "43",
number = "1",
pages = "24--26",
month = feb,
year = "1989",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 12:40:30 MST 2012",
bibsource = "http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326443;
https://www.math.utah.edu/pub/tex/bib/amstat1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2685163",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Rhee:1989:MII,
author = "W. T. Rhee and M. Talagrand",
title = "Martingale inequalities, interpolation and
{NP}-complete problems",
journal = j-MATH-OP-RES,
volume = "14",
number = "1",
pages = "91--96",
month = feb,
year = "1989",
CODEN = "MOREDQ",
ISSN = "0364-765x (print), 1526-5471 (electronic)",
ISSN-L = "0364-765X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ., Paris, Paris, France; Ohio State Univ.,
Columbus",
bibno = "67063",
catcode = "G.2.2; H.1.1; G.1.1; G.1.2; G.3; I.6.4; F.1.3",
CRclass = "G.2.2 Graph Theory; G.2.2 Path and circuit problems;
H.1.1 Systems and Information Theory; H.1.1 General
systems theory; G.1.1 Interpolation; G.1.1
Interpolation formulas; G.1.2 Approximation; G.1.2
Elementary function approximation; G.3 Probabilistic
algorithms (including Monte Carlo); I.6.4 Model
Validation and Analysis; F.1.3 Complexity Classes;
F.1.3 Reducibility and completeness",
descriptor = "Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory, Path and circuit problems; Information Systems,
MODELS AND PRINCIPLES, Systems and Information Theory,
General systems theory; Mathematics of Computing,
NUMERICAL ANALYSIS, Interpolation, Interpolation
formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, PROBABILITY AND STATISTICS,
Probabilistic algorithms (including Monte Carlo);
Computing Methodologies, SIMULATION AND MODELING, Model
Validation and Analysis; Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Classes,
Reducibility and completeness",
fjournal = "Mathematics of Operations Research",
genterm = "algorithms; theory; measurement",
guideno = "1989-09079",
journal-URL = "http://pubsonline.informs.org/loi/moor",
journalabbrev = "Math. Oper. Res.",
jrldate = "Feb. 1989",
subject = "F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT
DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3 PROBABILITY AND
STATISTICS; H. Information Systems; H.1 MODELS AND
PRINCIPLES; I. Computing Methodologies; I.6 SIMULATION
AND MODELING",
}
@Article{Ruymgaart:1989:SPB,
author = "F. H. Ruymgaart",
title = "Some properties of bivariate empirical hazard
processes under random censoring",
journal = j-J-MULTIVAR-ANAL,
volume = "28",
number = "2",
pages = "271--281",
month = feb,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259x (print), 1095-7243 (electronic)",
ISSN-L = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64343",
catcode = "G.3; G.1.2",
CRclass = "G.3 Statistical computing; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Statistical computing; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Journal of Multivariate Analysis",
genterm = "algorithms; theory; measurement",
guideno = "1989-08469",
journalabbrev = "J. Multivariate Anal.",
jrldate = "February 1989",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Rybicki:1989:DIS,
author = "George B. Rybicki",
title = "{Dawson}'s Integral and the Sampling Theorem",
journal = j-COMPUT-PHYS,
volume = "3",
number = "2",
pages = "85--87",
month = mar,
year = "1989",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4822832",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:17 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4822832",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@InCollection{Saigo:1989:FID,
author = "Megumi Saigo",
title = "Fractional integrals and derivatives associated with
elementary functions and {Bessel} functions",
crossref = "Srivastava:1989:UFF",
pages = "283--306",
year = "1989",
MRclass = "26A33 (33C10)",
MRnumber = "93h:26011",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Ellis Horwood Ser. Math. Appl.",
acknowledgement = ack-nhfb,
}
@Article{Sala:1989:TJA,
author = "Kenneth L. Sala",
title = "Transformations of the {Jacobian} amplitude function
and its calculation via the arithmetic-geometric mean",
journal = j-SIAM-J-MATH-ANA,
volume = "20",
number = "6",
pages = "1514--1528",
month = nov,
year = "1989",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33A25 (42A16 70D99)",
MRnumber = "90j:33003",
MRreviewer = "J. M. H. Peters",
bibdate = "Sun Nov 28 19:24:55 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/20/6;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Smith:1989:EMP,
author = "David M. Smith",
title = "Efficient multiple-precision evaluation of elementary
functions",
journal = j-MATH-COMPUT,
volume = "52",
number = "185",
pages = "131--134",
month = jan,
year = "1989",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D15 (26-04)",
MRnumber = "90c:65034",
MRreviewer = "Menachem Dishon",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Dept. of Math., Loyola Univ., Los Angeles, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "arithmetic; base b; elementary functions; function
evaluation; multiple-precision evaluation",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Stearns:1989:SFD,
author = "C. C. Stearns",
title = "Subtractive floating-point division and square root
for {VLSI DSP}",
crossref = "IEE:1989:EEC",
pages = "405--409",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes recent architectural developments
in VLSI design for real-time digital signal processing.
In particular, floating point division and floating
point square root architectures applicable to both
adaptive filtering, standard deviation computations,
and general purpose processing are discussed. Emphasis
here is on the internal architectures of the arithmetic
units not on their applications. The research presented
in this paper has been proven feasible and reliable
from extensive gate-level simulation and fabrication in
silicon.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B1270F
(Digital filters); B2570D (CMOS integrated circuits);
C5230 (Digital arithmetic methods); C5240 (Digital
filters); C5260 (Digital signal processing)",
keywords = "Adaptive filtering; Arithmetic units; CMOS technology;
Floating point division; Floating point square root
architectures; Gate-level simulation; General purpose
processing; Real-time digital signal processing;
Semiconductor; Standard deviation computations; VLSI
DSP",
thesaurus = "Adaptive filters; CMOS integrated circuits; Digital
arithmetic; Digital signal processing chips; VLSI",
}
@TechReport{Tang:1989:TCA,
author = "Ping Tak Peter Tang",
title = "Testing Computer Arithmetic by Elementary Number
Theory",
institution = "Mathematics and Computer Science Division, Argonne
National Laboratory",
address = "Argonne, IL, USA",
pages = "????",
month = aug,
year = "1989",
bibdate = "Fri Jun 11 12:38:06 1999",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Tang:1989:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Exponential
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "15",
number = "2",
pages = "144--157",
month = jun,
year = "1989",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 22:47:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/63522.214389;
http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/",
abstract = "Algorithms and implementation details for the
exponential function in both single- and
double-precision of IEEE 754 arithmetic are presented
here. With a table of moderate size, the
implementations need only working-precision arithmetic
and are provably accurate to within 0.54 ulp as long as
the final result does not underflow. When the final
result suffers gradual underflow, the error is still no
worse than 0.77 ulp.",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@TechReport{Thomas:1989:SNL,
author = "Marlin A. Thomas and Gary W. Gemmill and John R.
Crigler",
title = "{STATLIB}: {NSWC} Library of Statistical Programs and
Subroutines",
type = "Technical Report",
number = "NSWC TR 89-97",
institution = "Naval Surface Warfare Center",
address = "Dahlgren, VA 22448-5000, USA and Silver Spring, MD
20903-5000, USA",
pages = "viii + 280",
month = aug,
year = "1989",
bibdate = "Sat Nov 15 10:39:12 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.dtic.mil/dtic/tr/fulltext/u2/a221538.pdf",
abstract = "This document provides a description of each program
and subroutine in STATLIB, THE Naval Surface Warfare
Center library of statistical programs and subroutines
for its general purpose computers. The Library contains
thirty-four programs and twenty-four subroutines for
statistical analysis, probability evaluation, and
random number generation. It was written to enable
Center Scientists and Engineers to efficiently perform
a wide variety of analyses and to generate pseudo
random numbers from many different probability
distributions.",
acknowledgement = ack-nhfb,
onlinedate = "255",
tableofcontents = "Introduction / 1 \\
Overview of STATLIB / 1 \\
Origin of STATLIB / 1 \\
Establishment of STATLIB / 1 \\
Commercial Statistical Packages at NSWC / 2 \\
Using STATLIB / 5 \\
Library Organization / 5 \\
How to Call It / 5 \\
Information Needed to Run It / 5 \\
Examples / 9 \\
Program / 9 \\
Subroutine / 10 \\
Descriptions and Input Guides / 21 \\
Programs / 23 \\
Regression Analysis / 25 \\
GEMREG General Multiple Regression / 29 \\
DAMRCA Dahlgren Multiple Regression Comprehensive
Analysis / 35 \\
WEPORU Uncorrelated Weighted Polynomial Regression / 41
\\
WEPORC Correlated Weighted Polynomial Regression / 45
\\
MROP Multiple Regression Using Orthogonal Polynomials /
49 \\
CANON Canonical Analysis of Second Order Response
Functions / 57 \\
DURBWAT Durbin--Watson Test for Independence of
Residuals / 61 \\
NEARNEB Near Neighbor Estimation of Experimental Error
/ 63 \\
Goodness of Fit Analysis / 67 \\
UNORGOF Univariate Normal Goodness of Fit / 69 \\
BNORGOF Bivariate Normal Goodness of Fit / 75 \\
EXPGOF Exponential Goodness of Fit / 81 \\
WBLGOF Weibull Goodness ot / 83 \\
PERGOF Pearson System Goodness of Fit / 87 \\
UNKSGOF Univariate Normal Kolmogorov--Smirnov Test of
Fit / 93 \\
RANDOM Test of Fit for Uniform Random Number Generators
/ 99 \\
Power Evaluation / 103 \\
DISCRETE POWER EVALUATION / 107 \\
BINIPOW Power of the Test on a Binomial Proportion /
109 \\
BIN2POW Power of the Test on the Difference of Two
Binomial Proportions / 113 \\
POIIPOW Power of the Test on the Poisson Parameter /
121 \\
Continuous Power Evaluation / 125 \\
NORIPOW Power of the One-Sample Normal Test on the Mean
/ 127 \\
NOR2PWE Power of the Two-Simple Normal Test on Means
with ample Sizes / 131 \\
NOR2PWU Power of the Two-Sample Normal Test on Means
with Unequal Sample Sizes / 135 \\
T1POW Power of the One-Sample $t$ Test on the Mean /
141 \\
T2POW Power of the Two-Sample (Pooled) $t$ Test on
Means / 147 \\
CHIVPOW Power of the Chi-square Test on the Variance /
153 \\
FVARPOW Power of the $F$ Test for the Equality of
Variances / 157 \\
FEMPOW Power of the Test for One-Way Fixed Effects
Analysis of Variance / 163 \\
REMPOW Power of the Test for One-Way Random Effects
Analysis of Variance / 167 \\
Probability Evaluation / 171 \\
BINVARP Binomial Probability Distribution with Unequal
Single Trial Probabilities / 173 \\
NEGBIN Negative Binomial Probability Distribution / 177
\\
Confidence Limit Evaluation / 179 \\
BINCL Confidence Limits for the Binomial Parameter p /
181 \\
CEPCL Confidence Limits for the CEP (Circular Probable
Error) / 185 \\
SEPCL Confidence Limits for the SEP (Spherical Probable
Error) / 191 \\
Miscellaneous Statistical Analysis / 197 \\
LD50EST Estimation of LD50 (Lethal Dose 50th
Percentile) / 199 \\
FFAC2K Analysis of the 2**k Fractional Factorial
Experiment / 203 \\
Subroutines / 211 \\
Random Number Generation / 213 \\
Discrete Random Number Generators, / 217 \\
RANARB Arbitrary (User Specified) Discrete Distribution
/ 219 \\
RANBER Bernoulli Distribution / 221 \\
RANBIN Binomial Distribution / 223 \\
RANGEO Geometric Distribution / 225 \\
RANHYP Hypergeometric Distribution / 227 \\
RANNBI Negative Binomial Distribution / 229 \\
RANPOI Poisson Distribution / 231 \\
RANUWO Discrete Uniform Distribution (Without
Replacement) / 233 \\
RANUWR Discrete Uniform Distribution (With Replacement)
/ 235 \\
Continuous Random Number Generators / 237 \\
RANBET Beta Distribution / 239 \\
RANCSQ Chi-square Distribution / 241 \\
RANEXP Exponential Distribution / 243 \\
RANFDI $F$ Distribution / 245 \\
RANGAM Gamma Distribution / 247 \\
RANLGS Logistic Distribution / 249 \\
RANLOG Lognormal Distribution / 251 \\
RANNOR Normal Distribution / 255 \\
RANNVE Multivariate Normal Distribution / 257 \\
RANPDI Pearson Distributions / 261 \\
RANTDI Student's $t$ Distribution / 265 \\
RANUNI Continuous Uniform Distribution (On a Line) /
267 \\
RANCIR Continuous Uniform Distribution (Within a
Circle) / 269 \\
RANWEI Three-parameter Weibull Distribution / 271 \\
RANMK1 1st Order Markov Process / 273 \\
Glossary / 275 \\
Distribution / 277",
}
@Article{Ubhaya:1989:LAN,
author = "V. A. Ubhaya",
title = "{$ L_p $} approximation from nonconvex subsets of
special classes of functions",
journal = j-J-APPROX-THEORY,
volume = "57",
number = "2",
pages = "223--238",
month = may,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72277",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "verification; theory",
guideno = "1989-07833",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "May 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Vaidya:1989:LWB,
author = "P. M. Vaidya",
title = "A locally well-behaved potential function and a simple
{Newton}-type method for finding the center of a
polytype",
crossref = "Megiddo:1989:PMP",
pages = "79--90",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74176",
catcode = "G.1.6; G.1.6; F.2.2; G.1.2; G.1.5; G.1.5; I.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.6
Optimization; G.1.6 Gradient methods; F.2.2
Nonnumerical Algorithms and Problems; F.2.2 Geometrical
problems and computations; G.1.2 Approximation; G.1.2
Elementary function approximation; G.1.5 Roots of
Nonlinear Equations; G.1.5 Convergence; G.1.5 Roots of
Nonlinear Equations; G.1.5 Iterative methods; I.1.2
Algorithms; I.1.2 Nonalgebraic algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization, Gradient
methods; Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Convergence; Mathematics of
Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
Equations, Iterative methods; Computing Methodologies,
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms",
genterm = "algorithms; theory",
guideno = "1989-12478",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
xxpages = "131--158",
}
@Article{VanHalen:1989:AAA,
author = "P. {Van Halen}",
title = "Accurate analytical approximations for error function
and its integral",
journal = j-ELECT-LETTERS,
volume = "25",
number = "9",
pages = "561--563",
day = "27",
month = apr,
year = "1989",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19890383",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Dec 16 18:15:17 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/19780/",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@PhdThesis{Vavasis:1989:CFP,
author = "S. A. Vavasis",
title = "Complexity of fixed point computations",
type = "{Ph.D} Thesis",
school = "Stanford University",
address = "Stanford, CA, USA",
pages = "????",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "76220",
catcode = "J.4; G.1.2; F.1.3; G.1.2; G.2.2",
CRclass = "J.4 Economics; G.1.2 Approximation; G.1.2 Nonlinear
approximation; F.1.3 Complexity Classes; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.2.2 Graph Theory; G.2.2 Network problems",
descriptor = "Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES,
Economics; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Nonlinear approximation;
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Classes; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, DISCRETE
MATHEMATICS, Graph Theory, Network problems",
genterm = "algorithms; theory",
guideno = "1989-12859",
source = "UMI order no: GAX89-19486",
subject = "J. Computer Applications; J.4 SOCIAL AND BEHAVIORAL
SCIENCES; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY
ABSTRACT DEVICES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
DISCRETE MATHEMATICS",
}
@InProceedings{Vial:1989:APP,
author = "J.-P. Vial",
title = "Approximate projections in a projective method for the
linear feasibility problem",
crossref = "Megiddo:1989:PMP",
bookpages = "x + 158",
pages = "65--78",
year = "1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "74175",
catcode = "G.1.6; F.2.2; I.1.2; G.1.6; G.1.2; F.2.1; G.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; F.2.2
Nonnumerical Algorithms and Problems; F.2.2 Geometrical
problems and computations; I.1.2 Algorithms; I.1.2
Nonalgebraic algorithms; G.1.6 Optimization; G.1.6
Constrained optimization; G.1.2 Approximation; G.1.2
Elementary function approximation; F.2.1 Numerical
Algorithms and Problems; F.2.1 Computations on
matrices; G.1.2 Approximation; G.1.2 Minimax
approximation and algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations; Computing
Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
Nonalgebraic algorithms; Mathematics of Computing,
NUMERICAL ANALYSIS, Optimization, Constrained
optimization; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation; Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Minimax
approximation and algorithms",
genterm = "algorithms; experimentation; measurement; performance;
theory",
guideno = "1989-12477",
procdate = "March 1-4, 1987",
procloc = "Pacific Grove, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{vonRosen:1989:MLE,
author = "D. von Rosen",
title = "Maximum likelihood estimators in multivariate linear
normal models",
journal = j-J-MULTIVAR-ANAL,
volume = "31",
number = "2",
pages = "187--200",
month = nov,
year = "1989",
CODEN = "JMVAAI",
ISSN = "0047-259x (print), 1095-7243 (electronic)",
ISSN-L = "0047-259X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Stockholm, Stockholm, Sweden",
bibno = "69314",
catcode = "G.1.6; G.1.2; G.1.2",
CRclass = "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
Approximation; G.1.2 Linear approximation; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Linear programming; Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Linear
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Journal of Multivariate Analysis",
genterm = "algorithms; theory",
guideno = "1989-08484",
journalabbrev = "J. Multivariate Anal.",
jrldate = "Nov. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Wang:1989:SF,
author = "Z. X. Wang and D. R. Guo",
title = "Special Functions",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xvi + 695",
year = "1989",
ISBN = "1-283-63565-8, 661394811X, 981-277-936-1 (e-book),
9971-5-0659-9 (hardcover), 9971-5-0667-X (paperback)",
ISBN-13 = "978-1-283-63565-3, 661394811X, 978-981-277-936-6
(e-book), 978-9971-5-0659-9 (hardcover),
978-9971-5-0667-4 (paperback)",
LCCN = "QA331 .W296 1989",
bibdate = "Mon Sep 3 16:10:24 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Translation to English by D.R. Guo and X. J. Xia.",
acknowledgement = ack-nhfb,
remark = "Reprinted in 2010. Library catalogs record two rather
different pages values. The one chosen here matches the
tableofcontents value.",
shorttableofcontents = "1: The expansion of functions in infinite
series and infinite products \\
2: Linear ordinary differential equations of the second
order \\
3: The gamma function \\
4: Hypergeometric function \\
5: Legendre functions \\
6: Confluent hypergeometric functions \\
7: Bessel functions \\
8: Weierstrass elliptic functions \\
9: Theta functions \\
10: Jacobian elliptic functions \\
11: Lame functions \\
12: Mathieu functions",
subject = "Functions",
tableofcontents = "1: THE EXPANSION OF FUNCTIONS IN INFINITE SERIES
AND INFINITE PRODUCTS \\
1.1. Bernoulli Polynomials and Bernoulli Numbers / 1
\\
1.2. Euler Polynomials and Euler Numbers / 5 \\
1.3. Euler--Maclaurin Formula / 8 \\
1.4. Lagrange's Expansion Formula / 14 \\
1.5. Expansion of Meromorphic Functions in Rational
Fractions / 17 \\
1.6. Infinite Product / 21 \\
1.7. The Expansion of a Function in Infinite Product
Weierstrass Theorem / 25 \\
1.8. Asymptotic Expansion / 29 \\
1.9. The Asymptotic Expansion of the Laplace Integral,
Watson's Lemma / 34 \\
1.10. Expansion in Terms of Functions of an Orthonormal
Set / 36 \\
Exercise 1 / 41 \\
2: LINEAR ORDINARY DIFFERENTIAL EQUATIONS OF THE SECOND
ORDER \\
2.1. Singular Points of Linear Ordinary Differential
Equations of the Second Order / 47 \\
2.2. Solution of the Equation in the Vicinity of an
Ordinary Point / 48 \\
2.3. Solutions of the Equation in the Vicinity of a
Singular Point / 51 \\
2.4. Regular Solution. Regular Singularities / 55 \\
2.5. Frobenius Method / 61 \\
2.6. Point at Infinity / 63 \\
2.7. Equations of Fuchsian Type / 64 \\
2.8. Equations of Fuchsian Type Having Five Regular
Singular Points / 66 \\
2.9. Equations of Fuchsian Type Having Three Regular
Singularities / 68 \\
2.10. Irregular Singularities. Formal Regular Solution
/ 71 \\
2.11. Irregular Singularities. Normal Solutions and
Subnormal Solutions / 73 \\
2.12. Method of Solution by Integrals. Basic Principle
/ 78 \\
2.13. Equations of Laplacian Type and Laplace Transform
/ 81 \\
2.14. Euler Transform / 85 \\
Exercise 2 / 88 \\
3: THE GAMMA FUNCTION \\
3.1. Definition of the Gamma Function / 93 \\
3.2. Recurrence Relation / 94 \\
3.3. The Infinite-Product Expression of Euler / 95 \\
3.4. Weierstrass' Infinite Product / 97 \\
3.5. Relation between the $\Gamma$-Function and the
Trigonometric Function / 98 \\
3.6. Multiplication Formula / 99 \\
3.7. Contour Integral / 101 \\
3.8. Euler Integral of the First Kind. $B$-Function /
103 \\
3.9. Double-Contour Integral / 105 \\
3.10. Dirichlet Integral / 106 \\
3.11. Logarithmic Derivative of the $\Gamma$-Function /
107 \\
3.12. Asymptotic Expansions / 111 \\
3.13. Another Derivation of the Asymptotic Expansion /
112 \\
3.14. Riemann $\zeta$ Function / 114 \\
3.15. The Functional Equation of the $\zeta$-Function /
115 \\
3.16. The Value of $\zeta(s,a)$ when $s$ is an Integer
/ 117 \\
3.17. Hermite Formula / 118 \\
3.18. Relation to the $\Gamma$-Function / 120 \\
3.19. Euler Product of the $\zeta$-Function / 123 \\
3.20. Riemann Integral of the $\zeta$-Function / 124
\\
3.21. Another Derivation of the Asymptotic Expansion of
the $\Gamma$-Function / 125 \\
3.22. Evaluation of the $\zeta$-Function / 128 \\
Exercise 3 / 128 \\
4: HYPERGEOMETRIC FUNCTION \\
4.1. Hypergeometric Series and Hypergeometric Function
/ 135 \\
4.2. Recurrence Relations / 137 \\
4.3. Other Solutions of the Hypergeometric Equation
Expressed in Terms of Hypergeometric Functions / 139
\\
4.4. The Second Solution of the Hypergeometric Equation
when the Difference of the Exponents is an Integer /
144 \\
4.5. Integral Representation of the Hypergeometric
Function / 150 \\
4.6. Barnes' Integral Representation of the
Hypergeometric Function / 153 \\
4.7. The Value of $F(\alpha, \beta, \gamma, 1)$ / 156
\\
4.8. Connections between the Fundamental Solutions at
the Singular Points $0, 1, \infty$. Analytic
Continuation / 159 \\
4.9. When $\gamma - \alpha - \beta$, $\alpha - \beta$
are Integers / 162 \\
4.10. Jacobi Polynomials / 169 \\
4.11. Chebyshev Polynomials / 173 \\
4.12. Quadratic Transformations / 177 \\
4.13. Kummer's Formula and Summation Formula Derived
from It / 184 \\
4.14. Asymptotic Expansions for Large Parameters / 186
\\
4.15. Generalized Hypergeometric Series / 189 \\
4.16. Hypergeometric Series with Two Variables / 191
\\
4.17. The Transformation Formulae of $F_1$ and $F_2$ /
195 \\
4.18. Reducible Cases / 197 \\
Exercise 4 / 202 \\
5: LEGENDRE FUNCTIONS \\
5.1. Legendre Equation / 210 \\
5.2. Legendre Polynomials / 212 \\
5.3. The Generating Function of $P_n(i)$. Rodrigues
Formula / 215 \\
5.4. Integral Representations of $P_n(x)$ / 216 \\
5.5. Recurrence Relations of $P_n(x)$ / 218 \\
5.6. Legendre Polynomials as a Complete Set of
Orthonormal Functions / 219 \\
5.7. Zeros of $P_n(x)$ / 223 \\
5.8. Legendre Functions of the Second Kind, $Q_n(x)$ /
224 \\
5.9. Recurrence Relations of $Q_n(x)$ / 230 \\
5.10. Expansion of the Function $(x - t)^{-1}$ in Terms
of Legendre Functions. Neumann Expansion / 231 \\
5.11. Associate Legendre Functions $P_l^m(x)$ / 233 \\
5.12. Orthogonality Relations of $P_l^m(x)$ / 235 \\
5.13. Recurrence Relations for $P_l^m(x)$ and
$Q_l^m(x)$ / 239 \\
5.14. Addition Formula / 241 \\
5.15. Spherical Surface Harmonics $Y_{lm}(\theta,
\phi)$ / 244 \\
5.16. The General Associate Legendre Functions
$P_\nu^\mu(z)$ / 247 \\
5.17. $Q_\nu^\mu(z)$ / 251 \\
5.18. Definition of $P_\nu^\mu(x)$ on the Cut: $-\infty
< x < 1$ / 255 \\
5.19. Definition of $Q_\nu^\mu(x)$ on the Cut: $-\infty
< x < 1$ / 258 \\
5.20. Other Integral Expressions for $P_\nu(z)$ and
$P_\nu^m(z)$ / 262 \\
5.21. Addition Formulae / 267 \\
5.22. Asymptotic Expansions of $P_\nu^\mu(\cos \theta)$
and $Q_\nu^\mu(\cos \theta)$ when $\nu \to \infty$ /
270 \\
5.23. Ultra-Spherical Polynomials $C_n^\lambda(x)$ /
274 \\
Exercise 5 / 277 \\
6: CONFLUENT HYPERGEOMETRIC FUNCTIONS \\
6.1. Confluent Hypergeometric Functions / 296 \\
6.2. Relations among the Consecutive Functions / 299
\\
6.3. Whittaker Equation and Whittaker Functions
$M_{k,m}(z)$ / 300 \\
6.4. Integral Representations / 302 \\
6.5. Whittaker Functions $W_{k,m}(z)$ / 305 \\
6.6. Asymptotic Expansion of $W_{k,m}(z)$ when $z \to
\infty$ / 307 \\
6.7. Barnes' Integral Representation of $W_{k,m}(z)$ /
310 \\
6.8. Relations between $W_{\pm k,m}(\pm z)$ and $M_{\pm
k,m}(\pm z)$. Asymptotic Expansion of $F(\alpha,
\gamma, z)$. Stokes Phenomenon / 313 \\
6.9. The Case when $\gamma$ (or $2m$) is an Integer /
316 \\
6.10. The Asymptotic Expansions of $F(\alpha, \gamma,
z)$ for Large $|\alpha|$, $|\gamma|$ / 318 \\
6.11. Differential Equations Reducible to the Confluent
Hypergeometric Equation / 318 \\
6.12. Weber Equation. Parabolic Cylinder Functions
$D_n(z)$ / 320 \\
6.13. Hermite Functions and Hermite Polynomials / 325
\\
6.14. Laguerre Polynomials / 327 \\
6.15. Other Special Functions Expressible by Whittaker
Functions / 332 \\
Exercise 6 / 335 \\
7: BESSEL FUNCTIONS \\
7.1. Bessel Equation. Its Relation to the Confluent
Hypergeometric Equation / 345 \\
7.2. Bessel Functions of the First Kind: $J_{\pm
\nu}(z)$, $2\nu \neq$ integer / 347 \\
7.3. Bessel Functions of Order Half an Odd Integer:
$J_{n + 1/2}(z)$ $(n = 0, \pm 1, \pm 2, \ldots{})$ /
350 \\
7.4. Integral Representations of $J_\nu(z)$ / 351 \\
7.5. Bessel Functions of Integral Order $J_n(z)$ $(n =
0, 1, 2, \ldots{})$ / 359 \\
7.6. Bessel Functions of the Second Kind $Y_\nu(z)$ /
365 \\
7.7. Bessel Functions of the Third Kind (Hankel
Functions) $H_\nu^{(1)}(z)$, $H_\nu^{(2)}(z)$ / 368 \\
7.8. Modified (or Imaginary Argument) Bessel Functions
$I_\nu(z)$ and $K_\nu(z)$. Thomson Functions
$\ber_\nu(z)$ and $\bei_\nu(z)$; etc. / 374 \\
7.9. Spherical Bessel Functions $j_l(z)$, $n_l(z)$,
$h_l^{(1)}(z), $h_l^{(2)}(z) / 376 \\
7.10. Asymptotic Expansions for the Case $|z| \to
\infty$ / 378 \\
7.11. The Method of Steepest Descent / 381 \\
7.12. Asymptotic Expansions of Bessel Functions of
Order $\nu$ for Large $|\nu|$ and $|z|$ / 384 \\
7.13. Addition Formulae / 395 \\
7.14. Integrals Containing Bessel Functions. (1) Finite
Integrals / 399 \\
7.15. Integrals Containing Bessel Functions. (2)
Infinite Integrals / 401 \\
7.16. Neumann Expansion / 412 \\
7.17. Kapteyn Expansion / 415 \\
7.18. The Zeros of Bessel Functions / 420 \\
7.19. Fourier--Bessel Expansion / 424 \\
Exercise 7 / 425 \\
8: WEIERSTRASS ELLIPTIC FUNCTIONS \\
8.1. Elliptic Integrals and Elliptic Functions / 456
\\
8.2. The Periods of Elliptic Integrals / 460 \\
8.3. The General Properties of Doubly-Periodic
Functions and Elliptic Functions / 462 \\
8.4. The Function $\wp(z)$ / 466 \\
8.5. Algebraic Relation between $\wp(z)$ and $\wp'(z)$
/ 468 \\
8.6. The Function $\zeta(z)$ / 471 \\
8.7. The Function $\sigma(z)$ / 473 \\
8.8. Homogeneity of the Weierstrass Elliptic Function /
476 \\
8.9. Representations of a General Elliptic Function /
476 \\
8.10. Addition Formulae / 481 \\
8.11. Expressing the Coordinates of a Cubic Curve by
Elliptic Functions / 485 \\
8.12. The Problem of a Quartic Polynomial / 486 \\
8.13. Curves of Genus (Deficiency) 1 / 489 \\
Exercise 8 / 493 \\
9: THETA FUNCTIONS \\
9.1. The Theta Function $\theta(\nu)$ / 498 \\
9.2. The Functions $\vartheta_k(\nu)$ / 500 \\
9.3. Elliptic Functions Represented by Theta Functions
/ 502 \\
9.4. Relations among the Squares of $\vartheta_k(\nu)$
/ 503 \\
9.5. Addition Formulae / 504 \\
9.6. Differential Equations Satisfied by Theta
Functions / 506 \\
9.7. The Values of Some Constants / 508 \\
9.8. Legendre's Elliptic Integral of the First Kind /
510 \\
9.9. Jacobi's Imaginary Transformation / 514 \\
9.10. Transformation of Landen-Type / 516 \\
9.11. Representation of Theta Functions by Infinite
Product / 517 \\
9.12. Fourier Expansion of the Logarithmic Derivatives
of Theta Functions / 521 \\
9.13. The Functions $\Theta(u)$ and $H(u)$ / 522 \\
Exercise 9 / 523 \\
10: JACOBIAN ELLIPTIC FUNCTIONS \\
10.1. Jacobian Elliptic Functions $\sn u$, $\cn u$,
$\dn u$ / 530 \\
10.2. Geometric Representations of Jacobian Elliptic
Functions / 532 \\
10.3. Complete Elliptic Integrals / 535 \\
10.4. Addition Formulae / 537 \\
10.5. The Periodicity of Jacobian Elliptic Functions /
539 \\
10.6. The Zeros and Poles of Jacobian Elliptic
Functions / 540 \\
10.7. Transformations of Elliptic Functions / 542 \\
10.8. Reductions of Elliptic Integrals / 545 \\
10.9. Elliptic Integral of the Second Kind / 552 \\
10.10. Elliptic Integral of the Third Kind / 553 \\
10.11. Properties of the Function $E(u)$ / 555 \\
10.12. Differential Equations Satisfied by $K$ and $E$
with Respect to $k$ and Expansions of $K$ and $E$ with
Respect to $k$ / 558 \\
10.13. Relations between Jacobian Elliptic Functions
and Theta Functions / 561 \\
10.14. Expressing Jacobian Elliptic Functions in
Infinite Products and Fourier Series / 566 \\
Exercise 10 / 569 \\
11: LAM{\'E} FUNCTIONS \\
11.1. Ellipsoidal Coordinates / 575 \\
11.2. Representing the Coordinates with Elliptic
Functions / 578 \\
11.3. Lam{\'e} Equation / 580 \\
11.4. Four Types of Lam{\'e} Functions / 583 \\
11.5. Ellipsoidal Harmonics / 589 \\
11.6. Niven's Representation / 591 \\
11.7. On the Zeros of Lam{\'e} Polynomials / 595 \\
11.8. Lam{\'e} Functions of the Second Kind / 597 \\
11.9. Generalized Lam{\'e} Functions / 599 \\
11.10. Integral Equations of Lam{\'e} Functions / 602
\\
11.11. The Integral Representation of Ellipsoidal
Harmonics / 604 \\
Exercise 11 / 607 \\
12: MATHIEU FUNCTIONS \\
12.1. Mathieu Equation / 610 \\
12.2. General Properties of the Solution. Fundamental
Solutions / 612 \\
12.3. Floquet Solution / 614 \\
12.4. Periodic Solutions of Mathieu Equation / 615 \\
12.5. Fourier Expansion of the Floquet Solution / 617
\\
12.6. Formulae for Computing Eigenvalues $\lambda(q)$ /
620 \\
12.7. Mathieu Functions $\ce_m(z)$, $m = 0, 1, 2,
\ldots{}$ and $\se_m(z)$, $m = 1, 2 \ldots{}$ / 624 \\
12.8. Expansion of $\lambda_\nu(q)$ in Powers of $q$ /
627 \\
12.9. Fourier Expansions of $\ce_m(z)$ and $\se_m(z)$
for Small $q$ / 630 \\
12.10. Infinite Determinant / 632 \\
12.11. Hill Equation / 633 \\
12.12. Stable and Unstable Solutions of Mathieu
Equation. Stable Region and Unstable Region / 637 \\
12.13. Approximate Solutions of Mathieu Equation for
$\lambda \gg q > 0$ / 640 \\
12.14. Integral Equations for Mathieu Functions / 643
\\
Exercise 12 / 645 \\
Appendices \\
Appendix I. Roots of a Cubic Equation / 654 \\
Appendix II. Roots of the Quartic Equation / 656 \\
Appendix III. Orthogonal Curvilinear Coordinate Systems
/ 658 \\
Bibliography / 677 \\
Glossary / 679 \\
Index / 683",
xxpages = "xiii + 422",
}
@Article{Wasilkowski:1989:AIV,
author = "G. W. Wasilkowski",
title = "On adaptive information with varying cardinality for
linear problems with elliptically contoured measures",
journal = j-J-COMPLEXITY,
volume = "5",
number = "3",
pages = "363--368",
month = sep,
year = "1989",
CODEN = "JOCOEH",
ISSN = "0885-064X (print), 1090-2708 (electronic)",
ISSN-L = "0885-064X",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Kentucky, Lexington, KY",
bibno = "68756",
catcode = "G.1.2; G.1.2; F.1.3",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.2 Approximation; G.1.2 Nonlinear
approximation; F.1.3 Complexity Classes",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Nonlinear approximation; Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Classes",
fjournal = "Journal of complexity",
genterm = "algorithms; theory",
guideno = "1989-08045",
journal-URL = "http://www.sciencedirect.com/science/journal/0885064X",
journalabbrev = "J. Complexity",
jrldate = "Sept. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
Theory of Computation; F.1 COMPUTATION BY ABSTRACT
DEVICES",
}
@Article{Weniger:1989:NST,
author = "Ernst Joachim Weniger",
title = "Nonlinear sequence transformations for the
acceleration of convergence and the summation of
divergent series",
journal = j-COMPUT-PHYS-REP,
volume = "10",
number = "5--6",
pages = "189--371",
month = dec,
year = "1989",
CODEN = "CPHREF",
DOI = "https://doi.org/10.1016/0167-7977(89)90011-7",
ISSN = "0167-7977 (print), 1878-1004 (electronic)",
ISSN-L = "0167-7977",
bibdate = "Thu Dec 01 10:13:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Available as math.NA/0306302.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Reports",
keywords = "convergence acceleration",
}
@Article{Yortsos:1989:LSI,
author = "Y. C. Yortsos and F. J. Hickernell",
title = "Linear stability of immiscible displacement in porous
media",
journal = j-SIAM-J-APPL-MATH,
volume = "49",
number = "3",
pages = "730--748",
month = jun,
year = "1989",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "64942",
catcode = "G.1.8; G.1.0; J.2; G.1.2; G.1.4; G.1.8",
CRclass = "G.1.8 Partial Differential Equations; G.1.8 Parabolic
equations; G.1.0 General; G.1.0 Stability (and
instability); J.2 Earth and atmospheric sciences; G.1.2
Approximation; G.1.2 Elementary function approximation;
G.1.4 Quadrature and Numerical Differentiation; G.1.4
Finite difference methods; G.1.8 Partial Differential
Equations; G.1.8 Difference methods",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations, Parabolic equations;
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Stability (and instability); Computer Applications,
PHYSICAL SCIENCES AND ENGINEERING, Earth and
atmospheric sciences; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation,
Finite difference methods; Mathematics of Computing,
NUMERICAL ANALYSIS, Partial Differential Equations,
Difference methods",
fjournal = "SIAM Journal on Applied Mathematics",
genterm = "algorithms; theory; experimentation",
guideno = "1989-09711",
journal-URL = "http://epubs.siam.org/siap",
journalabbrev = "SIAM J. Appl. Math.",
jrldate = "June 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING",
}
@Article{Zalik:1989:NIE,
author = "R. A. Zalik",
title = "A new inequality for entire functions",
journal = j-J-APPROX-THEORY,
volume = "58",
number = "3",
pages = "281--283",
month = sep,
year = "1989",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
bibno = "72294",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
fjournal = "Journal of Approximation Theory",
genterm = "verification; theory",
guideno = "1989-07871",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
journalabbrev = "J. Approx. Theory",
jrldate = "Sept. 1989",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Book{Ziemer:1989:WDF,
author = "William P. Ziemer",
title = "Weakly differentiable functions: {Sobolev} spaces and
functions of bounded variation",
volume = "120",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 308",
year = "1989",
ISBN = "0-387-97017-7",
ISBN-13 = "978-0-387-97017-2",
LCCN = "QA323 .Z53 1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Graduate texts in mathematics",
acknowledgement = ack-nhfb,
affiliation = "Indiana Univ., Bloomington",
bibno = "69369",
catcode = "G.1.2; G.1.8; G.1.5",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.8 Partial Differential Equations;
G.1.5 Roots of Nonlinear Equations",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations; Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations",
genterm = "algorithms; theory",
guideno = "1989-01732",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Amos:1990:RPP,
author = "Donald E. Amos",
title = "Remark on ``{Algorithm 644}: a Portable Package for
{Bessel} Functions of a Complex Argument and
Nonnegative Order''",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "404--404",
month = dec,
year = "1990",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/98267.98299",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 09 10:26:24 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; theory",
subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems.",
}
@Article{Anderson:1990:FIC,
author = "G. D. Anderson and M. K. Vamanamurthy and M.
Vuorinen",
title = "Functional Inequalities for Complete Elliptic
Integrals and Their Ratios",
journal = j-SIAM-J-MATH-ANA,
volume = "21",
number = "2",
pages = "536--549",
month = mar,
year = "1990",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33E05 (30C62 33C75)",
MRnumber = "91d:33039",
MRreviewer = "K. C. Gupta",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Bellalij:1990:SPC,
author = "M. Bellalij",
title = "A simultaneous process for convergence acceleration
and error control",
journal = j-J-COMPUT-APPL-MATH,
volume = "33",
number = "2",
pages = "217--231",
day = "21",
month = dec,
year = "1990",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(90)90370-F",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65B99 (65G10)",
MRnumber = "1090897 (92a:65029)",
MRreviewer = "Thomas A. Atchison",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "convergence acceleration",
}
@Article{Bronstein:1990:IEF,
author = "Manuel Bronstein",
title = "Integration of elementary functions",
journal = j-J-SYMBOLIC-COMP,
volume = "9",
number = "2",
pages = "117--173",
month = feb,
year = "1990",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "12H05 (68Q40)",
MRnumber = "91h:12017",
MRreviewer = "Alexandru Buium",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Theory/cathode.bib",
acknowledgement = ack-nhfb,
classcodes = "C1120 (Analysis); C4160 (Numerical integration and
differentiation)",
corpsource = "Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson
Res. Center, Yorktown Heights, NY, USA",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "algebraic extension; algebraic function; decision
procedure; elementary function field; elementary
functions; exponential; finite terms; indefinite;
integration; integration Risch ODEs oderef; logarithm;
proof; Trager",
treatment = "T Theoretical or Mathematical",
}
@Article{Carre:1990:PEF,
author = "C. Carre",
title = "Plethysm of elementary functions",
journal = "Bayreuth. Math. Schr.",
volume = "31",
pages = "1--18",
year = "1990",
ISSN = "0172-1062",
MRclass = "20C30 (05E05 22E45)",
MRnumber = "91f:20013",
MRreviewer = "John R. Stembridge",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ciminiera:1990:HRS,
author = "L. Ciminiera and P. Montuschi",
title = "Higher radix square rooting",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "10",
pages = "1220--1231",
month = oct,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.59853",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A general discussion on nonrestoring square root
algorithms is presented, showing bounds and constraints
delimiting the space of feasible algorithms, for all
the choices of radix, digit set and representation of
the partial remainder. Two classes of \ldots{}",
}
@Article{Cody:1990:PEP,
author = "W. J. Cody",
title = "Performance Evaluation of Programs for the Error and
Complementary Error Functions",
journal = j-TOMS,
volume = "16",
number = "1",
pages = "29--37",
month = mar,
year = "1990",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/77626.77628",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65-04 (65G05)",
MRnumber = "1 073 407",
bibdate = "Tue Oct 09 09:29:47 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/;
http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html",
abstract = "This paper presents methods for performance evaluation
of computer programs for the functions $ \textrm
{erf}(x) $, $ \textrm {erfc}(x) $, and $ \e^{x^2}
\textrm {erfc}(x) $. Accuracy estimates are based on
comparisons using power series expansions and an
expansion in the repeated integrals of $ \textrm
{erfc}(x) $. Some suggestions for checking robustness
are also given. Details of a specific implementation of
a test program are included.",
acknowledgement = ack-nhfb,
affiliation = "Argonne Nat. Lab., IL, USA",
classification = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Complementary error functions; Computer programs;
FORTRAN; Power series expansions; Repeated integrals;
Robustness; Test program",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
thesaurus = "Error analysis; Function approximation; Performance
evaluation",
}
@TechReport{DiDonato:1990:SDC,
author = "Armido R. DiDonato",
title = "Significant Digit Computation of the Elliptical
Coverage Function",
type = "Technical Report",
number = "NAVSWC TR 90-513",
institution = "Naval Surface Warfare Center",
address = "Dahlgren, VA 22448-5000, USA and Silver Spring, MD
20903-5000, USA",
pages = "v + 13 + A-7 + B-9 + 5",
month = sep,
year = "1990",
bibdate = "Sat Nov 15 10:55:35 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.dtic.mil/dtic/tr/fulltext/u2/a230523.pdf",
acknowledgement = ack-nhfb,
}
@Article{Dunham:1990:FPF,
author = "C. B. Dunham",
title = "Feasibility of ``perfect'' function evaluation",
journal = j-SIGNUM,
volume = "25",
number = "4",
pages = "25--26",
month = oct,
year = "1990",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/122272.122276",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:19 MDT 2005",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Dvorak:1990:NCI,
author = "Steven L. Dvorak and Edward F. Kuester",
title = "Numerical computation of the incomplete
{Lipschitz--Hankel} integral {$ {\rm Je}_0 (a, z) $}",
journal = j-J-COMPUT-PHYS,
volume = "87",
number = "2",
pages = "301--327",
month = apr,
year = "1990",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(90)90255-Y",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:40 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199919090255Y",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Ercegovac:1990:RSR,
author = "M. D. Ercegovac and T. Lang",
title = "Radix-$4$ square root without initial {PLA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1016--1024",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57040",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Germain-Bonne:1990:CAN,
author = "B. Germain-Bonne",
title = "Convergence acceleration of number-machine sequences",
journal = j-J-COMPUT-APPL-MATH,
volume = "32",
number = "1--2",
pages = "83--88",
day = "26",
month = nov,
year = "1990",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(90)90419-Z",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65B05",
MRnumber = "1091778 (91m:65007)",
MRreviewer = "W. Govaerts",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Extrapolation and rational approximation (Luminy,
1989)",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "convergence acceleration",
}
@Article{Hashemian:1990:SRA,
author = "R. Hashemian",
title = "Square Rooting Algorithms for Integer and
Floating-Point Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-39",
number = "8",
pages = "1025--1029",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57041",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "An algorithm for evaluating the square root of
integers and real numbers is developed. The procedure
consists of two parts: one to obtain a close estimate
of the square root and the other to modify the initial
value, iteratively, until a precise root is evaluated.
The major effort in this development has been
concentrated on two objectives: high speed and no
division operation other than division by 2. The first
objective is achieved through a simple two-step
procedure for getting the first estimate, and then
modifying it by employing a fast converging iteration
technique. The second objective is also fulfilled
through applying bit-shift operation rather than
division operation. The algorithm is simulated for both
integer and real numbers, and the results are compared
to two methods being widely used. The results
(tabulated) show considerable improvement in speed
compared to these other two methods.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Dept. of Electr. Eng., Northern Illinois Univ.,
Dekalb, IL, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C5230
(Digital arithmetic methods)",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Bit-shift operation; Close estimate; Division by 2;
Fast converging iteration; Floating-point numbers;
Initial value modification; Integer numbers; Precise
root; Real numbers; Square rooting algorithms",
summary = "An algorithm for evaluating the square root of
integers and real numbers is developed. The procedure
consists of two parts: one to obtain a close estimate
of the square root and the other to modify the initial
value, iteratively, until a precise \ldots{}",
thesaurus = "Digital arithmetic; Iterative methods; Number theory",
}
@MastersThesis{Holton:1990:IJE,
author = "P. G. W. Holton",
title = "An Introduction to the {Jacobian} Elliptic Functions
with some Applications",
type = "Thesis (M.Sc.)",
school = "University of Newcastle upon Tyne",
address = "Newcastle upon Tyne, UK",
pages = "117",
year = "1990",
LCCN = "????",
bibdate = "Wed Mar 15 06:50:49 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ifantis:1990:DIP,
author = "E. K. Ifantis and P. D. Siafarikas",
title = "Differential inequalities for the positive zeros of
{Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "30",
number = "2",
pages = "139--143",
day = "28",
month = may,
year = "1990",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:45 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279090022R",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Kiernan:1990:FAE,
author = "J. M. Kiernan and T. B. Blachowiak",
title = "Fast, Accurate Elementary Functions For the {Cray
Y-MP} Computer",
crossref = "Cray:1990:PCU",
pages = "243--252",
year = "1990",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Kolbig:1990:BRC,
author = "K. S. K{\"o}lbig",
title = "Book Review: {{\booktitle{Computation of Functions on
Electronic Computers --- Handbook}} (in Russian).
Naukova Dumka, Kiev, 194, 599pp, by B. A. Popov, G. S.
Tesler}",
journal = j-MATH-COMPUT,
volume = "55",
number = "191",
pages = "395--397",
month = jul,
year = "1990",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008818",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Jan 24 08:35:37 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.jstor.org/stable/2008818",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Koren:1990:EEF,
author = "I. Koren and O. Zinaty",
title = "Evaluating Elementary Functions in a Numerical
Coprocessor Based on Rational Approximations",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-39",
number = "8",
pages = "1030--1037",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57042",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lentz:1990:CFC,
author = "William J. Lentz",
title = "Continued fraction calculation of spherical {Bessel}
functions",
journal = j-COMPUT-PHYS,
volume = "4",
number = "4",
pages = "403--407",
month = jul,
year = "1990",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.168382",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
MRnumber = "33C10 30B70 65-04",
bibdate = "Wed Mar 22 14:36:46 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.168382",
ZMnumber = "0703.33001",
abstract = "An efficient new method of calculating spherical
Bessel functions of complex argument based on continued
fractions is developed. The method does not depend on
recurrence relations, and it allows accurate
calculations on computers with differing word lengths.
The method may be easily extended to other types of
Bessel functions and to complex orders.",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys.",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Levrie:1990:CAN,
author = "Paul Levrie and Adhemar Bultheel",
title = "Convergence Acceleration for the Numerical Solution of
Second-Order Linear Recurrence Relations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "1",
pages = "166--177",
month = feb,
year = "1990",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65Q05 (40A15 65B99)",
MRnumber = "91a:65244",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "convergence acceleration",
}
@Article{Lin:1990:MSL,
author = "Jinn Tyan Lin",
title = "Miscellanea: a Simpler Logistic Approximation to the
Normal Tail Probability and its Inverse",
journal = j-APPL-STAT,
volume = "39",
number = "2",
pages = "255--257",
year = "1990",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
MRclass = "62E15",
MRnumber = "1 060 209",
bibdate = "Sat Apr 21 10:25:45 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/as1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@Article{Magnus:1990:CFL,
author = "Arne Magnus and John McCabe",
title = "On a continued fraction for $ \log^2_e(1 + x) $",
journal = j-J-COMPUT-APPL-MATH,
volume = "30",
number = "1",
pages = "81--86",
day = "10",
month = apr,
year = "1990",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:45 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279090007M",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Markstein:1990:CEF,
author = "P. W. Markstein",
title = "Computation of elementary functions on the {IBM RISC
System\slash 6000} processor",
journal = j-IBM-JRD,
volume = "34",
number = "1",
pages = "111--119",
month = jan,
year = "1990",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65-04 (65D20)",
MRnumber = "1 057 659",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The additional speed and precision of the IBM RISC
System\slash 6000 floating-point unit have motivated
reexamination of algorithms to perform division, square
root, and the elementary functions. New results are
obtained which avoid the necessity of doing special
testing to get the last bit rounded correctly in
accordance with all of the IEEE rounding modes in the
case of division and square root. For the elementary
function library, a technique is described for always
getting the last bit rounded correctly in the selected
IEEE rounding mode.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "Division; Elementary functions; Floating-point unit;
IBM RISC System\slash 6000 processor; IEEE rounding
modes; IEEE rounding modes, IBM RISC System/6000
processor; Square root",
thesaurus = "Digital arithmetic; IBM computers; Reduced instruction
set computing",
}
@Article{Matos:1990:CAM,
author = "Ana C. Matos",
title = "A convergence acceleration method based on a good
estimation of the absolute value of the error",
journal = j-IMA-J-NUMER-ANAL,
volume = "10",
number = "2",
pages = "243--251",
year = "1990",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65B99",
MRnumber = "91m:65010",
MRreviewer = "K. B{\"o}hmer",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "convergence acceleration",
}
@InProceedings{Matula:1990:HPD,
author = "D. Matula",
title = "Highly parallel divide and square root algorithms for
a new generation floating point processor",
crossref = "Ullrich:1990:CCA",
pages = "??--??",
year = "1990",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{McConnell:1990:LEP,
author = "C. R. McConnell",
title = "Letter to the {Editor}: Pocket computer approximation
for areas under the standard normal curve",
journal = j-AMER-STAT,
volume = "44",
number = "1",
pages = "63--63",
month = feb,
year = "1990",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Sat Dec 16 17:19:37 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2684963",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Montuschi:1990:SSR,
author = "P. Montuschi and P. M. Mezzalama",
title = "Survey of square rooting algorithms",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "137",
number = "1",
pages = "31--40",
month = jan,
year = "1990",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
summary = "The paper reviews the algorithms for the computation
of square roots for binary machines. After an initial
classification, the algorithms are analysed in detail
by considering their specific peculiarities and
properties. Finally, some comments are \ldots{}",
}
@InCollection{Mora:1990:EFI,
author = "Gerardo Mora and Edwin Castro and Ioan Muntean",
booktitle = "Mathematics in Costa Rica, Vol. 1 (Spanish) (San
Jos{\'e}, 1990)",
title = "Elementary functions. {I}. ({Spanish})",
publisher = "Univ. Costa Rica",
address = "San Jos{\'e}, Costa Rica",
pages = "76--86",
year = "1990",
MRclass = "26A09",
MRnumber = "1 111 714",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Spanish",
}
@TechReport{Morris:1990:NLM,
author = "Alfred H. {Morris, Jr.}",
title = "{NSWC} Library of Mathematics Subroutines",
type = "Report",
number = "NSWC TR 90-21",
institution = "Naval Surface Warfare Center",
address = "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
20903-5000, USA",
pages = "xii + 492 + 9",
month = jan,
year = "1990",
bibdate = "Tue Jun 13 08:47:19 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
note = "See also later edition \cite{Morris:1993:NLM}.",
URL = "https://apps.dtic.mil/sti/citations/ADA476840;
https://apps.dtic.mil/sti/pdfs/ADA476840.pdf;
https://people.math.sc.edu/Burkardt/f_src/nswc/nswc.f90;
https://people.math.sc.edu/Burkardt/f_src/nswc/nswc.html",
abstract = "The NSWC library is a library of general-purpose
Fortran subroutines that provide a basic computational
capability in a variety of mathematical activities and
emphasis has been placed on the transportability of the
codes. Subroutines are available in the following areas
Elementary Operations, Geometry, Special Functions,
Polynomials, Vectors, Matrices, Large Dense Systems of
Linear Equations, Banded Matrices, Sparse Matrices,
Eigenvalues and Eigenvectors, Solution of Linear
Equations, Least-Squares Solution of Linear Equations,
Optimization, Transforms, Approximation of Functions,
Curve Fitting, Surface Fitting, Manifold Fitting,
Numerical Integration, Integral Equations,
Ordinary--Differential Equations, Partial Differential
Equations, and Random Number Generation.",
acknowledgement = ack-nhfb,
remark = "The single Fortran 90 file of 99,021 nonblank lines
compiles into a library of 905 distinct functions and
subroutines: the source code appears to contain 139
functions and 762 subroutines (901 total entry
points).
The tableofcontents values in this entry is derived
from optical character recognition (OCR) of the 8-page
listing from the PDF files, with editorial correction
of spelling and OCR errors, and matching of uppercase
software names against the entry points of the compiled
library. There are about five names in the PDF table of
contents that disagree with subroutine names in the
source code: they have been edited here to reflect the
correct code names. There are numerous routine names in
the compiled library that are not mentioned in the
table of contents.",
tableofcontents = "Introduction / 1 \\
\\
Elementary Operations \\
\\
Machine Constants --- SPMPAR, DPMPAR, IPMPAR / 3 \\
Sorting Lists --- ISHELL, SHELL, AORD, RISORT, SHELL2,
DSORT, DAORD, DISORT, DDSORT / 5 \\
Cube Root --- CBRT, DCBRT / 7 \\
Four Quadrant Arctangent --- ARTNQ, DARTNQ / 7 \\
Length of a Two-Dimensional Vector --- CPABS, DCPABS /
7 \\
Reciprocal of a Complex Number --- CREC, DCREC / 9 \\
Square Root of a Double Precision Complex Number ---
DCSQRT / 9 \\
Conversion of Polar to Cartesian Coordinates --- POCA /
11 \\
Conversion of Cartesian to Polar Coordinates --- CAPO /
11 \\
Rotation of Axes --- ROTA / 11 \\
Planar Givens Rotations --- SROTG, DROTG / 13 \\
Three Dimensional Rotations --- ROT3 / 15 \\
Rotation of a Point on the Unit Sphere to the North
Pole --- CONSTR / 17 \\
Hyperbolic Sine and Cosine Functions --- SNHCSH / 19
\\
Exponentials --- REXP, DREXP / 21 \\
Logarithms --- ALNREL, RLOG, RLOG1, DLNREL, DRLOG,
DRLOG1 / 23 \\
\\
Geometry \\
\\
Determining if a Point is Inside or Outside a Polygon
--- LOCPT / 25 \\
The Convex Hull for a Finite Planar Set --- HULL / 27
\\
Areas of Planar Polygons --- PAREA / 29 \\
Hamiltonian Circuits --- HC / 31 \\
\\
Special Functions \\
\\
Error Function --- CERF, CERFC, ERF, ERFC, ERFC1,
DCERF, DCERFC, DERF, DERFC, DERFC1 / 35 \\
Inverse Error Function --- ERFINV / 41 \\
Normal Probability Distribution Function --- PNDF / 43
\\
Inverse Normal Probability Distribution Function ---
PNINV / 45 \\
Dawson's Integral --- DAWSON / 47 \\
Complex Fresnel Integral --- CFRNLI / 49 \\
Real Fresnel Integrals --- FRESNEL / 51 \\
Exponential Integral Function --- CEXPLI, EXPLI, DEI,
DEI1 / 53 \\
Sine and Cosine Integral Functions --- SI, CIN / 57 \\
Dilogarithm Function --- CLI, ALI / 59 \\
Gamma Function --- CGAMMA, GAMMA, GAMLN, DCGAMA,
DGAMMA, DGAMLN / 61 \\
Diganma Function --- CPSI, PSI, DCPSI, DPSI / 65 \\
Logarithm of the Beta Function --- BETALN, DBETLN / 67
\\
Incomplete Gamma Ratio Functions --- GRATIO, RCOMP / 69
\\
Inverse Incomplete Gamma Ratio Function --- GAMINV / 71
\\
Incomplete Beta Function --- BRATIO, ISUBX, BRCOMP / 73
\\
Bessel Function $J_\nu(z)$ --- CBSSLJ, BSSLJ, BESJ / 75
\\
Bessel Function $Y_\nu(z)$ --- BSSLY / 77 \\
Modified Bessel Function $I_\nu(z)$ --- BSSLI, BESI /
79 \\
Modified Bessel Function $K_\nu(z)$ --- CBSSLK, BSSLK /
81 \\
Airy functions --- CAI, CBI, AI, AIE, BI, BIE / 83 \\
Complete Complex Elliptic Integrals of the First and
Second Kinds --- CK, CKE / 87 \\
Real Elliptic Integrals of the First and Second Kinds
--- ELLPI, RFVAL, RDVAL, DELLPI, DRFVAL, DRDVAL / 91
\\
Real Elliptic Integrals of the Third Kind --- EPI,
RJVAL, DEPI, DRJVAL / 95 \\
Jacobian Elliptic Functions --- ELLPF, ELPFC1 / 99 \\
Weierstrass Elliptic Function for the Equianharmonic
and Lemniscatic Cases --- PEQ, PEQ1, PLEM, PLEM1 / 103
\\
Integral of the Bivariate Density Function over
Arbitrary Polygons and Semi-infinite Angular Regions
--- VALR2 / 107 \\
Circular Coverage Function --- CIRCV / 109 \\
Elliptical Coverage Function --- PKILL, PKILL3 / 111
\\
\\
Polynomials \\
\\
Copying Polynomials --- PLCOPY, DPCOPY / 113 \\
Addition of Polynomials --- PADD, DPADD / 115 \\
Subtraction of Polynomials --- PSUBT, DPSUBT / 117 \\
Multiplication of Polynomials --- PMULT, DPMULT / 119
\\
Division of Polynomials --- PDIV, DPDIV / 121 \\
Real Powers of Polynomials --- PLPWR, DPLPWR / 123 \\
Inverses of Power Series --- PINV, DPINV / 125 \\
Derivatives and Integrals of Polynomials --- MPLNMV /
127 \\
Evaluation of Chebyshev Expansions --- CSEVL, DCSEVL /
129 \\
Lagrange Polynomials --- LGRNGN, LGRNGV, LGRNGX / 131
\\
Orthogonal Polynomials on Finite Sets --- ORTHOS,
ORTHOV, ORTHOX / 133 \\
\\
Solutions of Nonlinear Equations \\
\\
Zeros of Continuous Functions --- ZEROIN / 135 \\
Solution, of Systems of Nonlinear Equations --- HBRD /
137 \\
Solutions of Quadratic, Cubic, and Quartic Equations
--- QDCRT, CBCRT, QTCRT, DQDCRT, DCBCRT, DQTCRT / 139
\\
Double Precision Roots of Polynomials --- DRPOLY,
DCPOLY / 141 \\
Accuracy of the Roots of a Real Polynomial --- RBND /
143 \\
\\
Vectors \\
\\
Copying Vectors --- SCOPY, DCOPY, CCOPY / 145 \\
Interchanging Vectors --- SSWAP, DSWAP, CSWAP / 147 \\
Planar Rotation of Vectors --- SROT, DROT, CSROT / 149
\\
Dot Products of Vectors --- SDOT, DDOT, CDOTC, CDOTU /
151 \\
Scaling Vectors --- SSCAL, DSCAL, CSCAL, CSSCAL / 153
\\
Vector Addition --- SAXPY, DAXPY, CAXPY / 155 \\
$L_1$ Norm of a Vector-- SASUM, DASUM, SCASUM / 157 \\
$L_2$ Norm of a Vector --- SNRM2, DNRM2, SCNRM2 / 159
\\
$L_\infty$ Norm of a Vector --- ISAMAX, IDAMAX, ICAMAX
/ 161 \\
\\
Matrices \\
\\
Packing and Unpacking Symmetric Matrices --- MCVFS,
DMCVFS, MCVSF, DMCVSF / 163 \\
Conversion of Real Matrices to and from Double
Precision Form --- MCVRD, MCVDR / 165 \\
Storage of Real Matrices in the Complex Matrix Format
--- MCVRC / 167 \\
The Real and Imaginary Parts of a Complex Matrix ---
CMREAL, CMIMAG / 169 \\
Copying Matrices --- MCOPY, SMCOPY, DMCOPY, CMCOPY /
171 \\
Computation of the Conjugate of a Complex Matrix ---
CMCONJ / 173 \\
Transposing Matrices --- TPOSE, DTPOSE, CTPOSE, TIP,
DTIP, CTIP / 175 \\
Computing Adjoints of Complex Matrices --- CMADJ,
CTRANS / 177 \\
Matrix Addition --- MADD, SMADD, DMADD, CMADD / 179 \\
Matrix Subtraction --- MSUBT, SMSUBT, DMSUBT, CMSUBT /
181 \\
Matrix Multiplication-- MTMS, DMTMS, CMTMS, MPROD,
DMPROD, CMPROD / 183 \\
Product of a Packed Symmetric Matrix and a Vector ---
SVPRD, DSVPRD / 185 \\
Transpose Matrix Products --- TMPROD / 187 \\
Symmetric Matrix Products --- SMPROD / 189 \\
Kronecker Product of Matrices --- KPROD, DKPROD, CKPROD
/ 191 \\
Inverting General Real Matrices and Solving General
Systems of Real Linear Equations --- CROUT, KROUT,
NPIVOT, MSLV, DSMSLV / 193 \\
Solutions of Real Equations with Iterative Improvement
--- SLVMP / 197 \\
Solution of Almost Block Diagonal Systems of Linear
Equations --- ARCECO, ARCESL / 199 \\
Solution of Almost Block Tridiagonal Systems of Linear
Equations --- BTSLV / 201 \\
Inverting Symmetric Real Matrices and Solving Symmetric
Systems of Real Linear Equations --- SMSLV, DSMSLV /
203 \\
Inverting Positive Definite Symmetric Matrices and
Solving Positive Definite Symmetric Systems of Linear
Equations --- PCHOL, DPCHOL / 207 \\
Solution of Toeplitz Systems of Linear Equations ---
TOPLX, DTOPLX / 209 \\
Inverting General Complex Matrices and Solving General
Systems of Complex Linear Equations --- CMSLV, CMSLV1,
DCMSLV / 211 \\
Solution of Complex Equations with Iterative
Improvement --- CSLVMP / 215 \\
Singular Value Decomposition of a Matrix --- SSVDC,
DSVDC, CSVDC / 217 \\
Evaluation of the Characteristic Polynomial of a Matrix
--- DET, DPDET, CDET / 219 \\
Solution of the Matrix Equation $A X + X B = C$ ---
ABSLV, DABSLV / 221 \\
Solution of the Matrix Equation $A^t X + X B = C$ when
$C$ is Symmetric --- TASLV, DTASLV / 223 \\
Solution of the Matrix Equation $A X^2 + X B + C = 0$
--- SQUINT / 225 \\
Exponential of a Real Matrix --- MEXP, DMEXP / 227 \\
\\
Large Dense Systems of Linear Equations \\
\\
Solving systems of 200--400 Linear Equations --- LE,
DPLE, CLE / 229 \\
\\
Banded Matrices \\
\\
Band Matrix Storage / 231 \\
Conversion of Banded Matrices to and from the Standard
Format --- CVBR, CVBC, CVRB, CVCB, CVRB1, CVCB1 / 233
\\
Conversion of Banded Matrices to and from Sparse Form
--- MCVBS, CMCVBS, MCVSB, CMCVSB / 235 \\
Transposing Banded Matrices --- BPOSE, CBPOSE / 237 \\
Addition of Banded Matrices --- BADD, CBADD / 239 \\
Subtraction of Banded Matrices --- BSUBT, CBSUBT / 241
\\
Multiplication of Banded Matrices --- BPROD, CBPROD /
243 \\
Product of a Real Banded Matrix and Vector --- BVPRD,
BVPRD1, BTPRD, BTPRD1 / 245 \\
Product of a Complex Banded Matrix and Vector ---
CBVPD, CBVPD1, CBTPD, CBTPD1 / 247 \\
Solution of Banded Systems of Real Linear Equations ---
BSLV, BSLV1 / 249 \\
Solution of Banded Systems of Complex Linear Equations
--- CBSLV, CBSLV1 / 251 \\
\\
Sparse Matrices \\
\\
Storage of Sparse Matrices / 253 \\
Conversion of Sparse Matrices to and from the Standard
Format --- CVRS, CVDS, CVCS, CVSR, CVSD, CVSC / 255 \\
Conversion of Sparse Real Matrices to and from Double
Precision Form --- SCVRD, SCVDR / 257 \\
The Real and Imaginary Parts of a Sparse Complex Matrix
--- CSREAL, CSIMAG / 259 \\
\\
Computing $A + i D$ for Sparse Real Matrices $A$ and
$B$ --- SCVRC / 261 \\
Copying Sparse Matrices --- RSCOPY, DSCOPY, CSCOPY /
263 \\
Computing Conjugates of Sparse Complex Matrices ---
SCONJ / 265 \\
Transposing Sparse Real Matrices --- RPOSE, RPOSE1 /
267 \\
Transposing Sparse Double Precision Matrices --- DPOSE,
DPOSE1 / 269 \\
Transposing Sparse Complex Matrices --- CPOSE, CPOSE1 /
271 \\
Addition of Sparse Matrices --- SADD, DSADD, CSADD /
273 \\
Subtraction of Sparse Matrices --- SSUBT, DSSUBT,
CSSUBT / 275 \\
Multiplication of Sparse Matrices --- SPROD, DSPROD,
CSPROD / 277 \\
Product of a Real Sparse Matrix and Vector --- MVPRD,
MVPRD1, MTPRD, MTPRD1 / 279 \\
Product of a Double Precision Sparse Matrix and Vector
--- DVPRD, DVPRD1, DTPRD, DTPRD1 / 281 \\
Product of a Complex Sparse Matrix and Vector ---
CVPRD, CVPRD1, CTPRD, CTPRD1 / 283 \\
Ordering the Rows of a Sparse Matrix by Increasing
Length --- SPORD / 285 \\
Reordering Sparse Matrices into Block Triangular Form
--- BLKORD / 287 \\
Solution of Sparse Systems of Real Linear Equations ---
SPSLV, RSLV, TSLV / 289 \\
Double Precision Solution of Sparse Systems of Real
Linear Equations --- DSPSLV, DSLV, DTSLV / 293 \\
Solution of Sparse Systems of Complex Linear Equations
--- CSPSLV, CSLV, CTSLV / 297 \\
\\
Eigenvalues and Eigenvectors \\
\\
Computation of Eigenvalues of General Real Matrices ---
EIG, EIG1 / 301 \\
Computation of Eigenvalues and Eigenvectors of General
Real Matrices --- EIGV, EIGV1 / 303 \\
Double Precision Computation of Eigenvalues of Real
Matrices --- DEIG / 305 \\
Double Precision Computation of Eigenvalues and
Eigenvectors of Real Matrices --- DEIGV / 307 \\
Computation of Eigenvalues of Symmetric Real Matrices
--- SEIG, SEIG1 / 309 \\
Computation of Eigenvalues and Eigenvectors of
Symmetric Real Matrices --- SEIGV, SEIGV1 / 311 \\
Computation of Eigenvalues of Complex Matrices --- CEIG
/ 313 \\
Computation of Eigenvalues and Eigenvectors of Complex
Matrices --- CEIGV / 315 \\
Double Precision Computation of Eigenvalues of Complex
Matrices --- DCEIG / 317 \\
Double Precision Computation of Eigenvalues and
Eigenvectors of Complex Matrices --- DCEIGV / 319 \\
\\
$\ell_1$ Solution of Linear Equations \\
\\
$\ell_1$ Solution of Systems of Linear Equations with
Equality and Inequality Constraints --- CL1 / 321 \\
\\
Least Squares Solution of Linear Equations \\
\\
Least Squares Solution of Systems of Linear Equations
--- LLSQ, HFTI, HFTI2 / 323 \\
Least Squares Solution of Overdetermined Systems of
Linear Equations with Iterative Improvement --- LLSQMP
/ 327 \\
Double Precision Least Squares Solution of Systems of
Linear Equations --- DLLSQ, DHFTI, DHFTI2 / 329 \\
Least Squares Solution of Systems of Linear Equations
with Equality and Inequality Constraints --- LSEI / 333
\\
Least Squares Solution of Systems of Linear Equations
with Equality and Nonnegativity Constraints --- WNNLS /
337 \\
Least Squares Iterative Improvement Solution of Systems
of Linear Equations with Equality Constraints --- L2SLV
/ 341 \\
Iterative Least Squares Solution of Banded Linear
Equations --- BLSQ / 345 \\
Iterative Least Squares Solution of Sparse Linear
Equations --- SPLSQ, STLSQ / 347 \\
\\
Optimization \\
\\
Minimization of Functions of a Single Variable --- FMIN
/ 349 \\
Minimization of Functions of n Variables --- OPTF / 351
\\
Unconstrained Minimum of the Sum of Squares of
Nonlinear Functions --- LMDIFF / 353 \\
Linear Programming --- SMPLX, SSPLX / 355 \\
The Assignment Problem --- ASSGN / 359 \\
$0$--$1$ Knapsack Problem --- MKP / 361 \\
\\
Transforms \\
\\
Inversion of the Laplace Transform --- LAINV / 363 \\
Fast Fourier Transform --- FFT, FFT1 / 367 \\
Multivariate Fast Fourier Transform --- MFFT, MFFT1 /
369 \\
Discrete Cosine and Sine Transforms --- COSQI, COSQB,
COSQF, SINQB, SINQF / 371 \\
\\
Approximation of Functions \\
\\
Rational Minimax Approximation of Functions --- CHEBY /
375 \\
$L_p$ Approximation of Functions --- ADAPT / 377 \\
Calculation of the Taylor Series of a Complex Analytic
Function --- CPSC, DCPSC / 381 \\
\\
Curve Fitting \\
\\
Linear Interpolation --- TRP / 385 \\
Lagrange Interpolation --- LTRP / 387 \\
Hermite Interpolation --- HTRP / 389 \\
Conversion of Real Polynomials from Newton to Taylor
Series Form --- PCOEFF / 391 \\
Least Squares Polynomial Fit --- PFIT / 393 \\
Weighted Least Squares Polynomial Fit --- WPFIT / 395
\\
Cubic Spline Interpolation --- CBSPL, SPLIFT / 397 \\
Weighted Least Squares Cubic Spline Fitting --- SPFIT /
399 \\
Cubic Spline Evaluation --- SCOMP, SCOMP1, SCOMP2 / 401
\\
Cubic Spline Evaluation and Differentiation --- SEVAL,
SEVAL1, SEVAL2 / 403 \\
Integrals of Cubic Splines --- CSINT, CSINT1, CSINT2 /
405 \\
N-Dimensional Cubic Spline Closed Curve Fitting ---
CSLOOP, LOPCMP, LOPDF / 407 \\
Spline under Tension Interpolation --- CURV1 / 409 \\
Spline under Tension Evaluation --- CURV2 / 411 \\
Differentiation and Integration of Splines under
Tension --- CURVD, CURVI / 413 \\
Two Dimensional Spline under Tension Curve Fitting ---
KURV1, KURV2 / 415 \\
Two Dimensional Spline under Tension Closed Curve
Fitting --- KURVP1, KURVP2 / 417 \\
Three Dimensional Spline under Tension Curve Fitting
--- QURV1, QURV2 / 419 \\
B-Splines / 421 \\
Piecewise Polynomial Interpolation --- BSTRP / 423 \\
Conversion of Piecewise Polynomials from B-Spline to
Taylor Series Form --- BSPP / 425 \\
Piecewise Polynomial Evaluation --- PPVAL / 427 \\
Weighted Least Squares Piecewise Polynomial Fitting ---
BSL2 / 429 \\
\\
Surface Fitting over Rectangular Grids \\
\\
Bi-Splines under Tension / 431 \\
Bi-Spline under Tension Surface Interpolation --- SURF
/ 433 \\
Bi-Spline under Tension Evaluation --- SURF2, NSURF2 /
435 \\
\\
Surface Fitting over Arbitrarily Positioned Data Points
\\
\\
Surface Interpolation for Arbitrarily Positioned Data
Points --- BVIP, BVIP2 / 437 \\
\\
Manifold Fitting \\
\\
Weighted Least Squares Fitting with Polynomials of $n$
Variables --- MFIT, DMFIT, MEVAL, DMEVAL / 441 \\
\\
Numerical Integration \\
\\
Evaluation of Integrals over Finite Intervals --- QAGS,
QSUBA, DQAGS / 445 \\
\\
Evaluation of Integrals over Infinite Intervals ---
QAGI, DQAGI / 449 \\
Evaluation of Double Integrals over Triangles ---
CUBTRI / 453 \\
\\
Integral Equations \\
\\
Solution of Fredholm Integral Equations of the Second
Kind --- IESLV / 455 \\
\\
Ordinary Differential Equations/Initial Value Problems
\\
\\
The Initial Value Solvers --- Introductory Comments /
459 \\
Adaptive Adams Solution of Nonstiff Differential
Equations --- ODE / 461 \\
Adaptive RKF Solution of Nonstiff Differential
Equations --- RKF45 / 465 \\
Adaptive RKF Solution of Nonstiff Differential
Equations with Global Error Estimation --- GERK / 469
\\
Adaptive Solution of Stiff Differential Equations ---
SFODE, SFODE1 / 473 \\
Fourth-Order Runge-Kutta --- RK / 477 \\
Eighth-Order Runge-Kutta --- RK8 / 479 \\
\\
Partial Differential Equations \\
\\
Separable Second-Order Elliptic Equations on
Rectangular Domains --- SEPDE / 481 \\
\\
Random Number Generation \\
\\
Uniform Random Number Generator --- URNG / 485 \\
Gaussian Random Number Generator using the
Box--M{\"u}ller Transformation --- NRNG / 487 \\
\\
Appendix. Installation of the NSWC Library / 489 \\
\\
Index / 491 \\
\\
Distribution",
}
@MastersThesis{Muller:1990:HCA,
author = "Volker M{\"u}ller",
title = "{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle
Standardfunktionen mittels dynamischer
Defektberechnung} \toenglish {High-accuracy CORDIC
Algorithms for Real Elementary Functions by Means of
Dynamic Error Computation} \endtoenglish",
type = "Diplomarbeit",
school = "Institut f{\"u}r angewandte Mathematik,
Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
month = dec,
year = "1990",
bibdate = "Fri Jun 11 12:38:17 1999",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Osada:1990:CAM,
author = "Naoki Osada",
title = "A Convergence Acceleration Method for Some
Logarithmically Convergent Sequences",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "1",
pages = "178--189",
month = feb,
year = "1990",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0727012",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65B05",
MRnumber = "1034928 (91b:65002)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "convergence acceleration",
}
@Article{Palmore:1990:CAC,
author = "J. Palmore and C. Herring",
title = "Computer arithmetic, chaos and fractals",
journal = j-PHYSICA-D,
volume = "42",
number = "1--3",
pages = "99--110",
month = jun,
year = "1990",
CODEN = "PDNPDT",
DOI = "https://doi.org/10.1016/0167-2789(90)90069-2",
ISSN = "0167-2789 (print), 1872-8022 (electronic)",
ISSN-L = "0167-2789",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Ninth Annual International Conference of the Center
for Nonlinear Studies on Self-Organizing, Collective
and Cooperative Phenomena in Natural and Artificial
Networks",
abstract = "The authors explore aspects of computer arithmetic
from the viewpoint of dynamical systems. They
demonstrate the effects of finite precision arithmetic
in three uniformly hyperbolic chaotic dynamical
systems: Bernoulli shifts, cat maps, and pseudorandom
number generators. They show that elementary
floating-point operations in binary computer arithmetic
possess an inherently fractal structure. Each of these
dynamical systems allows us to compare the exact
results in integer arithmetic with those obtained by
using floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Illinois Univ., Urbana, IL, USA",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
confdate = "22-26 May 1989",
conflocation = "Los Alamos, NM, USA",
fjournal = "Physica. D, Nonlinear phenomena",
journal-URL = "http://www.sciencedirect.com/science/journal/01672789",
keywords = "Bernoulli shifts; Binary computer arithmetic; Cat
maps; Chaos; Computer arithmetic; Dynamical systems;
Elementary floating-point operations; Finite precision
arithmetic; Floating-point arithmetic; Fractal
structure; Integer arithmetic; Pseudorandom number
generators; Self-similar structure; Uniformly
hyperbolic chaotic dynamical systems",
pubcountry = "Netherlands",
thesaurus = "Chaos; Digital arithmetic; Fractals; Random number
generation; Roundoff errors",
}
@Article{Poppe:1990:AEC,
author = "G. P. M. Poppe and C. M. J. Wijers",
title = "{Algorithm 680}: Evaluation of the Complex Error
Function",
journal = j-TOMS,
volume = "16",
number = "1",
pages = "47--47",
month = mar,
year = "1990",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/77626.77630",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "47. 65G05 (65-04)",
MRnumber = "91h:65068b",
bibdate = "Sun Sep 04 23:03:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See remark \cite{Zaghloul:2019:RO}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p47-poppe/",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Rational approximation.",
}
@Article{Poppe:1990:MEC,
author = "G. P. M. Poppe and C. M. J. Wijers",
title = "More Efficient Computation of the Complex Error
Function",
journal = j-TOMS,
volume = "16",
number = "1",
pages = "38--46",
month = mar,
year = "1990",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/77626.77629",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G05 (65D20)",
MRnumber = "91h:65068a",
bibdate = "Sun Sep 04 23:03:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p38-poppe/",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Algorithm analysis. {\bf G.1.2}: Mathematics
of Computing, NUMERICAL ANALYSIS, Approximation,
Rational approximation.",
}
@Article{Press:1990:EI,
author = "William H. Press and Saul A. Teukolsky",
title = "Elliptic Integrals",
journal = j-COMPUT-PHYS,
volume = "4",
number = "1",
pages = "92--??",
month = jan,
year = "1990",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4822893",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:21 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4822893",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Reemtsen:1990:MFR,
author = "Rembert Reemtsen",
title = "Modifications of the First {Remez} Algorithm",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "2",
pages = "507--518",
month = apr,
year = "1990",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0727031",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65D15",
MRnumber = "91a:65039",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Revfeim:1990:LEM,
author = "K. J. A. Revfeim",
title = "Letter to the {Editor}: More approximations for the
cumulative and inverse normal distribution",
journal = j-AMER-STAT,
volume = "44",
number = "1",
pages = "63--63",
month = feb,
year = "1990",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 14:51:19 MST 2012",
bibsource = "http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326447;
https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2684963",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Sedogbo:1990:CAS,
author = "Guy Antoine Sedogbo",
title = "Convergence acceleration of some logarithmic
sequences",
journal = j-J-COMPUT-APPL-MATH,
volume = "32",
number = "1--2",
pages = "253--260",
day = "26",
month = nov,
year = "1990",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(90)90435-3",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65B10 (40A25 65B99)",
MRnumber = "1091794 (91m:65009)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Extrapolation and rational approximation (Luminy,
1989)",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "convergence acceleration",
}
@Book{Swartzlander:1990:CA,
author = "Earl E. Swartzlander",
title = "Computer arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1990",
ISBN = "0-8186-8931-5 (v. 1), 0-8186-5931-9 (v. 1
microfiche)",
ISBN-13 = "978-0-8186-8931-4 (v. 1), 978-0-8186-5931-7 (v. 1
microfiche)",
LCCN = "QA76.6.C633 1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Two volumes.",
series = "IEEE Computer Society Press tutorial",
acknowledgement = ack-nhfb,
annote = "Vol. 1 is a reprint. Originally published:
Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980.
Originally published in series: Benchmark papers in
electrical engineering and computer science; 21. Vol 2
is a sequel to the earlier collection. Vol. 1: 2nd
ed.",
keywords = "Computer arithmetic.; Electronic digital computers ---
Programming.; Floating-point arithmetic.",
tableofcontents = "Arithmetic operations in a binary computer / R. F.
Shaw \\
High-speed arithmetic in binary computers / O. L.
MacSorley \\
Fast carry logic for digital computers / B. Gilchrist,
J. H. Pomerene, and S. Y. Wong \\
A logic for high-speed addition / A. Weinberger and J.
L. Smith \\
Conditional-sum addition logic / J. Sklansky \\
An evaluation of several two-summand binary adders / J.
Sklansky \\
Adder with distributed control / A. Svoboda \\
Multiple addition by residue threshold functions and
their representation by array logic / I. T. Ho and T.
C. Chen \\
Counting responders in an associative memory / C. C.
Foster and F. D. Stockton \\
Parallel counters / E. E. Swartzlander, Jr. \\
A signed binary multiplication technique / A. D. Booth
\\
Multiplying made easy for digital assemblies / C.
Ghest. A binary multiplication scheme based on squaring
/ T. C. Chen \\
A suggestion for a fast multiplier / C. S. Wallace \\
Some schemes for parallel multipliers / L. Dadda \\
On parallel digital multipliers / L. Dadda \\
A compact high-speed parallel multiplication scheme /
W. J. Stenzel, W. J. Kubitz, and G. H. Garcia \\
A two's complement parallel array multiplication
algorithm / C. R. Baugh and B. A. Wooley \\
Comments on ``A two's complement parallel array
multiplication algorithm'' / P. E. Blankenship \\
The quasi-serial multiplier / E. E. Swartzlander, Jr.
\\
The two's complement quasi-serial multiplier / T. G.
McDaneld and R. K. Guha \\
A new class of digital division methods / J. E
Robertson \\
An algorithm for rapid binary division / J. B. Wilson
and R. S. Ledley. Digit-by-digit
transcendental-function computation / R. J. Linhardt
and H. S. Miller \\
A unified algorithm for elementary functions / J. S.
Walther \\
Some properties of iterative square-rooting methods
using high-speed multiplication /C. V. Ramamoorthy, J.
R. Goodman, and K. H. Kim \\
Radix-16 evaluation of certain elementary functions /
M. D. Ercegovac \\
On the distribution of numbers / R. W. Hamming \\
An analysis of floating-point addition / D. W. Sweeney
\\
The IBM\ldots{}Model 91: floating-point execution unit
/ S. F. Anderson \ldots{} [et al.] \\
Design of large high-speed floating-point-arithmetic
units / J. B. Gosling \\
Analysis of rounding methods in floating-point
arithmetic / D. J. Kuck,D. S. Parker, Jr., and A. H.
Sameh. \\
cos x, tan-p1s x, and cot-p1s x / W. H. Specker.",
}
@Article{Tang:1990:AET,
author = "Ping Tak Peter Tang",
title = "Accurate and Efficient Testing of the Exponential and
Logarithm Functions",
journal = j-TOMS,
volume = "16",
number = "3",
pages = "185--200",
month = sep,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65-04 (65G99)",
MRnumber = "1 070 797",
bibdate = "Sun Sep 04 23:14:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/79505.79506;
http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
abstract = "Table-driven techniques can be used to test highly
accurate implementation of EXP LOG. The largest error
observed in EXP and LOG accurately to within 1/500 unit
in the last place are reported in our tests. Methods to
verify the tests' reliability are discussed. Results of
applying the tests to our own as well as to a number of
other implementations of EXP and LOG are presented.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; languages; verification",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Certification and testing. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Portability.",
}
@InProceedings{Tang:1990:FAL,
author = "Ping Tak Peter Tang",
title = "A fast algorithm for linear complex {Chebyshev}
approximation",
crossref = "Mason:1990:AAI",
pages = "265--274",
year = "1990",
bibdate = "Wed Nov 29 14:12:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Tang:1990:PGE,
author = "Ping Tak Peter Tang",
title = "A Portable Generic Elementary Function Package in
{Ada} and an Accurate Test Suite",
type = "Technical report",
number = "ANL-90/35",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "iii + 35",
month = nov,
year = "1990",
bibdate = "Fri Dec 28 11:36:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.osti.gov/bridge/servlets/purl/6310184-4n5sOR/6310184.PDF",
abstract = "A comprehensive set of elementary functions has been
implemented portably in Ada. The high accuracy of the
implementation has been confirmed by rigorous analysis.
Moreover, we present new test methods that are
efficient and offer a high resolution of 0.005 unit in
the last place, Tbese test methods have been
implemented portably here and confirm the accuracy of
our implemented functions. Reports on the accuracy of
other function libraries obtained by our test programs
are also presented.",
acknowledgement = ack-nhfb,
}
@TechReport{Tang:1990:SSI,
author = "Ping Tak Peter Tang",
title = "Some Software Implementations of the Functions Sine
and Cosine",
type = "Technical report",
number = "ANL-90/3",
institution = inst-ANL,
address = inst-ANL:adr,
month = apr,
year = "1990",
bibdate = "Fri Dec 28 11:21:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www-fp.mcs.anl.gov/division/publications/abstracts/abstracts90.htm",
abstract = "This document presents several software
implementations of the elementary functions sin and cos
designed to fit a large class of machines.
Implementation details are provided. Also provided is a
detailed error analysis that bounds the errors of these
implementations, over the full range of input
arguments, from 0.721 to 0.912 units in the last place.
Tests performed on these codes give results that are
consistent with the error bounds.",
acknowledgement = ack-nhfb,
xxnote = "Where is this? I can find no electronic version
online, other than the abstract at the given URL.",
}
@Article{Tang:1990:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Logarithm Function
in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "378--400",
month = dec,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 23:26:09 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/98267.98294;
http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
abstract = "Algorithms and implementation details for the
logarithm functions in both single and double precision
of IEEE 754 arithmetic are presented here. With a table
of moderate size, the implementation need only working-
precision arithmetic and are provably accurate to
within 0.57 ulp.",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; design; performance; reliability;
standardization; theory; verification",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@Article{Todd:1990:WMP,
author = "John Todd",
title = "The {Weierstrass} mean. {I}. The periods of $ \wp (z
\vert e_1, e_2, e_3) $",
journal = j-NUM-MATH,
volume = "57",
number = "8",
pages = "737--746",
month = aug,
year = "1990",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D20 (33E05)",
MRnumber = "91m:65057",
MRreviewer = "Syvert P. N{\o}rsett",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "B0290 (Numerical analysis); C4100 (Numerical
analysis)",
corpsource = "California Inst. of Technol., Pasadena, CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence; elliptic objects; limits; numerical
methods; Weierstrass mean",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Watson:1990:NMC,
author = "G. Alistair Watson",
title = "Numerical methods for {Chebyshev} approximation of
complex-valued functions",
crossref = "Mason:1990:AAI",
pages = "246--264",
year = "1990",
bibdate = "Wed Nov 29 14:09:32 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Wells:1990:LE,
author = "Martin T. Wells and Ram C. Tiwari and I. Arizono and
H. Ohta and James W. Mergerson and Gabriella M. Belli
and Christopher Cox and Murray A. Jorgensen and Jacques
Benichou and Mitchell H. Gail and Warren F. Kuhfeld and
Brian Dawkins and Walter B. Studdiford and Colin
Goodall and W. D. Kaigh and Stephen W. Looney and
Robert Kinnison and James A. Gibbons and Joel R. Levin
and Ronald C. Serlin and K. J. A. Revfeim and Charles
R. McConnell and Robert M. Norton and R. W. Farebrother
and I. J. Good and Stanley Lebergott and Vedula N.
Murty",
title = "Letters to the Editor",
journal = j-AMER-STAT,
volume = "44",
number = "1",
pages = "56--65",
month = feb,
year = "1990",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 14:51:19 MST 2012",
bibsource = "http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326447;
https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2684963",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Weniger:1990:RAM,
author = "Ernst Joachim Weniger and Ji{\v{r}}i
C{\'\i}{\v{z}}ek",
title = "Rational approximations for the modified {Bessel}
function of the second kind",
journal = j-COMP-PHYS-COMM,
volume = "59",
number = "3",
pages = "471--493",
month = jul,
year = "1990",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(90)90089-J",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:29:12 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/001046559090089J",
abstract = "Various different rational approximations for the
modified Bessel function $ K_\nu (z) $ are compared
with respect to their ability of computing $ K_\nu (z)
$ efficiently and reliably in the troublesome region of
moderately large arguments $z$. The starting point for
the construction of the rational approximations is the
asymptotic series $_2 F_0$ for $ K_\nu (z) $, which
diverges for all finite arguments $z$ but is Borel
summable and Stieltjes summable. The numerical tests
showed that Pad{\'e} approximants for $ K_\nu (z) $ are
significantly less efficient than the other rational
approximations which were considered. The best results
were produced by some recently derived sequence
transformations (E. J. Weniger, Comput. Phys. Rep. {\bf
10} (1989) 189), which are closely related to Levin's
sequence transformations (D. Levin, Int. J. Comput.
Math. B {\bf 3} (1973) 371).",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Bartoloni:1991:MFU,
author = "A. Bartoloni and C. Battista and S. Cabasino and N.
Cabibbo and F. Del Prete and F. Marzano and P. S.
Paolucci and R. Sarno and G. Salina and G. M. Todesco
and M. Torelli and R. Tripiccione and W. Tross and E.
Zanetti",
title = "{MAD}, a floating-point unit for massively-parallel
processors",
journal = "Particle World",
volume = "2",
number = "3",
pages = "65--73",
month = "????",
year = "1991",
CODEN = "PARWEG",
ISSN = "1043-6790",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The authors describe in detail the architecture and
implementation of the MAD chip. It is a floating point
unit, used as the elementary processing element of the
APE100 array processor. The design has been accurately
tailored to the requirements of a SIMD floating point
intensive machine.",
acknowledgement = ack-nhfb,
affiliation = "Roma Univ., Italy",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods); C7320 (Physics and
Chemistry)",
keywords = "APE100 array processor; Architecture; Elementary
processing element; Floating-point unit;
Massively-parallel processors; SIMD floating point
intensive machine",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Microprocessor chips; Parallel
architectures; Physics computing",
}
@TechReport{Beebe:1991:ASR,
author = "Nelson H. F. Beebe",
title = "Accurate Square Root Computation",
institution = inst-CSC,
address = inst-CSC:adr,
pages = "23",
day = "4",
month = feb,
year = "1991",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supplemental class notes prepared for Mathematics
118.",
}
@Article{Boersma:1991:UAB,
author = "J. Boersma",
title = "Uniform asymptotics of a {Bessel}-function series
occurring in a transmission-line problem",
journal = j-J-COMPUT-APPL-MATH,
volume = "37",
number = "1--3",
pages = "143--159",
day = "18",
month = nov,
year = "1991",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:02:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279190113X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Bohlender:1991:SEF,
author = "G. Bohlender and W. Walter and P. Kornerup and D. W.
Matula",
title = "Semantics for exact floating point operations",
crossref = "Kornerup:1991:PIS",
bookpages = "xiii + 282",
pages = "22--26",
year = "1991",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE Catalog number 91CH3015-5.",
abstract = "Semantics are given for the four elementary arithmetic
operations and the square root, to characterize what
are termed exact floating point operations. The
operands of the arithmetic operations and the argument
of the square root are all floating point numbers in
one format. In every case, the result is a pair of
floating point numbers in the same format with no
accuracy lost in the computation. These semantics make
it possible to realize the following principle: it
shall be a user option to discard any information in
the result of a floating point arithmetic operation.
The reliability and portability previously associated
with only mathematical software implementations in
integer arithmetic can thus be attained exploiting the
generally higher efficiency of floating point
hardware.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
confdate = "26-28 June 1991",
conflocation = "Grenoble, France",
confsponsor = "IEEE; CNRS; IMAG",
keywords = "Argument; Elementary arithmetic operations; Exact
floating point operations; Floating point arithmetic;
Floating point hardware; Floating point numbers;
Integer arithmetic; Mathematical software; Operands;
Portability; Reliability; Semantics; Square root",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Number theory",
}
@Book{Brezinski:1991:EMT,
author = "Claude Brezinski and Michela {Redivo Zaglia}",
title = "Extrapolation Methods: Theory and Practice",
volume = "2",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "ix + 464",
year = "1991",
ISBN = "0-444-88814-4",
ISBN-13 = "978-0-444-88814-3",
LCCN = "QA281 .B74 1991",
bibdate = "Mon May 24 09:18:52 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
series = "Studies in computational mathematics",
acknowledgement = ack-nhfb,
subject = "extrapolation; data processing",
tableofcontents = "Preface / v \\
1 INTRODUCTION TO THE THEORY / 1 \\
1.1 First steps / 1 \\
1.2 What is an extrapolation method? / 5 \\
1.3 What is an extrapolation algorithm? / 8 \\
1.4 Quasi-linear sequence transformations / 11 \\
1.5 Sequence transformations as ratios of determinants
/ 18 \\
1.6 Triangular recursive schemes / 21 \\
1.7 Normal forms of the algorithms / 26 \\
1.8 Progressive forms of the algorithms / 28 \\
1.9 Particular rules of the algorithms / 34 \\
1.10 Accelerability and non-accelerability / 39 \\
1.11 Optimality / 42 \\
1.12 Asymptotic behaviour of sequences / 47 \\
\\
2 SCALAR EXTRAPOLATION ALGORITHMS / 55 \\
2.1 The $E$-algorithm / 55 \\
2.2 Richardson extrapolation process T2 \\
2.3 The $\epsilon$-algorithm / 78 \\
2.4 The $G$-transformation / 95 \\
2.5 Rational extrapolation / 101 \\
2.6 Generalizations of the $\epsilon$-algorithm / 108
\\
2.7 Levin's transforms / 113 \\
2.8 Overholt's process / 119 \\
2.9 $\Theta$-type algorithms / 121 \\
2.10 The iterated $\Delta^2$ process / 128 \\
2.11 Miscellaneous algorithms / 131 \\
\\
3 SPECIAL DEVICES / 145 \\
3.1 Error estimates and acceleration / 145 \\
3.2 Convergence tests and acceleration 151 \\
3.3 Construction of asymptotic expansions / 159 \\
3.4 Construction of extrapolation processes / 165 \\
3.5 Extraction procedures / 171 \\
3.6 Automatic selection / 178 \\
3.7 Composite sequence transformations / 185 \\
3.8 Error control / 193 \\
3.9 Contractive sequence transformations / 201 \\
3.10 Least squares extrapolation / 210 \\
\\
4 VECTOR EXTRAPOLATION ALGORITHMS / 213 \\
4.1 The vector $\epsilon$-algorithm / 216 \\
4.2 The topological $\epsilon$-algorithm / 220 \\
4.3 The vector $E$-algorithm / 228 \\
4.4 The recursive projection algorithm / 233 \\
4.5 The H-algorithm / 238 \\
4.6 The Ford--Sidi algorithms / 244 \\
4.7 Miscellaneous algorithms / 247 \\
\\
5 CONTINUOUS PREDICTION ALGORITHMS / 253 \\
5.1 The Taylor expansion / 254 \\
5.2 Confluent Overholt's process / 255 \\
5.3 Confluent $\epsilon$-algorithms / 256 \\
5.4 Confluent $\rho$-algorithm / 262 \\
5.5 Confluent $G$-transform / 265 \\
5.6 Confluent $E$-algorithm / 266 \\
5.7 $\Theta$-type confluent algorithms / 267 \\
\\
6 APPLICATIONS / 269 \\
6.1 Sequences and series / 270 \\
6.1.1 Simple sequences / 270 \\
6.1.2 Double sequences / 278 \\
6.1.3 Chebyshev and Fourier series / 282 \\
6.1.4 Continued fractions / 284 \\
6.1.5 Vector sequences / 208 \\
6.2 Systems of equations / 302 \\
6.2.1 Linear systems / 303 \\
6.2.2 Projection methods / 2307 \\
6.2.3 Regularization and penalty techniques / 309 \\
6.2.4 Nonlinear equations / 315 \\
6.2.5 Continuation methods / 330 \\
6.3 Eigenelements / 332 \\
6.3.1 Eigenvalues and eigenvectors / 333 \\
6.3.2 Derivatives of eigensystems / 336 \\
6.4 Integral and differential equations / 338 \\
6.4.1 Implicit Runge--Kutta methods / 339 \\
6.4.2 Boundary value problems / 340 \\
6.4.3 Nonlinear methods / 346 \\
6.4.4 Laplace transform inversion / 348 \\
6.4.5 Partial differential equations / 352 \\
6.5 Interpolation and approximation / 354 \\
6.6 Statistics / 357 \\
6.6.1 The jackknife / 358 \\
6.6.2 ARMA models / 359 \\
6.6.3 Monte--Carlo methods / 361 \\
6.7 Integration and differentiation / 365 \\
6.7.1 Acceleration of quadrature formulae / 366 \\
6.7.2 Nonlinear quadrature formulae / 372 \\
6.7.3 Cauchy's principal values / 373 \\
6.7.4 Infinite integrals / 378 \\
6.7.5 Multiple integrals / 387 \\
6.7.6 Numerical differentiation / 389 \\
6.8 Prediction / 5389 \\
\\
7 SOFTWARE / 397 \\
7.1 Programming the algorithms / 397 \\
7.2 Computer arithmetic / 400 \\
73 Programs / 403 \\
\\
Bibliography / 413 \\
\\
Index / 455",
}
@Article{Bunch:1991:DFA,
author = "K. J. Bunch and W. N. Cain and R. W. Grow",
title = "A data fitting approach to series convergence
acceleration",
journal = j-APPL-MATH-COMP,
volume = "42",
number = "2 (part II)",
pages = "189--195",
month = "????",
year = "1991",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/0096-3003(91)90050-W",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "65B10 (65D10)",
MRnumber = "1094414 (91k:65015)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "convergence acceleration",
}
@Article{Carlson:1991:TEI,
author = "B. C. Carlson",
title = "A table of elliptic integrals: {One} quadratic
factor",
journal = j-MATH-COMPUT,
volume = "56",
number = "193",
pages = "267--280",
month = jan,
year = "1991",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33E05 (65A05)",
MRnumber = "92b:33056",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290R (Integral equations); B0290M (Numerical
integration and differentiation); C4180 (Integral
equations); C4160 (Numerical integration and
differentiation)",
corpsource = "Dept. of Math., Iowa State Univ., Ames, IA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "conjugate complex zeros; elliptic integrals; Fortran
programs; integral equations; integration; polynomial;
R-functions; square root",
treatment = "P Practical",
}
@TechReport{Cody:1991:CPT,
author = "W. J. Cody",
title = "{CELEFUNT}: a Portable Test Package for Complex
Elementary Functions",
type = "Technical Report",
number = "ANL-91/1",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "iii + 21",
month = jan,
year = "1991",
bibdate = "Fri Sep 23 23:39:07 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Corless:1991:NEA,
author = "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
title = "Numerical evaluation of {Airy} functions with complex
arguments",
journal = j-J-COMPUT-PHYS,
volume = "93",
number = "1",
pages = "252--253",
month = mar,
year = "1991",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(91)90089-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:47 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999191900894",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Crenshaw:1991:SRS,
author = "J. W. Crenshaw",
title = "Square roots are simple?",
journal = j-EMBED-SYS-PROG,
volume = "4",
number = "11",
pages = "30--52",
month = nov,
year = "1991",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Wed Sep 14 19:14:52 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Embedded Systems Programming",
}
@Article{DeDoelder:1991:SSC,
author = "P. J. {De Doelder}",
title = "On some series containing $ \psi (x) - \psi (y >) $
and $ (\psi (x) - \psi (y >))^2 $ for certain values of
$x$ and $y$",
journal = j-J-COMPUT-APPL-MATH,
volume = "37",
number = "1--3",
pages = "125--141",
day = "18",
month = nov,
year = "1991",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(91)90112-W",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:02:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279190112W",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Dritz:1991:IPS,
author = "Kenneth W. Dritz",
title = "Introduction to the proposed standard for the
elementary functions in {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "3--8",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics)",
corpsource = "Dept. of Math. and Comput. Sci., Argonne Nat. Lab.,
IL, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; committees; elementary functions; generic
package; ISO standard; mathematics computing;
secondary; standards",
treatment = "P Practical",
}
@Article{Dritz:1991:PSGa,
author = "K. W. Dritz",
title = "Proposed standard for a generic package of elementary
functions for {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "9--46",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C6110B (Software
engineering techniques); C7310 (Mathematics)",
corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics
Working Group; basic; elementary functions;
ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package;
GENERIC-ELEMENTARY-FUNCTIONS; Group; international
standard; joint proposal; mathematical routines;
mathematics computing; NRG; Rapporteur Group; reusable
applications; SC22; software reusability;
specification; standards; WG9 Numerics",
treatment = "P Practical",
}
@Article{Dritz:1991:PSGb,
author = "K. W. Dritz",
title = "Proposed standard for a generic package of primitive
functions for {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "66--82",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics)",
corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; compliable Ada; elementary functions; generic
package; GENERIC-; mathematical; mathematics computing;
primitive functions; primitive operations;
PRIMITIVE-FUNCTIONS; software; specification;
standards",
treatment = "P Practical",
}
@Article{Dritz:1991:RPS,
author = "K. W. Dritz",
title = "Rationale for the proposed standard for a generic
package of elementary functions for {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "47--65",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics);
C6110 (Systems analysis and programming)",
corpsource = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "ACM SIGAda Numerics Working Group; Ada; Ada-Europe
Numerics; collateral; elementary functions standard;
mathematics computing; numerical software; portability;
programming; robustness; standards; Working Group",
treatment = "P Practical",
}
@Article{Duprat:1991:WND,
author = "J. Duprat and J.-M. Muller",
title = "Writing numbers differently for faster calculation",
journal = j-TECHNIQUE-SCI-INFORMATIQUES,
volume = "10",
number = "3",
pages = "211--224",
month = "????",
year = "1991",
CODEN = "TTSIDJ",
ISSN = "0752-4072, 0264-7419",
ISSN-L = "0752-4072",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Instead of Avizienis' or the carry save methods a
borrow save (BS) notation is proposed. Examples are
given of BS addition, subtraction, shifting and
multiplication with the necessary elementary cells
being proposed and circuits for testing zero and sign
being described. Floating point arithmetic is
explained, involving pseudo normalisation and
applications are covered including the Cordic
algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure de Lyon, France",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Technique et science informatiques : TSI",
keywords = "Addition; Borrow save; Carry save methods; Cordic
algorithm; Floating point arithmetic; Multiplication;
Pseudo normalisation; Shifting; Subtraction; Zero",
language = "French",
pubcountry = "France",
thesaurus = "Digital arithmetic",
}
@InProceedings{Ferguson:1991:AMA,
author = "W. E. {Ferguson, Jr.} and T. Brightman",
title = "Accurate and Monotone Approximations of Some
Transcendental Functions",
crossref = "Kornerup:1991:PIS",
pages = "237--244",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Article{Gal:1991:AEM,
author = "Shmuel Gal and Boris Bachelis",
title = "An Accurate Elementary Mathematical Library for the
{IEEE} Floating Point Standard",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "26--45",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65-04 65D15)",
MRnumber = "92a:65069",
bibdate = "Sun Sep 04 23:33:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/toms/103151.html",
abstract = "The algorithms used by the IBM Israel Scientific
Center for the elementary mathematical library using
the IEEE standard for binary floating point arithmetic
are described. The algorithms are based on the
``accurate tables method.'' This methodology achieves
high performance and produces very accurate results. It
overcomes one of the main problems encountered in
elementary mathematical functions computations:
achieving last bit accuracy. The results obtained are
correctly rounded for almost all argument values.
\par
Our main idea in the accurate tables method is to use
``nonstandard tables,'' which are different from the
natural tables of equally spaced points in which the
rounding error prevents obtaining last bit accuracy. In
order to achieve a small error we use the following
idea: Perturb the original, equally spaced, points in
such a way that the table value (or tables values in
case we need several tables) will be very close to
numbers which can be exactly represented by the
computer (much closer than the usual double precision
representation). Thus we were able to control the error
introduced by the computer representation of real
numbers and extended the accuracy without actually
using extended precision arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; theory",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation.",
}
@Article{Gray:1991:GMA,
author = "H. L. Gray and Suojin Wang",
title = "A General Method for Approximating Tail
Probabilities",
journal = j-J-AM-STAT-ASSOC,
volume = "86",
number = "413",
pages = "159--166",
month = mar,
year = "1991",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:06:12 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314297;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1990.bib",
URL = "http://www.jstor.org/stable/2289726",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@InProceedings{Gustafson:1991:CAA,
author = "Sven-{\AA}ke Gustafson and Frank Stenger",
title = "Convergence acceleration applied to {Sinc}
approximation with application to approximation of $
|x|^\alpha $",
crossref = "Bowers:1991:CCI",
pages = "161--171",
year = "1991",
MRclass = "41A30 (93B40)",
MRnumber = "MR1140021",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0746.41034",
abstract = "The author studies mainly the role of Chebyshev
acceleration of Sinc approximation. Then he considers
various methods of approximating $ \vert x \vert^\alpha
$ and applies Chebyshev acceleration to the various
type of approximants for the case of $ \alpha = 1 $.",
acknowledgement = ack-nhfb,
classmath = "*41A65 (Abstract approximation theory)",
keywords = "Chebyshev acceleration; convergence acceleration",
reviewer = "Zhang Ganglu (Dongying)",
}
@Article{Hamza:1991:MBD,
author = "K. M. Hamza and M. A. H. Abdul-Karim",
title = "Microprocessor Based Direct Square Root Extractor",
journal = "Modelling",
volume = "34",
number = "1",
pages = "45--48",
month = "????",
year = "1991",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Ifantis:1991:PZS,
author = "E. K. Ifantis and C. G. Kokologiannaki and C. B.
Kouris",
title = "On the positive zeros of the second derivative of
{Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "34",
number = "1",
pages = "21--31",
day = "10",
month = feb,
year = "1991",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:48 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042791901449",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Ikebe:1991:CZO,
author = "Yasuhiko Ikebe and Yasushi Kikuchi and Issei
Fujishiro",
title = "Computing zeros and orders of {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "38",
number = "1--3",
pages = "169--184",
day = "23",
month = dec,
year = "1991",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:02:23 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279190169K",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Iserles:1991:CDC,
author = "A. Iserles",
title = "Complex dynamics of convergence acceleration",
journal = j-IMA-J-NUMER-ANAL,
volume = "11",
number = "2",
pages = "205--240",
year = "1991",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65B05 (65E05)",
MRnumber = "92h:65006",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "convergence acceleration",
}
@Article{Laforgia:1991:BMB,
author = "Andrea Laforgia",
title = "Bounds for modified {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "34",
number = "3",
pages = "263--267",
day = "26",
month = apr,
year = "1991",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:49 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279190087Z",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Levrie:1991:CAF,
author = "Paul Levrie",
title = "Convergence acceleration for $n$-fractions",
journal = j-APPL-NUM-MATH,
volume = "7",
number = "6",
pages = "481--492",
month = jun,
year = "1991",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "40A15 (65B05)",
MRnumber = "92k:40001",
MRreviewer = "Claude Brezinski",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@Article{Levrie:1991:CFC,
author = "Paul Levrie",
title = "$ {G} $-continued fractions and convergence
acceleration in the solution of third-order linear
recurrence relations of {Poincar{\'e}} type",
journal = j-APPL-NUM-MATH,
volume = "8",
number = "3",
pages = "225--242",
month = oct,
year = "1991",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1090/surv/037",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65B99 (65Q05)",
MRnumber = "92m:65012",
MRreviewer = "J. Albrycht",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@InProceedings{Lyons:1991:FMF,
author = "Ken Lyons",
title = "A fast method for finding an integer square root",
crossref = "Koopman:1991:PST",
pages = "27--30",
year = "1991",
bibdate = "Tue May 4 05:57:50 MDT 1999",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
acknowledgement = ack-nhfb,
}
@InProceedings{Markstein:1991:WFF,
author = "V. Markstein and P. Markstein and T. Nguyen and S.
Poole",
title = "Wide Format Floating-Point Math Libraries",
crossref = "IEEE:1991:PSA",
pages = "130--138",
year = "1991",
bibdate = "Wed Dec 13 18:34:51 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The authors present the performance and accuracy
evaluations of eleven transcendental functions found in
64- and 128-bit floating-point formats in math
libraries on the Cray Y-MP, the IBM 3090E/VF, the
Convex C-240, the Hewlett--Packard 9000/720, and the
IBM System/6000. Both architecture and algorithms are
shown to impact the results.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "ISQUARE, Inc., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods); C5470
(Performance evaluation and testing); C7310
(Mathematics)",
confdate = "18-22 Nov. 1991",
conflocation = "Albuquerque, NM, USA",
confsponsor = "IEEE; ACM",
keywords = "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
Cray Y-MP; Floating-point formats; Hewlett--Packard
9000/720; IBM 3090E/VF; IBM System/6000; Math
libraries; Performance; Transcendental functions; Wide
format floating point math libraries",
numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Mathematics computing; Parallel
processing; Performance evaluation",
}
@Article{Maximon:1991:EIP,
author = "Leonard C. Maximon",
title = "On the evaluation of the integral over the product of
two spherical {Bessel} functions",
journal = j-J-MATH-PHYS,
volume = "32",
number = "3",
pages = "642--648",
month = mar,
year = "1991",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.529405",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33C55",
MRnumber = "92f:33018",
MRreviewer = "S. K. Chatterjea",
bibdate = "Tue Nov 1 08:57:23 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v32/i3/p642_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "7",
}
@Article{McQuillan:1991:HPV,
author = "S. E. McQuillan and J. V. McCanny and R. F. Woods",
title = "High performance {VLSI} architecture for division and
square root",
journal = j-ELECT-LETTERS,
volume = "27",
number = "1",
pages = "19--21",
day = "3",
month = jan,
year = "1991",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "A novel high performance bit parallel architecture to
perform square root and division is proposed. Relevant
VLSI design issues have been addressed. By employing
redundant arithmetic and a semisystolic schedule, the
throughput has been made \ldots{}",
}
@InProceedings{McQuillan:1991:VAM,
author = "S. E. McQuillan and J. V. McCanny",
booktitle = "1991 International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP-91, 14--17} April 1991",
title = "A {VLSI} architecture for multiplication, division and
square root",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1205--1208",
year = "1991",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A high-performance VLSI architecture to perform
combined multiply-accumulate, divide, and square root
operations is proposed. The circuit is highly regular,
requires only minimal control, and can be reconfigured
for every cycle. The execution time \ldots{}",
}
@Article{Midy:1991:CSE,
author = "P. Midy and Y. Yakovlev",
title = "Computing some elementary functions of a complex
variable",
journal = j-MATH-COMP-SIM,
volume = "33",
number = "1",
pages = "33--49",
year = "1991",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
MRclass = "65Y10 (65D20)",
MRnumber = "MR1122989",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics and Computers in Simulation",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
}
@Article{Montuschi:1991:OAE,
author = "P. Montuschi and M. Mezzalama",
title = "Optimal Absolute Error Starting Values for
{Newton--Raphson} Calculation of Square Root",
journal = j-COMPUTING,
volume = "46",
number = "1",
pages = "67--86",
month = mar,
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65H05 (65G99)",
MRnumber = "92a:65161",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
affiliation = "Politecnico di Torino",
affiliationaddress = "Torino, Italy",
classification = "723; 921",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput Vienna New York",
keywords = "Absolute Error; Computer Programming --- Algorithms;
Mathematical Techniques; Newton--Raphson Method;
Optimization; Square Roots",
}
@InProceedings{Montuschi:1991:SRD,
author = "Paolo Montuschi and Luigi Ciminiera",
title = "Simple radix 2 division and square root with skipping
of some addition steps",
crossref = "Kornerup:1991:PIS",
pages = "202--209",
year = "1991",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
summary = "The authors present a novel algorithm for shared radix
2 division and square root whose main characteristic is
the ability to avoid any addition when the digit 0 has
been selected. The solution presented uses a redundant
representation of the \ldots{}",
}
@Article{OGrady:1991:HOA,
author = "E. Pearse O'Grady and Baek-Kyu Young",
title = "A hardware-oriented algorithm for floating-point
function generation",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "2",
pages = "237--241",
month = feb,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.73596",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "An algorithm is presented for performing accurate,
high-speed, floating-point function generation for
univariate functions defined at arbitrary breakpoints.
Rapid identification of the breakdown interval, which
includes the input argument, is the key operation in
the algorithm. A hardware implementation which makes
extensive use of read/write memories illustrates the
algorithm.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Okabe:1991:LDC,
author = "Y. Okabe and N. Takagi and S. Yaima",
key = "OTY91",
title = "Log-Depth Circuits for Elementary Functions Using
Residue Number System",
journal = j-ELECTRON-COMMUN-JPN,
volume = "74",
number = "8",
pages = "31--37",
year = "1991",
CODEN = "ECOJAL",
ISSN = "0424-8368",
bibdate = "Mon May 19 15:16:09 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan",
}
@Article{Olver:1991:UEIb,
author = "F. W. J. Olver",
title = "Uniform, Exponentially Improved, Asymptotic Expansions
for the Confluent Hypergeometric Function and Other
Integral Transforms",
journal = j-SIAM-J-MATH-ANA,
volume = "22",
number = "5",
pages = "1475--1489",
month = sep,
year = "1991",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "41A60 (33C15)",
MRnumber = "92g:41035",
MRreviewer = "Hans-J{\"u}rgen Glaeske",
bibdate = "Sun Nov 28 19:25:21 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/22/5;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Press:1991:BFF,
author = "William H. Press and Saul A. Teukolsky",
title = "{Bessel} Functions of Fractional Order",
journal = j-COMPUT-PHYS,
volume = "5",
number = "2",
pages = "244--??",
month = mar,
year = "1991",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4822982",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:28 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4822982",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Press:1991:MBF,
author = "William H. Press and Saul A. Teukolsky",
title = "Modified {Bessel} Functions of Fractional Order",
journal = j-COMPUT-PHYS,
volume = "5",
number = "3",
pages = "330--??",
month = may,
year = "1991",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4822991",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:29 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4822991",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Book{Saan:1991:VFP,
author = "T. Saan",
title = "{{\cyr Vychislenie {\`e}lementarnykh funktsi{\u\i}s
pomoshch'yu drobno-ratsional'nykh priblizheni{\u\i}}}.
({Russian}) [Calculation of elementary functions by
means of rational approximations]",
publisher = "{\`E}ston. Nauchno-Proizvod. Ob\cdprime ed. Vychisl.
Tekhn. Inform., Tartu",
pages = "139",
year = "1991",
MRclass = "65-04 (65D15)",
MRnumber = "94f:65008",
MRreviewer = "W. Govaerts",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Smith:1991:AFP,
author = "David M. Smith",
title = "Algorithm 693: {A FORTRAN} Package for Floating-Point
Multiple-Precision Arithmetic",
journal = j-TOMS,
volume = "17",
number = "2",
pages = "273--283",
month = jun,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 23:44:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/toms/108585.html",
abstract = "FM is a collection of FORTRAN-77 routines which
performs floating-point multiple-precision arithmetic
and elementary functions. Results are almost always
correctly rounded, and due to improved algorithms used
for elementary functions, reasonable efficiency is
obtained.",
acknowledgement = ack-nhfb,
affiliation = "Loyola Marymount Univ., Los Angeles, CA, USA",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods); C7310
(Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Accuracy; Algorithms; Elementary functions;
Floating-point multiple-precision arithmetic; FM;
FORTRAN-77 routines; Mathematical library; Portable
software; Rounding off",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 77.",
thesaurus = "Digital arithmetic; Function approximation;
Mathematics computing; Software packages; Subroutines",
}
@Article{Squire:1991:ANS,
author = "Jon S. Squire",
title = "{Ada} numerics standardization and testing",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
address = "New York, NY, USA",
pages = "1--286",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
annote = "``A special edition from SIGAda \ldots{} presented by
SIGAda Numerics Working Group and Ada-Europe Numerics
Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
Rapporteur Group.''--Cover. Includes bibliographies.
Introduction to the proposed standard for the
elementary functions in Ada / Kenneth W. Dritz ---
Proposed standard for a generic package of elementary
functions for Ada / edited by Kenneth W. Dritz ---
Rationale for the proposed standard for a generic
package of elementary functions for Ada; Proposed
standard for a generic package of primitive functions
for Ada; Rationale for the proposed standard for a
generic package of primitive functions for Ada /
Kenneth W. Dritz --- Proposed standard for packages of
real and complex type declarations and basic operations
for Ada (including vector and matrix types) / edited by
Graham S. Hodgson --- Rationale for the proposed
standard for packages of real and complex type
declarations and basic operations for Ada (including
vector and matrix types) / Graham S. Hodgson. Proposed
standard for a generic package of complex elementary
functions / edited by Jon S. Squire --- Rationale for
the proposed standard for a generic package of complex
elementary functions / Jon S. Squire --- A portable
generic elementary function package in Ada and an
accurate test suite / Ping Tak Peter Tang --- Towards
validation of generic elementary functions and other
standard Ada numerics packages / Jon S. Squire ---
Floating point attributes in Ada / Dik T. Winter --- An
Ada math library for real-time avionics / Donald A.
Celarier and Donald W. Sando --- Predifined floating
point type names, uniformity rapporteur group UI-48 /
edited by Jon S. Squire.",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada (Computer program language)",
}
@Article{Squire:1991:PSG,
author = "J. S. Squire",
title = "Proposed standard for a generic package of complex
elementary functions ({Ada})",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "140--165",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics);
C6110B (Software engineering techniques)",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "ACM SIGAda; Ada; Ada-Europe Numerics Working Group;
applications; complex elementary functions; complex
mathematical routines; COMPLEX-ELEMENTARY-FUNCTIONS;
generic package; GENERIC-; international standard;
joint proposal; mathematics computing; Numerics Working
Group; portable; reusable; software reusability;
standards; WG9 Numerics Rapporteur Group",
treatment = "P Practical",
}
@Article{Squire:1991:RPS,
author = "Jon S. Squire",
title = "Rationale for the proposed standard for a generic
package of complex elementary functions ({Ada})",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "166--179",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C7310 (Mathematics);
C6110B (Software engineering techniques)",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "ACM SIGAda Numerics Working Group; Ada; Ada-; basic
complex mathematical; complex;
COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions;
error bounds; Europe Numerics Working Group; generic
package; GENERIC-; mathematics computing; proposed
standard; reusable applications; routines; software
reusability; specification; standards",
treatment = "P Practical",
}
@Article{Squire:1991:TVG,
author = "J. S. Squire",
title = "Towards validation of generic elementary functions and
other standard {Ada} numerics packages",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "217--243",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C6150G (Diagnostic, testing, debugging and evaluating
systems); C7310 (Mathematics); C6140D (High level
languages)",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; Ada listings; computing; conformance testing;
conformance tests; generic elementary functions;
implementors guide; mathematics; program testing;
proposed ISO; prototype tests; standard Ada numerics
packages; standards; test suite",
treatment = "P Practical",
}
@Article{Takagi:1991:RCM,
author = "N. Takagi and T. Asada and S. Yajima",
title = "Redundant {CORDIC} Methods with a Constant Scale
Factor for Sine and Cosine Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "9",
pages = "989--995",
month = sep,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83660",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:24 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83660",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Tang:1991:PGE,
author = "Ping Tak Peter Tang",
title = "A portable generic elementary function package in
{Ada} and an accurate test suite",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "181--216",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics); C6140D (High level languages);
C6110B (Software engineering techniques); C6150G
(Diagnostic, testing, debugging and evaluating
systems)",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "accurate test; Ada; function libraries; mathematics
computing; portability; portable generic elementary
function package; program testing; resolution; rigorous
analysis; software; suite; test programs",
treatment = "P Practical",
}
@InProceedings{Tang:1991:TLA,
author = "Ping Tak Peter Tang",
title = "Table-Lookup Algorithms for Elementary Functions and
Their Error Analysis",
crossref = "Kornerup:1991:PIS",
pages = "232--236",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@InProceedings{Wong:1991:FHA,
author = "W. F. Wong and E. Goto",
title = "Fast Hardware-based Algorithms for Elementary Function
Computations",
crossref = "Anonymous:1991:PIS",
pages = "56--65",
year = "1991",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
searchkey = "ti:elementary function",
}
@Article{Zeilberger:1991:MPP,
author = "Doron Zeilberger",
title = "A {Maple} program for proving hypergeometric
identities",
journal = j-SIGSAM,
volume = "25",
number = "3",
pages = "4--13",
month = jul,
year = "1991",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Fri Feb 8 18:27:01 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Gives the listing of a MAPLE program for implementing
an algorithm for proving any terminating definite
hypergeometric identity, and more generally, for
finding the linear recurrence satisfied by any definite
hypergeometric sum R(n):= Sigma /sub k/F(n,k), where
F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/(
alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub
i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub
i'/)!). The algorithm for definite hypergeometric
summation relies on Gosper's (1978) ingenious decision
procedure for indefinite summation, but not in the
obvious way!.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Drexel Univ.,
Philadelphia, PA, USA",
classcodes = "C7310 (Mathematics)",
classification = "C7310 (Mathematics)",
corpsource = "Dept. of Math. and Comput. Sci., Drexel Univ.,
Philadelphia, PA, USA",
fjournal = "SIGSAM Bulletin",
issue = "97",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
keywords = "definite; Definite hypergeometric summation;
hypergeometric identity; hypergeometric summation;
linear recurrence; Linear recurrence; manipulation;
MAPLE program; mathematics computing; proofs; Proofs;
public domain software; shareware; Shareware; symbol;
terminating definite; Terminating definite
hypergeometric identity; theorem proving",
thesaurus = "Mathematics computing; Public domain software; Symbol
manipulation; Theorem proving",
treatment = "P Practical",
}
@Article{Ziv:1991:FEE,
author = "Abraham Ziv",
title = "Fast Evaluation of Elementary Mathematical Functions
with Correctly Rounded Last Bit",
journal = j-TOMS,
volume = "17",
number = "3",
pages = "410--423",
month = sep,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/toms/116813.html",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; standardization; theory",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Efficiency.",
}
@Book{Achieser:1992:TA,
author = "N. I. Achieser",
title = "Theory of Approximation",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 307",
year = "1992",
ISBN = "0-486-67129-1 (paperback)",
ISBN-13 = "978-0-486-67129-1 (paperback)",
LCCN = "QA221 .A533 1992",
bibdate = "Fri Oct 20 08:06:59 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Dover books on advanced mathematics",
acknowledgement = ack-nhfb,
remark = "Translation of Russian original, Lek{\"e}t{\`\i}sii po
teorii approksima{\"e}t{\`\i}sii. Reprint of English
translation \cite{Achieser:1956:TA}.",
subject = "Mathematical analysis",
tableofcontents = "Approximation Problems in Linear Normalized Spaces
\\
Formulation of the Principal Problem in the Theory of
Approximation / 1 \\
The Concept of Metric Space / 1 \\
The Concept of Linear Normalized Space / 2 \\
Examples of Linear Normalized Spaces / 3 \\
The Inequalities of Holder and Minkowski / 4 \\
Additional Examples of Linear Normalized Spaces / 7 \\
Hilbert Space / 8 \\
The Fundamental Theorem of Approximation Theory in
Linear Normalized Spaces / 10 \\
Strictly Normalized Spaces / 11 \\
An Example of Approximation in the Space $L^p$ / 12 \\
Geometric Interpretation / 13 \\
Separable and Complete Spaces / 14 \\
Approximation Theorems in Hilbert Space / 15 \\
An Example of Approximation in Hilbert Space / 19 \\
More About the Approximation Problem in Hilbert Space /
21 \\
Orthonormalized Vector Systems in Hilbert Space / 22
\\
Orthogonalization of Vector Systems / 23 \\
Infinite Orthonormalized Systems / 25 \\
An Example of a Non-Separable System / 29 \\
Weierstrass' First Theorem / 29 \\
Weierstrass' Second Theorem / 32 \\
The Separability of the Space C / 33 \\
The Separability of the Space $L^p$ / 34 \\
Generalization of Weierstrass' Theorem to the Space
$L^p$ / 37 \\
The Completeness of the Space $L^p$ / 38 \\
Examples of Complete Orthonormalized Systems in
L[superscript 2] / 40 \\
Muntz's Theorem / 43 \\
The Concept of the Linear Functional / 46 \\
F. Riesz's Theorem / 47 \\
A Criterion for the Closure of a Set of Vectors in
Linear Normalized Spaces / 49 \\
P. L. Tchebysheff's Domain of Ideas \\
Statement of the Problem / 51 \\
A Generalization of the Theorem of de la Vallee-Poussin
/ 52 \\
The Existence Theorem / 53 \\
Tchebysheff's Theorem / 55 \\
A Special Case of Tchebysheff's Theorem / 57 \\
The Tchebysheff Polynomials of Least Deviation from
Zero / 57 \\
A Further Example of P. Tchebysheff's Theorem / 58 \\
An Example for the Application of the General Theorem
of de la Vallee-Poussin / 60 \\
An Example for the Application of P. L. Tchebysheff's
General Theorem / 62 \\
The Passage to Periodic Functions / 64 \\
An Example of Approximating with the Aid of Periodic
Functions / 66 \\
The Weierstrass Function / 66 \\
Haar's Problem / 67 \\
Proof of the Necessity of Haar's Condition / 68 \\
Proof of the Sufficiency of Haar's Condition / 69 \\
An Example Related to Haar's Problem / 72 \\
P. L. Tchebysheff's Systems of Functions / 73 \\
Generalization of P. L. Tchebysheff's Theorem / 74 \\
On a Question Pertaining to the Approximation of a
Continuous Function in the Space $L$ / 76 \\
A. A. Markoff's Theorem / 82 \\
Special Cases of the Theorem of A. A. Markoff / 85 \\
Elements of Harmonic Analysis \\
The Simplest Properties of Fourier Series / 89 \\
Fourier Series for Functions of Bounded Variation / 93
\\
The Parseval Equation for Fourier Series / 97 \\
Examples of Fourier Series / 98 \\
Trigonometric Integrals / 101 \\
The Riemann--Lebesgue Theorem / 103 \\
Plancherel's Theory / 104 \\
Watson's Theorem / 106 \\
Plancherel's Theorem / 108 \\
Fejer's Theorem / 110 \\
Integral-Operators of the Fejer Type / 113 \\
The Theorem of Young and Hardy / 116 \\
Examples of Kernels of the Fejer Type / 118 \\
The Fourier Transformation of Integrable Functions /
120 \\
The Faltung of two Functions / 122 \\
V. A. Stekloff's Functions / 123 \\
Multimonotonic Functions / 125 \\
Conjugate Functions / 126 \\
Certain Extremal Properties of Integral Transcendental
Functions of the Exponential Type \\
Integral Functions of the Exponential Type / 130 \\
The Borel Transformation / 132 \\
The Theorem of Wiener and Paley / 134 \\
Integral Functions of the Exponential Type which are
Bounded along the Real Axis / 137 \\
S. N. Bernstein's Inequality / 140 \\
B. M. Levitan's Polynomials / 146 \\
The Theorem of Fejer and Riesz. A Generalization of
This Theorem / 152 \\
A Criterion for the Representation of Continuous
Functions as Fourier--Stieltjes Integrals / 154 \\
Questions Regarding the Best Harmonic Approximation of
Functions Preliminary Remarks / 160 \\
The Modulus of Continuity / 161 \\
The Generalization to the Space $L^p$ ($p \geq 1$) /
162 \\
An Example of Harmonic Approximation / 165 \\
Some Estimates for Fourier Coefficients / 169 \\
More about V. A. Stekloff's Functions / 173 \\
Two Lemmas / 175 \\
The Direct Problem of Harmonic Approximation / 176 \\
A Criterion due to B. Sz.-Nagy / 183 \\
The Best Approximation of Differentiable Functions /
187 \\
Direct Observations Concerning Periodic Functions / 195
\\
Jackson's Second Theorem / 199 \\
The Generalized Fejer Method / 201 \\
Berstein's Theorem / 206 \\
Priwaloff's Theorem / 210 \\
Generalizations of Bernstein's Theorems to the Space
$L^p$ ($p \geq 1$) / 211 \\
The Best Harmonic Approximation of Analytic Functions /
214 \\
A Different Formulation of the Result of the Preceding
Section / 218 \\
The Converse of Bernstein's Theorem / 221 \\
Wiener's Theorem on Approximation \\
Wiener's Problem / 224 \\
The Necessity of Wiener's Condition / 224 \\
Some Definitions and Notation / 225 \\
Several Lemmas / 227 \\
The Wiener--Levy Theorem / 230 \\
Proof of the Sufficiency of Wiener's Condition / 233
\\
Wiener's General Tauber Theorem / 234 \\
Weakly Decreasing Functions / 235 \\
Remarks on the Terminology / 237 \\
Ikehara's Theorem / 238 \\
Carleman's Tauber Theorem / 241 \\
Various Addenda and Problems \\
Elementary Extremal Problems and Certain Closure
Criteria / 243 \\
Szego's Theorem and Some of Its Applications / 256 \\
Further Examples of Closed Sequences of Functions / 267
\\
The Caratheodory--Fejer Problem and Similar Problems /
270 \\
Solotareff's Problems and Related Problems / 280 \\
The Best Harmonic Approximation of the Simplest
Analytic Functions / 289 \\
Notes / 296 \\
Index / 306",
}
@Article{Anderson:1992:FIH,
author = "G. D. Anderson and M. K. Vamanamurthy and M.
Vuorinen",
title = "Functional Inequalities for Hypergeometric Functions
and Complete Elliptic Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "23",
number = "2",
pages = "512--524",
month = mar,
year = "1992",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33C05 (33C75)",
MRnumber = "93b:33001",
MRreviewer = "J. M. H. Peters",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Book{Baker:1992:CMF,
author = "Louis Baker",
title = "{C} Mathematical Function Handbook",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xviii + 757",
year = "1992",
ISBN = "0-07-911158-0",
ISBN-13 = "978-0-07-911158-6",
LCCN = "QA351.B17 1991; QA351 .B17 1992",
bibdate = "Fri Aug 31 18:54:02 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
series = "McGraw-Hill programming tools for scientists and
engineers",
acknowledgement = ack-nhfb,
remark = "System requirements for computer disk: PC; C or C++
compiler.",
subject = "Functions, Special; Computer programs; C (Computer
program language)",
tableofcontents = "Preface / xv \\
1. Special Functions and Numerical Analysis / 1 \\
\\
Correspondence with Abramowitz and Stegun / 1 \\
Numerical Analysis / 1 \\
The IEEE-754 Standard / 1 \\
Practical Considerations / 3 \\
Reference / 6 \\
\\
2. Special Functions in C and C++ / 8 \\
C and C++ / 8 \\
Portability, ANSI C, and C++ / 8 \\
Infinite Loops / 9 \\
Header Files COMPLEX.H, CMLIB.H, PROTOM.H / 10 \\
Error Handling / 10 \\
Pitfalls with Special Functions / 11 \\
Normalization Conventions / 12 \\
Tips and Pitfalls in C / 12 \\
Calling C from C++ / 14 \\
References / 15 \\
Cmlib.h / 16 \\
COMPLEX.H Header File / 17 \\
Prototypes for \booktitle{C Mathematical Function
Handbook} / 19 \\
\\
3. Elementary Analytical Methods / 33 \\
Powers and Roots / 33 \\
Complex Numbers / 34 \\
Roots of Polynomials / 35 \\
Quadratics / 35 \\
Cubics / 35 \\
Quartics (biquadratics) / 36 \\
Implementation Considerations / 37 \\
Ouintics / 38 \\
References / 38 \\
Complex Variable Auxiliary Routines / 39 \\
Powers and Roots / 45 \\
Polynomial Root Finders / 48 \\
Test Driver for Programs of Chapters 3-4 / 60 \\
\\
4. Elementary Transcendental Functions / 72 \\
Elementary Functions / 72 \\
Complex Elementary Functions / 73 \\
Gudermannian / 74 \\
References / 74 \\
\\
5. Exponential Integral and Relatives / 75 \\
Exponential and Related Integrals / 75 \\
Methods / 76 \\
References / 76 \\
Shi(x) and Chi(x) / 76 \\
Exponential Integral / 78 \\
Test Driver Results: Exponential Integral and Relatives
/ 95 \\
\\
6. Gamma Function and Related Integrals / 100 \\
Gamma Function and Relatives / 100 \\
The Pochhammer Symbol / 100 \\
Methods / 101 \\
Asymptotic Series / 101 \\
Reference / 101 \\
Gamma Function and Relatives / 102 \\
Digamma and First 2 Polygamma Functions / 111 \\
\\
7. Error Function and Relatives / 115 \\
Error Function and Relatives / 115 \\
Methods / 117 \\
Recurrence Relations / 117 \\
C Code / 118 \\
References / 118 \\
Figure: Dawson's Integral / 118 \\
Plasma Dispersion Function / 120 \\
Iterated Error Function / 127 \\
Boehmer (generalized Fresnel) Integral / 129 \\
Complementary Error Function for Complex Arguments /
133 \\
Test Driver Chapter 7 / 134 \\
\\
8. Legendre Functions / 142 \\
Legendre Functions / 142 \\
Derivatives / 143 \\
Applications / 143 \\
Methods / 144 \\
References / 144 \\
Legendre and Associated Legendre Functions / 146 \\
Legendre Functions for $|x| > 1$ / 155 \\
Toroidal $P|x| > 1$ / 163 \\
Mehler (Conical Legendre) Functions / 164 \\
Test Driver for Legendre Functions of Chapter 8 / 166
\\
\\
9. Bessel Functions / 177 \\
Struve Functions / 178 \\
Anger and Weber Functions / 179 \\
Relationship to Confluent Hypergeometric Function / 179
\\
Derivatives / 179 \\
Other Related Functions / 179 \\
Zeros of Bessel Functions / 180 \\
Applications / 180 \\
Methods / 180 \\
References / 181 \\
Bessel Functions for Complex Arguments / 182 \\
Bessel Functions: Rational Approximations / 194 \\
Bessel Function Tables as a Function of (Integral) n /
201 \\
Zeros of Bessel Functions / 205 \\
Test Driver for Bessel Functions / 211 \\
Test Driver Bessel Zero / 220 \\
Output of Bessel Function Test Driver / 221 \\
Output of Test Driver for Zerobess() / 237 \\
\\
10. Bessel Functions of Fractional Order / 239 \\
Introduction / 239 \\
Spherical Bessel Functions / 239 \\
Airy Functions / 239 \\
Applications / 240 \\
Asymptotics / 240 \\
Caustics / 240 \\
Schroedinger's Equation, Turning Points and the WKB
Method / 242 \\
Methods / 243 \\
The $|A|$ Function / 243 \\
References / 244 \\
Spherical Bessel Functions and Allied Routines / 245
\\
Airy, Bessel Functions and Integrals Thereof / 250 \\
\\
11. Integrals of Bessel Functions / 265 \\
Introduction / 265 \\
Applications / 265 \\
Methods / 265 \\
Bickley Functions / 265 \\
Adaptive Quadrature / 266 \\
Repeated Integrals of Jn / 266 \\
Other Integrals / 266 \\
References / 266 \\
Figures of Integrals of Bessel Functions / 267 \\
Integrals of Bessel Functions / 277 \\
Adaptive Integration Routine / 242 \\
\\
12. Struve and Anger--Weber Functions / 284 \\
Introduction / 284 \\
Struve Functions / 284 \\
Anger--Weber Functions / 284 \\
Methods / 285 \\
References / 285 \\
Figures / 286 \\
Struve Functions General Order / 289 \\
Struve Functions Lowest Order / 291 \\
Integrals of Struve HO, HO/t, LO / 295 \\
Integral of Anger--Weber Function / 297 \\
\\
13. Confluent Hypergeometric Functions and Relatives /
301 \\
Introduction / 301 \\
Airy Functions / 303 \\
Applications / 303 \\
Methods / 304 \\
References / 304 \\
Confluent Hypergeometric Function Complex Arguments /
305 \\
Test Drive Confluent Hypergeometric Function / 318 \\
Confluent Hypergeometric Function U / 322 \\
Test Driver U.c / 331 \\
Test Output: Confluent-Hypergeometric Function / 332
\\
Test Output: U / 334 \\
\\
14. Coulomb Wave Functions / 335 \\
Introduction / 335 \\
Methods / 336 \\
References / 337 \\
Coulomb Wave Functions / 339 \\
Test Driver Coulomb Wave Functions / 343 \\
Test Output: Coulomb wave Functions / 344 \\
\\
15. The Hypergeometric Function / 345 \\
Introduction / 345 \\
Applications / 346 \\
Methods / 346 \\
References / 346 \\
Hypergeometric Function Complex Arguments / 347 \\
Legendre Function $P$ for Complex Parameters / 364 \\
Legendre $Q$ for Complex Arguments / 366 \\
Test Driver $_2F_1$ / 369 \\
Output: Gauss Hypergeometric Functions / 370 \\
Real Hypergeometric Function and Relatives / 371 \\
\\
16. The Elliptic Functions / 373 \\
Introduction / 373 \\
Applications / 376 \\
Methods / 376 \\
References / 377 \\
Figure / 378 \\
Basic Elliptic Functions Real Arguments / 380 \\
Elliptic Integral of Third Kind / 391 \\
Jacobian Elliptic Function Complex Argument / 397 \\
Complex Elliptic Theta Functions / 406 \\
Output: Test Driver for Elliptic Functions / 411 \\
\\
17. The Elliptic Integrals / 416 \\
Introduction / 415 \\
Caveat / 416 \\
References / 417 \\
Figures / 417 \\
\\
18. The Weierstrass Elliptic Function and Relatives /
425 \\
Introduction / 425 \\
Methods / 427 \\
References / 427 \\
Inverse of Weierstrass Elliptic P . / 428 \\
Brent Root Finder / 430 \\
\\
19. The Parabolic Cylinder Functions / 432 \\
Introduction / 432 \\
Methods / 432 \\
Figures / 432 \\
Parabolic Cylinder Functions / 435 \\
Test Driver Parabolic Cylinder Function / 442 \\
\\
20. The Mathieu Functions / 444 \\
Introduction / 444 \\
Method / 443 \\
References / 445 \\
Figures / 445 \\
Mathieu Functions / 449 \\
Mathieu Functions Test Driver / 465 \\
Test Output: Mathieu Functions / 467 \\
\\
21. The Spheroidal Wave Functions / 475 \\
Introduction / 475 \\
Spheroidal Wave Functions / 475 \\
Generalized Spheroidal Wave Functions / 477 \\
Caveat / 477 \\
Method / 477 \\
References / 478 \\
Figures / 478 \\
Spheroidal Wave Functions / 486 \\
Legptable Pn,m for n = m to ntop / 500 \\
Test Driver Spheroidal Wave Functions / 501 \\
Test Output: Spheroidal Wave Functions / 504 \\
\\
22. Orthogonal Polynomials / 509 \\
Introduction / 509 \\
Contents / 509 \\
Applications / 509 \\
Method / 509 \\
Orthogonal Polynomials / 510 \\
Test Driver Orthogonal Polynomials / 513 \\
\\
23. Bernoulli and Euler Numbers and Polynomials,
Riemann Zeta Function / 516 \\
Introduction / 516 \\
Riemann Zeta Function / 516 \\
Bernoulli Polynomials and Numbers / 517 \\
Euler Polynomials and Numbers / 517 \\
Methods / 517 \\
References / 517 \\
Riemann Zeta (real arguments) / 519 \\
Test Driver Riemann Zeta (Real) / 527 \\
Test Output: Riemann Zeta, Bernoulli, Euler Numbers /
324 \\
\\
24. Combinatorics. Stirling Numbers / 529 \\
Introduction / 529 \\
Methods / 529 \\
References / 529 \\
Stirling Numbers First and Second Kind / 530 \\
Fibonacci Numbers / 531 \\
Binomial Coefficients / 532 \\
Test Driver for Stirling Numbers / 533 \\
Test Output: Stirling, Fibonacci, Binomial Coefficients
/ 534 \\
\\
25. Numerical Analysis / 535 \\
Discussion / 535 \\
Reference / 536 \\
\\
26. Statistical Functions, Probability Distributions,
and Random Variables / 537 \\
Introduction / 537 \\
Methods / 537 \\
References / 537 \\
Random Numbers / 538 \\
Random Distributions / 544 \\
Test Driver for Random Number / 551 \\
Test Output: Random Numbers and Distributions / 560 \\
Calculator Version of Stat.c Routines / 565 \\
\\
27. Miscellaneous Functions / 592 \\
Introduction / 592 \\
Debye Functions / 592 \\
Method / 593 \\
Sievert / 593 \\
Method / 593 \\
Abramowitz and Kruse--Ramsey / 593 \\
Method / 593 \\
Ritchie / 593 \\
Method / 593 \\
Dilogarithm and Polylogarithms / 593 \\
Method / 594 \\
Claussen / 594 \\
Method / 594 \\
Lobachevsky / 594 \\
Method / 594 \\
Clebsch--Gordon and Relatives / 594 \\
Method / 595 \\
v and Relatives / 595 \\
Method / 596 \\
References / 596 \\
Figures / 595 \\
Sievert Integral Chapter 27 / 605 \\
Dilogarithm / 606 \\
Polylogarithm Function / 607 \\
``Abramowitz'' Functions f1, f2, f3 from Chapter 27 /
608 \\
Nu and Mu Integrals of Erdelyi Vol III p. 217 / 612 \\
Lobachevsky Function / 614 \\
Test Driver Miscellaneous Functions / 616 \\
Test Driver Ritchie's Integral / 619 \\
Test Output: Miscellaneous Functions / 620 \\
Test Output: Ritchie's Integral / 624 \\
Clebsch--Gordon, Wigner, Related Coefficients / 625 \\
Test Driver Wigner / 631 \\
Wigner Sample Output / 635 \\
\\
28. Scales of Notation / 636 \\
\\
29. C++ Programs / 637 \\
Hurwitz Zeta and Lerch Phi Transcendent / 638 \\
Methods / 638 \\
Meijer $G$ and Generalized Hypergeometric Functions /
638 \\
Methods / 639 \\
Elliptic Functions / 639 \\
Applications / 639 \\
Methods / 639 \\
Fock Functions / 640 \\
Methods / 541 \\
References / 641 \\
// Complex.hpp / 643 \\
Elliptic Functions / 646 \\
Arithmetic--Geometric Mean (AGM) Supplemental / 656 \\
Test Driver for: Elliptic Functions / 662 \\
// Cvector.hpp / 665 \\
// cmatrix.hpp / 666 \\
Test Output: Elliptic Functions / 667 \\
Complex C++ Utilities / 669 \\
Fock Functions / 674 \\
Test Output: Fock Functions / 682 \\
``Abramowitz'' Functions f1, f2, f3 from Chapter 27 /
697 \\
Test Output: Abramowitz Functions, Complex Arguments /
701 \\
Riemann and Hurwitz / 712 \\
Riemann and Hurwitz: Pad{\'e} / 716 \\
Lerch Phi Transcendent / 720 \\
Generalized Hypergeometric Function and Meijer $G$ /
723 \\
Test Output: Meijer $G$ / 730 \\
Generalized Hypergeometric Function and Meijer $G$ /
731 \\
Test Output: Meijer $G$ with Pad{\'e} / 738 \\
MacRobert E Function / 739 \\
\\
30. Xref / 740 \\
Other Listings / 741 \\
Adaptive Quadrature (from C loops) / 741 \\
Test Driver Chaps. 16--18 / 743 \\
Index to C Functions / 747 \\
Index / 753",
}
@Article{Baker:1992:LCE,
author = "H. G. Baker",
title = "Less Complex Elementary Functions",
journal = j-SIGPLAN,
volume = "27",
number = "11",
pages = "15--16",
month = nov,
year = "1992",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Sep 08 08:11:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Bohman:1992:FRP,
author = "Jan Bohman and Carl-Erik Fr{\"o}berg",
title = "The {$ \Gamma $}-function revisited: power series
expansions and real-imaginary zero lines",
journal = j-MATH-COMPUT,
volume = "58",
number = "197",
pages = "315--322",
month = jan,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33B15 (11Y70 65D20)",
MRnumber = "92e:33001",
MRreviewer = "A. de Castro Brzezicki",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Borwein:1992:FEG,
author = "J. M. Borwein and I. J. Zucker",
title = "Fast evaluation of the gamma function for small
rational fractions using complete elliptic integrals of
the first kind",
journal = j-IMA-J-NUMER-ANAL,
volume = "12",
number = "4",
pages = "519--526",
year = "1992",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65D20",
MRnumber = "93g:65028",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Buhring:1992:GHF,
author = "Wolfgang B{\"u}hring",
title = "Generalized hypergeometric functions at unit
argument",
journal = j-PROC-AM-MATH-SOC,
volume = "114",
number = "1",
pages = "145--153",
month = "????",
year = "1992",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "33C20",
MRnumber = "MR1068116 (92c:33004)",
bibdate = "Thu Dec 01 09:52:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "Zbl 0754.33003",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
remark = "The paper treats $_{p + 1F}_p$ (or equivalently, $_p
F_{p - 1}$ ).",
}
@Article{Carlson:1992:TEI,
author = "B. C. Carlson",
title = "A Table of Elliptic Integrals: Two Quadratic Factors",
journal = j-MATH-COMPUT,
volume = "59",
number = "199",
pages = "165--180",
month = jul,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33C75 33E05)",
MRnumber = "92k:65027",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Corless:1992:NEAa,
author = "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
title = "Numerical evaluation of {Airy} functions with complex
arguments",
journal = j-J-COMPUT-PHYS,
volume = "98",
number = "2",
pages = "347--347",
month = feb,
year = "1992",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(92)90150-W",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:53 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199919290150W",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Corless:1992:NEAb,
author = "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
title = "Numerical evaluation of {Airy} functions with complex
arguments",
journal = j-J-COMPUT-PHYS,
volume = "99",
number = "1",
pages = "106--114",
month = mar,
year = "1992",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(92)90279-8",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
MRclass = "65D20 (33E30)",
MRnumber = "92k:65028",
bibdate = "Mon Jan 2 07:55:54 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999192902798",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
keywords = "Maple",
}
@Article{Croft:1992:ACA,
author = "A. Croft",
title = "An application of convergence acceleration techniques
to a class of two-point boundary value problems on a
semi-infinite domain",
journal = j-NUMER-ALGORITHMS,
volume = "2",
number = "3--4",
pages = "307--320",
month = sep,
year = "1992",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65L10 (65B99)",
MRnumber = "93g:65097",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation);
C4170 (Differential equations)",
corpsource = "Dept. of Math. Sci., Leicester Polytech., UK",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "boundary condition; boundary-value problems;
convergence acceleration; convergence acceleration
algorithms; convergence of numerical methods;
extrapolate; extrapolation; semi-infinite domain;
two-point boundary value problems; unbounded domains",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{Dattoli:1992:GFM,
author = "G. Dattoli and C. Chiccoli and S. Lorenzutta and G.
Maino and M. Richetta and A. Torre",
title = "Generating functions of multivariable generalized
{Bessel} functions and {Jacobi}-elliptic functions",
journal = j-J-MATH-PHYS,
volume = "33",
number = "1",
pages = "25--36",
month = jan,
year = "1992",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.529959",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "33E05 (33C10 34B30 42A16 42A85)",
MRnumber = "92m:33037",
MRreviewer = "J. M. H. Peters",
bibdate = "Tue Nov 1 08:57:37 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v33/i1/p25_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "12",
}
@Article{DiDonato:1992:ASD,
author = "Armido R. {DiDonato} and Alfred H. {Morris, Jr.}",
title = "{Algorithm 708}: Significant Digit Computation of the
Incomplete Beta Function Ratios",
journal = j-TOMS,
volume = "18",
number = "3",
pages = "360--373",
month = sep,
year = "1992",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 19 13:14:47 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Brown:1994:CAS}.",
URL = "http://doi.acm.org/10.1145/131766.131776;
http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p360-didonato/",
abstract = "An algorithm is given for evaluating the incomplete
beta function ratio $ I_x(a, b) $ and its complement $
1 - I^x(a, b) $. A new continued fraction and a new
asymptotic series are used with classical results. A
transportable Fortran subroutine based on this
algorithm is currently in use. It is accurate to 14
significant digits when precision is not restricted by
inherent error.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation.",
}
@InProceedings{Dubois:1992:CFQ,
author = "D. Dubois and H. Prade",
title = "Calculation with fuzzy quantities",
crossref = "EC2:1992:DJN",
bookpages = "384",
pages = "24--27",
year = "1992",
bibdate = "Thu Dec 14 17:22:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In some instances where numerical data are either
provisional, incomplete, or variable within a limited
range, the classical calculation of confidence
intervals can be extended in a fuzzy-set approach,
distinguishing between more or less plausible values.
The simultaneous use of relatively wide intervals
containing all possible values, and generally much
narrower intervals covering only the most likely ones,
can give sufficiently informative results. Some
precautions advisable in arithmetic operations on
imprecisely known quantities are outlined. Examples of
application include provisional budgeting, resource
estimation, evaluation of candidates, and extension of
PERT to projects involving precedence among elementary
tasks with uncertain durations and/or starting times.
Computer-aided engineering design can also benefit from
fuzzy specifications for values eventually to be
optimised.",
acknowledgement = ack-nhfb,
affiliation = "IRIT, Paul Sabatier Univ., Toulouse, France",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic); C7310 (Mathematics)",
confdate = "2-3 Nov. 1992",
conflocation = "Nimes, France",
keywords = "Arithmetic operations; Candidates; Confidence
intervals; Engineering design; Fuzzy quantities; Fuzzy
specifications; Fuzzy-set approach; Imprecisely known
quantities; Numerical data; PERT; Provisional
budgeting; Resource estimation",
language = "French",
pubcountry = "France",
thesaurus = "Fuzzy logic; Fuzzy set theory; Statistical analysis",
}
@Article{Feinsilver:1992:BFR,
author = "P. Feinsilver and R. Schott",
title = "On {Bessel} functions and rate of convergence of zeros
of {Lommel} polynomials",
journal = j-MATH-COMPUT,
volume = "59",
number = "199",
pages = "153--156",
month = jul,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33C10 (33C45)",
MRnumber = "93a:33007",
MRreviewer = "Boro D{\"o}ring",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
affiliation = "Southern Illinois Univ., Carbondale, IL, USA",
classcodes = "B0220 (Analysis); B0290P (Differential equations);
B0290F (Interpolation and function approximation);
B0210 (Algebra); C1120 (Analysis); C4170 (Differential
equations); C4130 (Interpolation and function
approximation); C1110 (Algebra)",
classification = "B0210 (Algebra); B0220 (Analysis); B0290F
(Interpolation and function approximation); B0290P
(Differential equations); C1110 (Algebra); C1120
(Analysis); C4130 (Interpolation and function
approximation); C4170 (Differential equations)",
corpsource = "Southern Illinois Univ., Carbondale, IL, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "average case analysis; Average case analysis; Bessel
function; Bessel functions; convergence of numerical
methods; convergence rate; Convergence rate; data
structures; differential equations; dynamic; Dynamic
data structures; Lommel; Lommel polynomials; Maple
program; polynomials; rate of convergence; Rate of
convergence; zeros; Zeros",
thesaurus = "Bessel functions; Convergence of numerical methods;
Differential equations; Polynomials",
treatment = "T Theoretical or Mathematical",
}
@Article{Fillebrown:1992:FCB,
author = "Sandra Fillebrown",
title = "Faster computation of {Bernoulli} numbers",
journal = j-J-ALG,
volume = "13",
number = "3",
pages = "431--445",
month = sep,
year = "1992",
CODEN = "JOALDV",
DOI = "https://doi.org/10.1016/0196-6774(92)90048-H",
ISSN = "0196-6774 (print), 1090-2678 (electronic)",
ISSN-L = "0196-6774",
bibdate = "Tue Dec 11 09:15:18 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jalg.bib",
URL = "http://www.sciencedirect.com/science/article/pii/019667749290048H",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms",
journal-URL = "http://www.sciencedirect.com/science/journal/01966774",
remark = "The author gives algorithms for computing Bernoulli
numbers of high order that require at most $ \lfloor 2
n \lg n \rfloor $ bits. One algorithm requires $ O(n^2
\log n) $ multiplications of numbers of $ O(n \log n) $
bits, and the other need $ O(n) $ multiplications of
numbers of $ O(n \log n) $ bits.",
}
@Article{Giordano:1992:FMC,
author = "Carla Giordano and Lucia G. Rodon{\`o}",
title = "Further monotonicity and convexity properties of the
zeros of cylinder functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "42",
number = "2",
pages = "245--251",
day = "12",
month = oct,
year = "1992",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:54 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279290078C",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Ifantis:1992:DIP,
author = "E. K. Ifantis and P. D. Siafarikas",
title = "A differential inequality for the positive zeros of
{Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "44",
number = "1",
pages = "115--120",
day = "9",
month = dec,
year = "1992",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:56 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042792900553",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Jiang:1992:CCM,
author = "Thomas J. Jiang and Joseph B. Kadane and James M.
Dickey",
title = "Computation of {Carlson}'s Multiple Hypergeometric
Function {$R$} for {Bayesian} Applications",
journal = j-J-COMPUT-GRAPH-STAT,
volume = "1",
number = "3",
pages = "231--251",
month = sep,
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1080/10618600.1992.10474583",
ISSN = "1061-8600 (print), 1537-2715 (electronic)",
ISSN-L = "1061-8600",
MRclass = "33C90 (62F15 65D20)",
MRnumber = "95e:33021",
MRreviewer = "P. N. Rathie",
bibdate = "Thu Aug 13 10:27:39 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputgraphstat.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/10618600.1992.10474583",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Graphical Statistics",
journal-URL = "http://www.amstat.org/publications/jcgs/;
http://www.tandfonline.com/loi/ucgs20",
onlinedate = "21 Feb 2012",
xxtitle = "Computation of {Carlson}'s multiple hypergeometric
function {$ {\cal R} $} for {Bayesian} applications",
}
@Book{Johnson:1992:UDD,
author = "Norman Lloyd Johnson and Samuel Kotz and Adrienne W.
Kemp",
title = "Univariate Discrete Distributions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xx + 565",
year = "1992",
ISBN = "0-471-54897-9 (hardcover)",
ISBN-13 = "978-0-471-54897-3 (hardcover)",
LCCN = "QA273.6 .J64 1992",
bibdate = "Sat Feb 7 17:19:01 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley series in probability and mathematical
statistics. Applied probability and statistics",
URL = "http://www.loc.gov/catdir/description/wiley031/92011685.html;
http://www.loc.gov/catdir/enhancements/fy0607/92011685-b.html;
http://www.loc.gov/catdir/toc/onix01/92011685.html",
acknowledgement = ack-nhfb,
remark = "Revised edition of \booktitle{Discrete distributions},
Norman L. Johnson, Samuel Kotz. 1969.",
shorttableofcontents = "Preface \\
Preliminary Information \\
Families of Discrete Distributions \\
Binomial Distributions \\
Poisson Distributions \\
Neggative Binomial Distributions \\
Hypergeometric Distributions \\
Logarithmic and Lagrangian Distributions \\
Mixture Distributions \\
Stopped-Sum Distributions \\
Matching, Occupancy, Runs, and q-Series Distributions
\\
Parametric Regression Models and Miscellanea \\
Bibliography \\
Abbreviations \\
Index",
subject = "Distribution (Probability theory)",
tableofcontents = "Preface / xv \\
List of Tables / xix \\
1. Preliminary Information / 1 \\
A. Mathematical Preliminaries \\
B. Probability and Statistical Preliminaries \\
C. Computer Generation of Univariate Discrete Random
Variables \\
2. Families of Discrete Distributions / 69 \\
1. Lattice Distributions \\
2. Power Series Distributions \\
3. Difference Equation Systems \\
4. Kemp Families \\
5. Distributions Based on Lagrangian Expansions \\
6. Factorial Series Distributions \\
3. Binomial Distribution / 105 \\
1. Definition \\
2. Historical Remarks and Genesis \\
3. Moments \\
4. Properties \\
5. Order Statistics \\
6. Approximations, Bounds, and Transformations \\
7. Computation and Tables \\
8. Estimation \\
9. Characterizations \\
10. Applications \\
11. Truncated Binomial Distributions \\
12. Other Related Distributions \\
4. Poisson Distribution / 151 \\
1. Definition \\
2. Historical Remarks and Genesis \\
3. Moments \\
4. Properties \\
5. Approximations, Bounds, and Transformations \\
6. Computation and Tables \\
7. Estimation \\
8. Characterizations \\
9. Applications \\
10. Truncated and Misrecorded Poisson Distributions \\
11. Poisson-Stopped-Sum Distributions \\
12. Other Related Distributions \\
5. Negative Binomial Distribution / 199 \\
1. Definition \\
2. Geometric Distribution \\
3. Historical Remarks and Genesis \\
4. Moments \\
5. Properties \\
6. Approximations and Transformations \\
7. Computation and Tables \\
8. Estimation \\
9. Characterizations \\
10. Applications \\
11. Truncated Negative Binomial Distributions \\
12. Other Related Distributions \\
6. Hypergeometric Distributions / 237 \\
1. Definition \\
2. Historical Remarks and Genesis \\
3. Moments \\
4. Properties \\
5. Approximations and Bounds \\
6. Tables and Computation \\
7. Estimation \\
8. Characterizations \\
9. Applications \\
10. Special Cases \\
11. Extended Hypergeometric Distributions \\
12. Other Related Distributions \\
7. Logarithmic Distribution / 285 \\
1. Definition \\
2. Historical Remarks and Genesis \\
3. Moments \\
4. Properties \\
5. Approximations and Bounds \\
6. Computation and Tables \\
7. Estimation \\
8. Characterizations \\
9. Applications \\
10. Truncated and Modified Logarithmic Distributions
\\
11. Other Related Distributions \\
8. Mixture Distributions / 305 \\
1. Introduction \\
2. Finite Mixtures of Discrete Distributions \\
3. Continuous and Countable Mixtures of Discrete
Distributions \\
9. Generalized (Stopped-Sum) Distributions / 343 \\
1. Introduction \\
2. Damage Processes \\
3. Poisson-Stopped-Sum Distributions: Generalized
Poisson Distributions \\
4. Hermite Distribution \\
5. Poisson-Binomial Distribution \\
6. Neyman Type A Distribution \\
7. Polya--Aeppli Distribution \\
8. Poisson--Pascal Distribution: Poisson-Negative
Binomial Distribution, Generalized Polya--Aeppli
Distribution \\
9. Generalizations of the Neyman Type A Distribution
\\
10. Thomas Distribution \\
11. Lagrangian Poisson Distribution: Shifted
Borel--Tanner Distribution \\
12. Other Families of Stopped-Sum Distributions \\
10. Matching, Occupancy, and Runs Distributions / 405
\\
1. Introduction \\
2. Probabilities of Combined Events \\
3. Matching Distributions \\
4. Occupancy Distributions \\
5. Runs Distributions \\
6. Distributions of Order k \\
11. Miscellaneous Discrete Distributions / 433 \\
1. Absorption Distribution \\
2. Dandekar's Modified Binomial and Poisson
Distributions \\
3. Digammma and Trigamma Distributions \\
4. Discrete Ad{\`e}s Distribution \\
5. Discrete Student's $t$-Distribution \\
6. Geeta Distribution \\
7. Gegenbauer Distribution: Negative Binomial*
Pseudo-Negative Binomial Convolution \\
8. Gram-Charlier Type B Distributions \\
9. ``Interrupted'' Distributions \\
10. Lost-Games Distributions \\
11. Naor's Distribution \\
12. Partial-Sums Distributions \\
13. Queueing Theory Distributions \\
14. Record-Value Distributions \\
15. Sichel Distribution: Poisson-Inverse Gaussian
Distribution \\
16. Skellam's Gene Frequency Distribution \\
17. Steyn's Two-Parameter Power Series Distributions
\\
18. Univariate Multinomial-Type Distributions \\
19. Urn Models with Stochastic Replacements \\
20. Zipf and Zeta Distributions \\
Bibliography / 473 \\
Abbreviations / 549 \\
Index / 551",
}
@Article{Kearfott:1992:IPF,
author = "Baker Kearfott and Milind Dawande and Kaisheng Du and
Chen-Yi Hu",
title = "{INTLIB}: a Portable {FORTRAN} 77 Elementary Function
Library",
journal = j-INTERVAL-COMP,
volume = "3",
number = "5",
pages = "96--105",
year = "1992",
ISSN = "0135-4868",
MRclass = "65G10",
MRnumber = "1 253 132",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Interval '92 (Moscow, 1992).",
acknowledgement = ack-nhfb,
fjournal = "Interval Computations = Interval'nye vychisleniia",
}
@Article{Kzaz:1992:CAS,
author = "M. Kzaz",
title = "Convergence acceleration of some {Gaussian} quadrature
formulas for analytic functions",
journal = j-APPL-NUM-MATH,
volume = "10",
number = "6",
pages = "481--496",
month = nov,
year = "1992",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65B10 (65D32)",
MRnumber = "93j:65004",
MRreviewer = "J. Kofro{\v{n}}",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@Article{Lang:1992:HRS,
author = "T. Lang and P. Montuschi",
title = "Higher radix square root with prescaling",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "996--1009",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156542",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A scheme for performing higher radix square root based
on prescaling of the radicand is presented to reduce
the complexity of the result-digit selection. The
scheme requires several steps, namely multiplication
for prescaling the radicand, square \ldots{}",
}
@Article{Lee:1992:LCF,
author = "Chu-In Charles Lee",
title = "On {Laplace} continued fraction for the normal
integral",
journal = j-ANN-INST-STAT-MATH-TOKYO,
volume = "44",
number = "1",
pages = "107--120",
month = mar,
year = "1992",
CODEN = "AISXAD",
DOI = "https://doi.org/10.1007/BF00048673",
ISSN = "0020-3157 (print), 1572-9052 (electronic)",
ISSN-L = "0020-3157",
bibdate = "Sat Jan 31 16:59:48 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/BF00048673",
acknowledgement = ack-nhfb,
fjournal = "Annals of the Institute of Statistical Mathematics",
journal-URL = "http://link.springer.com/journal/10463",
}
@InProceedings{Liu:1992:QBS,
author = "K. J. R. Liu and E. Frantzeskakis",
booktitle = "Workshop on {VLSI} Signal Processing, V, 1992",
title = "Qrd-based Square Root Free and Division Free
Algorithms and Architectures",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "459--468",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@Misc{Lynch:1992:HSD,
author = "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
T. Hurson",
title = "High speed divider with square root capability",
year = "1992",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,128,891.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Martin:1992:TPQa,
author = "Pablo Martin and Ricardo P{\'e}rez and Antonio L.
Guerrero",
title = "Two-point quasi-fractional approximations to the
{Airy} function {$ {\rm Ai}(x) $}",
journal = j-J-COMPUT-PHYS,
volume = "98",
number = "2",
pages = "349--349",
month = feb,
year = "1992",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(92)90165-U",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:53 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199919290165U",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Martin:1992:TPQb,
author = "Pablo Mart{\'\i}n and Ricardo P{\'e}rez and Antonio L.
Guerrero",
title = "Two-point quasi-fractional approximations to the
{Airy} function {$ {\rm Ai}(x) $}",
journal = j-J-COMPUT-PHYS,
volume = "99",
number = "2",
pages = "337--340",
month = apr,
year = "1992",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(92)90212-H",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:55 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199919290212H",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Matos:1992:CAP,
author = "Ana C. Matos",
title = "Convergence and acceleration properties for the vector
$ \epsilon $-algorithm",
journal = j-NUMER-ALGORITHMS,
volume = "3",
number = "1--4",
pages = "313--319",
month = dec,
year = "1992",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65B99",
MRnumber = "93h:65006",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Extrapolation and rational approximation (Puerto de la
Cruz, 1992).",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
conflocation = "Puerto de la Cruz, Spain; 13-17 Jan. 1992",
conftitle = "International Mathematical Congress on Extrapolation
and Rational Approximation",
corpsource = "Fac. de Ciencias, Porto Univ., Portugal",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "acceleration; convergence acceleration; convergence of
numerical methods; convergence speed; exactness;
extrapolation; extrapolation algorithm; speed of
convergence; vector $\epsilon$-algorithm; vector
sequences",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{McQuillan:1992:VMH,
author = "S. E. McQuillan and J. V. McCanny",
title = "{VLSI} module for high-performance multiply, square
root and divide",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "139",
number = "6",
pages = "505--510",
month = nov,
year = "1992",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
summary = "A high-performance VLSI architecture to perform
multiply-accumulate, division and square root
operations is proposed. The circuit is highly regular,
requires only minimal control and ean be pipelined
right down to the bit level. The system can also
\ldots{}",
}
@Article{Mikami:1992:NDO,
author = "N. Mikami and M. Kobayashi and Y. Yokoyama",
title = "A New {DSP}-Oriented Algorithm for Calculation of the
Square Root Using a Nonlinear Digital Filter",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "7",
pages = "1663--1669",
month = jul,
year = "1992",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.143438",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "A high-speed algorithm for calculating the square root
is proposed. This algorithm, which can be regarded as
calculation of the step response of a kind of nonlinear
IIR filter, requires no divisions. Therefore, it is
suitable for a VLSI digital \ldots{}",
}
@Article{Mitchell:1992:VFA,
author = "H. B. Mitchell",
title = "Very fast accurate square-root algorithm for use with
gradient edge operators",
journal = j-ELECT-LETTERS,
volume = "28",
number = "10",
pages = "922--923",
day = "7",
month = may,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "Commonly used gradient edge operators such as the
Sobel, Prewitt and Roberts operators all required a
square root operation; this is, however,
computationally intensive and, consequently, simple but
very inaccurate approximations are often used
\ldots{}",
}
@Article{Paris:1992:EIA,
author = "R. B. Paris and A. D. Wood",
title = "Exponentially-improved asymptotics for the gamma
function",
journal = j-J-COMPUT-APPL-MATH,
volume = "41",
number = "1--2",
pages = "135--143",
day = "20",
month = aug,
year = "1992",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:53 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279290243Q",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Paszkowski:1992:CAC,
author = "Stefan Paszkowski",
title = "Convergence acceleration of continued fractions of
{Poincar{\'e}}'s type $1$",
journal = j-NUMER-ALGORITHMS,
volume = "2",
number = "2",
pages = "155--170",
month = "????",
year = "1992",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65B05 (40A15)",
MRnumber = "93c:65006",
MRreviewer = "A. Bultheel",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Instytut Niskich Temp. i Badan Strukturalnych PAN,
Wroclaw, Poland",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "asymptotic behaviour; continued fractions; convergence
acceleration; convergence of numerical methods;
function approximation",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Book{Prudnikov:1992:IS,
author = "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
Oleg I. Mari{\v{c}}ev",
title = "Integrals and series. {More} special functions",
volume = "3",
publisher = "Gordon and Breach Science Publishers",
address = "New York, NY, USA",
pages = "xx + 618",
year = "1992",
ISBN = "2-88124-097-6",
ISBN-13 = "978-2-88124-097-3",
LCCN = "QA308 P68 1986",
bibdate = "Thu Nov 2 15:54:36 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Translated from the Russian by N. M. Queen.",
seriestableofcontents = "v. 1. Elementary functions \\
v. 2. Special functions \\
v. 3. More special functions \\
v. 4. Direct Laplace transforms \\
v. 5. Inverse Laplace transforms",
subject = "Mathematics",
}
@Article{Salwin:1992:UPE,
author = "Arthur E. Salwin",
title = "Using the Proposed Elementary Functions Standard to
Build a Strongly Typed Trig Package",
journal = j-SIGADA-LETTERS,
volume = "12",
number = "5",
pages = "59--63",
month = sep # "\slash " # oct,
year = "1992",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:46 MDT 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages)",
corpsource = "Mitre Corp., McLean, VA, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; compiler; elementary functions standard;
standards; strong typing; strongly typed trig package;
trigonometric functions",
treatment = "P Practical",
}
@Article{Saunders:1992:EFS,
author = "L. R. Saunders",
title = "An Exact Formula for the Symmetrical Incomplete Beta
Function Where the Parameter Is an Integer or
Half-Integer",
journal = j-AUST-J-STAT,
volume = "34",
number = "2",
pages = "261--264",
month = jun,
year = "1992",
CODEN = "AUJSA3",
DOI = "https://doi.org/10.1111/j.1467-842X.1992.tb01358.x",
ISSN = "0004-9581",
ISSN-L = "0004-9581",
bibdate = "Fri Jul 15 14:28:59 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/anzjs.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Australian Journal of Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-842X/issues",
}
@MastersThesis{Schulte:1992:AHD,
author = "Michael Joseph Schulte and Function generation",
title = "Algorithms and hardware designs for parallel
elementary function generation",
type = "Thesis ({M.S.} in Engin.)",
school = "University of Texas at Austin",
address = "Austin, TX, USA",
pages = "ix + 73",
year = "1992",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "Computer input-output equipment -- Design and
construction.; Computer science -- Mathematics.;
Numerical analysis.; Parallel processing (Electronic
computers)",
searchkey = "ti:elementary n1 function",
}
@Article{Tang:1992:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the {{\tt Expm1}}
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "18",
number = "2",
pages = "211--222",
month = jun,
year = "1992",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/146847.146928",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15",
MRnumber = "1 167 891",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See independent analysis and accuracy confirmation of
this algorithm in \cite{Kramer:1998:PWC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
abstract = "Algorithms and implementation details for the function
$ e^x - 1 $ in both single and double precision of IEEE
754 arithmetic are presented here. With a table of
moderate size, the implementations need only
working-precision arithmetic and are provably accurate
to within 0.58 ulp.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@Article{Temme:1992:AII,
author = "N. M. Temme",
title = "Asymptotic Inversion of Incomplete Gamma Functions",
journal = j-MATH-COMPUT,
volume = "58",
number = "198",
pages = "755--764",
month = apr,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33B20",
MRnumber = "93a:33003",
MRreviewer = "F. W. J. Olver",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wong:1992:DSR,
author = "W. F. Wong and E. Goto",
title = "Division and square-rooting using a split multiplier",
journal = j-ELECT-LETTERS,
volume = "28",
number = "18",
pages = "1758--1759",
day = "27",
month = aug,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "A modification is proposed to the traditional design
of a fast floating point multiplication circuit such
that instead of just performing A$\times$B where A and
B are m bits long, it is also capable of \ldots{}",
}
@TechReport{Wood:1992:CP,
author = "David C. Wood",
title = "The Computation of Polylogarithms",
type = "Report",
institution = "University of Kent",
address = "Canterbury, Kent CT2 7NZ, UK",
year = "1992",
bibdate = "Fri Jun 30 10:12:54 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.cs.kent.ac.uk/pubs/1992/110/content.pdf",
abstract = "The polylogarithm function, $ \Li_p(z) $, is defined,
and a number of algorithms are derived for its
computation, valid in different ranges of its real
parameter $p$ and complex argument $z$.",
acknowledgement = ack-nhfb,
keywords = "polylogarithm",
remark = "Undated, but its URL suggests the year. The PDF file
was created 20-Mar-2014. The latest reference is to a
1992 journal article.",
}
@InProceedings{Woods:1992:HPD,
author = "R. F. Woods and S. E. McQuillan and J. Dowling and J.
V. McCanny",
booktitle = "Proceedings of Fifth Annual {IEEE} International
{ASIC} Conference and Exhibit, 1992",
title = "High performance {DSP} {ASIC} for multiply, divide and
square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "209--213",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The design of a high-speed ASIC that combines the
operations of multiplication, division and square root
is described. The chip is based on a systolic array
architecture that uses a redundant number system and
allows multiplication, division, and \ldots{}",
}
@Article{Yeyios:1992:TSA,
author = "A. K. Yeyios",
title = "On two sequences of algorithms for approximating
square roots",
journal = j-J-COMPUT-APPL-MATH,
volume = "40",
number = "1",
pages = "63--72",
month = jun,
year = "1992",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Alzer:1993:SGF,
author = "Horst Alzer",
title = "Some gamma function inequalities",
journal = j-MATH-COMPUT,
volume = "60",
number = "201",
pages = "337--346",
month = jan,
year = "1993",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33B15 (26D20)",
MRnumber = "93f:33001",
MRreviewer = "Aurelio Cannizzo",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Periodical{Anonymous:1993:ITS,
author = "Anonymous",
title = "Integral transforms and special functions",
publisher = "Gordon and Breach Science Publishers",
address = "Yverdon, Switzerland",
year = "1993",
ISSN = "1065-2469, 1476-8291",
ISSN-L = "1065-2469",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Appears with variable frequency from 1993--2001, and
six times yearly from 2002--date.",
acknowledgement = ack-nhfb,
}
@Article{Arenstorf:1993:SMZ,
author = "R. F. Arenstorf and L. L. Brewer",
title = "A study of the motion of zeros of the {Epstein} zeta
function associated to $ m^2 + y^2 n^2 $ as $y$ varies
from $1$ to $ \sqrt {6}$",
journal = j-COMPUT-MATH-APPL,
volume = "26",
number = "5",
pages = "57--69",
month = sep,
year = "1993",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(93)90074-6",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122193900746",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Bailey:1993:AMT,
author = "D. H. Bailey",
title = "Algorithm 719: Multiprecision Translation and
Execution of {FORTRAN} Programs",
journal = j-TOMS,
volume = "19",
number = "3",
pages = "288--319",
month = sep,
year = "1993",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Dec 13 18:37:31 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The author describes two Fortran utilities for
multiprecision computation. The first is a package of
Fortran subroutines that perform a variety of
arithmetic operations and transcendental functions on
floating point numbers of arbitrarily high precision.
This package is in some cases over 200 times faster
than that of certain other packages that have been
developed for this purpose. The second utility is a
translator program, which facilitates the conversion of
ordinary Fortran programs to use this package. By means
of source directives (special comments) in the original
Fortran program, the user declares the precision level
and specifies which variables in each subprogram are to
be treated as multiprecision. The translator program
reads this source program and outputs a program with
the appropriate multiprecision subroutine calls. This
translator supports multiprecision integer, real, and
complex datatypes. The required array space for
multiprecision data types is automatically allocated.
In the evaluation of computational expressions, all of
the usual conventions for operator precedence and mixed
mode operations are upheld. Furthermore, most of the
Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
are supported and produce true multiprecision values.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "NASA Ames Res. Center, Moffett Field, CA, USA",
classification = "C5230 (Digital arithmetic methods); C6120 (File
organisation); C6140D (High level languages); C6150C
(Compilers, interpreters and other processors); C7310
(Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Algorithm 719; Arithmetic operations; Array space;
Complex data types; Computational expressions; Floating
point numbers; Fortran programs; Fortran subroutines;
Fortran utilities; Fortran-77 intrinsics; Mixed mode
operations; Multiprecision computation; Multiprecision
data types; Multiprecision subroutine calls;
Multiprecision translation; Operator precedence; Source
directives; Transcendental functions; Translator
program",
pubcountry = "USA",
thesaurus = "Data structures; Digital arithmetic; FORTRAN;
Mathematics computing; Program interpreters;
Subroutines",
}
@Article{Barrera:1993:IBS,
author = "Tony Barrera and Pelle Olsson",
title = "An Integer Based Square Root Algorithm",
journal = j-BIT,
volume = "33",
number = "2",
pages = "253--261",
month = jun,
year = "1993",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01989748",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68M07",
MRnumber = "1 326 017",
bibdate = "Wed Jan 4 18:52:23 MST 2006",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=33&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit33.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
abstract = "The authors propose a fast integer based method for
computing square roots of floating point numbers. This
implies high accuracy and robustness, since no
precision will be lost during the computation. Only
integer addition and shifts are necessary to obtain the
square root. Comparisons made with the modified Newton
method indicate that the suggested method is twice as
fast for computing floating point square roots. (5
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "AB Consonant, Uppsala, Sweden",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Floating point numbers; floating-point arithmetic;
Integer based square root algorithm; Modified Newton
method; Robustness",
pubcountry = "Denmark",
thesaurus = "Digital arithmetic",
xxpages = "254--261??",
}
@InCollection{Bohlender:1993:PAF,
author = "G. Bohlender and D. Cordes and A. Knofel and U.
Kulisch and R. Lohner and W. V. Walter",
title = "Proposal for accurate floating-point vector
arithmetic",
crossref = "Adams:1993:ACA",
bookpages = "x + 612",
pages = "87--102",
year = "1993",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Many computers provide accurate and reliable scalar
arithmetic for floating point numbers. An accurate
definition of the four elementary floating-point
operations +, -, *, / is given in the IEEE standards
for floating-point arithmetic and was well established
long before. An increasing number of computers
(especially PC's and workstations) feature IEEE
arithmetic. In many numerical algorithms, however,
compound operations such as the summation of a sequence
of numbers or the dot product of two vectors are highly
common. A simulation of these compound operations by
means of elementary floating-point operations leads to
accumulation of rounding errors and may suffer from
catastrophic cancellation of leading digits. Existing
standards for floating-point arithmetic do not improve
this situation. The goal of the proposal is to define
vector operations in a manner consistent with the
elementary scalar arithmetic operations. The rounding
modes and accuracy requirements as well as the data
formats of the operands and results of the vector
operations described in the proposal are chosen to be
fully consistent with the existing scalar
floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C7310 (Mathematics)",
keywords = "Accuracy requirements; Catastrophic cancellation;
Compound operations; Data formats; Dot product;
Elementary floating-point operations; Elementary scalar
arithmetic operations; Floating point numbers; IEEE
arithmetic; IEEE standards; Leading digits; Numerical
algorithms; Operands; Rounding errors; Rounding modes;
Scalar floating-point arithmetic; Sequence; Standards;
Summation; Vector operations",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Mathematics computing; Roundoff
errors; Standards",
}
@Article{Cody:1993:ACP,
author = "W. J. Cody",
title = "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
for Complex Elementary Functions",
journal = j-TOMS,
volume = "19",
number = "1",
pages = "1--21",
month = mar,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/151271.151272",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Sep 20 18:24:35 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/;
http://www.acm.org/pubs/toc/Abstracts/toms/151272.html",
abstract = "This paper discusses CELEFUNT, a package of Fortran
programs for testing complex elementary functions.",
abstract-2 = "The author discusses CELEFUNT, a package of Fortran
programs for testing complex elementary functions.
CELEFUNT is a collection of test programs for the
complex floating-point elementary functions required by
the 1978 ANSI Fortran Standard (CABS), CSQRT, CLOG,
CEXP, CSIN/CCOS, and the complex power function.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
classification = "C4100 (Numerical analysis); C5230 (Digital
arithmetic methods); C7310 (Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex
elementary functions; Complex power function;
CSIN/CCOS; CSQRT; Floating-point elementary functions;
Fortran programs; measurement; performance; Portable
test package",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
thesaurus = "Conformance testing; Digital arithmetic; FORTRAN;
Mathematics computing; Numerical analysis; Program
testing; Software packages",
}
@Article{Cody:1993:ASP,
author = "W. J. {Cody, Jr.}",
title = "Algorithm 715: {SPECFUN}: a Portable {FORTRAN} Package
of Special Function Routines and Test Drivers",
journal = j-TOMS,
volume = "19",
number = "1",
pages = "22--32",
month = mar,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/151271.151273",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Sep 20 18:24:38 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/0098-3500/151273.html",
abstract = "SPECFUN is a package containing transportable FORTRAN
special function programs for real arguments and
accompanying test drivers. Components include Bessel
functions, exponential integrals, error functions and
related functions, and gamma functions and related
functions.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
USA",
classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "algorithms; Bessel functions; Error functions;
Exponential integrals; Gamma functions; Portable
FORTRAN package; Real arguments; SPECFUN; Special
function routines; Test drivers",
pubcountry = "USA",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
thesaurus = "FORTRAN; Mathematics computing; Numerical analysis;
Software packages; Software portability",
}
@Article{duToit:1993:BFI,
author = "C. F. du Toit",
title = "{Bessel} functions {$ J_n(z) $} and {$ Y_n(z) $} of
integer order and complex argument",
journal = j-COMP-PHYS-COMM,
volume = "78",
number = "1--2",
pages = "181--189",
month = dec,
year = "1993",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(93)90153-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:29:41 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465593901534",
abstract = "This paper describes computer subroutines which were
developed to compute Bessel functions of the first and
second kind ($ J_n(z) $ and $ Y_n(z) $, respectively)
for a complex argument $z$ and a range of integer
orders. A novel way of determining the starting point
of backward recurrence is used, and the algorithm for $
Y_n(z) $ improves on previous algorithms in terms of
accuracy and restrictions on the range of orders.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Book{Feinsilver:1993:ASO,
author = "Philip J. (Philip Joel) Feinsilver and Ren{\'e}
Schott",
title = "Algebraic Structures and Operator Calculus",
volume = "241, 292, 347",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "?????",
year = "1993, 1994, 1996",
ISBN = "0-7923-2116-2 (v. 1), 0-7923-2921-X (v. 2),
0-7923-3834-0 (v. 3)",
ISBN-13 = "978-0-7923-2116-3 (v. 1), 978-0-7923-2921-3 (v. 2),
978-0-7923-3834-5 (v. 3)",
LCCN = "QA432 .F45 1993",
bibdate = "Sat Oct 30 17:31:34 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Volume 1: Representations and probability theory.
Volume 2: Special functions and computer science.
Volume 3: Representations of Lie groups",
series = "Mathematics and its applications",
acknowledgement = ack-nhfb,
subject = "Calculus, Operational; Probabilities; Representations
of groups",
}
@Article{Fowkes:1993:HEA,
author = "R. E. Fowkes",
title = "Hardware Efficient Algorithms for Trigonometric
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "2",
pages = "235--239",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.204796",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204796",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Frappier:1993:QFI,
author = "Cl{\'e}ment Frappier and Patrick Olivier",
title = "A quadrature formula involving zeros of {Bessel}
functions",
journal = j-MATH-COMPUT,
volume = "60",
number = "201",
pages = "303--316",
month = jan,
year = "1993",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "41A55 (65D32)",
MRnumber = "93d:41025",
MRreviewer = "Hans Strauss",
bibdate = "Tue Mar 25 15:38:13 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
B0290M (Numerical integration and differentiation);
C4130 (Interpolation and function approximation); C4160
(Numerical integration and differentiation)",
corpsource = "Dept. de Math. Appliqu{\'e}es, Montreal, Que.,
Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; integration; interpolation; poles
and; polynomials; quadrature formula; sampling theorem;
zeros",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Han:1993:CAS,
author = "Weimin Han and Florian A. Potra",
title = "Convergence acceleration for some rootfinding
methods",
crossref = "Albrecht:1993:VNT",
volume = "9",
pages = "67--78",
year = "1993",
CODEN = "COSPDM",
ISSN = "0344-8029",
bibdate = "Sun Oct 17 11:55:48 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = j-COMPUTING-SUPPLEMENTUM,
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Article{Higginbotham:1993:ISR,
author = "T. F. Higginbotham",
title = "The integer square root of {$N$} via a binary search",
journal = j-SIGCSE,
volume = "25",
number = "4",
pages = "41--45",
month = dec,
year = "1993",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/164205.164229",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sat Nov 17 18:57:24 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
abstract = "An algorithm is presented which may be used to find
the integer square root of N. The method is intended
for use on a binary computer, where only addition,
subtraction, multiplication, or division by 2 is
required. The problem arose when the author was working
on factoring large numbers, where the machine, the
Honeywell DPS 8, had double precision integer addition
and subtraction, and the simulation of multiplication
was easy. The actual factoring of the large number was
to be Fermat's Method, requiring only addition and
subtraction, but the integer square root is required in
order to test for termination. The algorithm is
implemented in FORTRAN for ease of reading. Students
enjoy the unconventional approach to solving this
problem. It isn't long before some of them think of
other unusual solutions.",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Hu:1993:BRS,
author = "Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad",
title = "On Bounding the Range of Some Elementary Functions in
{FORTRAN} 77",
journal = j-INTERVAL-COMP,
volume = "1993",
number = "3",
pages = "29--39",
year = "1993",
ISSN = "0135-4868",
MRclass = "65G10",
MRnumber = "1 305 844",
bibdate = "Wed Dec 4 11:13:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the International Conference on
Numerical Analysis with Automatic Result Verification
(Lafayette, LA, 1993)",
acknowledgement = ack-nhfb,
fjournal = "Interval Computations = Interval'nye vychisleniia",
}
@TechReport{Karp:1993:HPD,
author = "A. H. Karp and P. Markstein",
title = "High precision division and square root",
number = "HPL-93-42",
institution = "Hewlett--Packard Lab.",
address = "Palo Alto, CA, USA",
pages = "20",
month = jun,
year = "1993",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present division and square root
algorithms for calculations with more bits than are
handled by the floating point hardware. These
algorithms avoid the need to multiply two high
precision numbers, speeding up the last iteration by as
much as a factor of ten.",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
keywords = "Division; Floating point hardware; Square root
algorithms",
thesaurus = "Digital arithmetic",
}
@InCollection{Kramer:1993:MPC,
author = "Walter Kr{\"a}mer",
booktitle = "Mathematics in Science and Engineering: Scientific
Computing with Automatic Result Verification",
title = "Multiple-Precision Computations with Result
Verification",
volume = "189",
publisher = "Elsevier BV",
address = "Amsterdam, The Netherlands",
pages = "325--356",
year = "1993",
DOI = "https://doi.org/10.1016/s0076-5392(08)62851-9",
bibdate = "Tue Mar 14 19:20:47 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "arithmetic-geometric mean iteration; computation of $
e^\pi $; computation of a large number of digits of
$\pi$; computation of elliptic integrals; computation
of guaranteed bounds for the natural logarithm;
interval arithmetic; PASCAL-XSC",
}
@Article{Laforgia:1993:AMR,
author = "Andrea Laforgia and Maria Luisa Mathis",
title = "Additional monotonicity results for the zeros of
{Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "47",
number = "1",
pages = "135--139",
day = "28",
month = jun,
year = "1993",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:58 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279390095S",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Lee:1993:DAE,
author = "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
title = "Design of an area efficient unit for floating-point
division and square root",
journal = j-J-KOREA-INFO-SCI-SOCIETY,
volume = "20",
number = "7",
pages = "1060--1071",
month = jul,
year = "1993",
CODEN = "HJKHDC",
ISSN = "0258-9125",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors propose an algorithm for a high
performance floating point division and square root
unit that uses a parallel multiplier. The basic
algorithm used in the design is the continued-product
normalization method. In this method, an arbitrary
number is constantly multiplied to the divisor and
dividend and dividend/divisor ends up with quotient/1
and the desired result attained. However this method
requires computation of x*(2-x) and x*(3-x)/2 and this
is quite an overhead. Therefore they propose a new
algorithm to compute (2-x) and (3-x)/2 by using the
modified Booth algorithm. When applied to the
continued-product normalization method, this algorithm
can maximize the inherent parallelism of the
continued-product normalization method, and reduce
computation time by effectively applying pipelining,
and also achieve area efficient design by eliminating
one register and one carry propagate adder needed for
computing (2-x) and (3-x)/2. When the designed unit is
used with the seed generator which has the accuracy of
2/sup -7/, division can be executed in eight cycles and
the square root operation in 13 cycles.",
acknowledgement = ack-nhfb,
classification = "B1265B (Logic circuits); C4240P (Parallel
programming and algorithm theory); C5120 (Logic and
switching circuits); C5230 (Digital arithmetic
methods)",
fjournal = "Journal of the Korea Information Science Society =
Chongbo Kwahakhoe nonmunji",
keywords = "Area efficient unit; Continued-product normalization
method; Floating-point division; Modified Booth
algorithm; Parallel multiplier; Pipelining; Seed
generator; Square root",
language = "Korean",
pubcountry = "South Korea",
thesaurus = "Adders; Digital arithmetic; Parallel algorithms",
}
@Article{Li:1993:CAF,
author = "Y. Li and X. Dong and S. Pan",
title = "Computation of Auxiliary Functions in {STO} Molecular
Integrals up to Arbitrary Accuracy. {I}. {Evaluation}
of Incomplete Gamma Function {E$_n$ (X)} by Forward
Recursion",
journal = j-IJQC,
volume = "45",
number = "1",
pages = "3--??",
year = "1993",
CODEN = "IJQCB2",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Wed Jan 3 14:24:13 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ijqc.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
}
@TechReport{Litvinov:1993:ACR,
author = "Grigori L. Litvinov",
title = "Approximate construction of rational approximations
and the effect of error autocorrection",
type = "Technical report",
number = "8",
institution = "Institute of Mathematics, University of Oslo",
address = "Oslo, Norway",
month = may,
year = "1993",
bibdate = "Tue Mar 24 20:51:52 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Litvinov:1994:ACR}.",
acknowledgement = ack-nhfb,
}
@Article{Liu:1993:DSC,
author = "Hui Min Liu",
title = "Determination of several classes of elementary
functions by functional inequalities. ({Chinese})",
journal = "Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)",
volume = "11",
number = "2",
pages = "30--35, 12",
year = "1993",
ISSN = "1001-6074",
MRclass = "26A09 (39B72)",
MRnumber = "94g:26003",
MRreviewer = "Ling Yau Chan",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Louie:1993:DRS,
author = "M. E. Louie and M. D. Ercegovac",
booktitle = "Proceedings of the {IEEE} Workshop on {FPGAs} for
Custom Computing Machines, 5--7 April 1993",
title = "A digit-recurrence square root implementation for
field programmable gate arrays",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "178--183",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Creating efficient arithmetic processors requires a
pairing of high speed arithmetic algorithms with
optimal mapping strategies for a given technology. The
authors propose bit reduction as key to an efficient
pairing process for lookup table based \ldots{}",
}
@InProceedings{Lozier:1993:ABF,
author = "Daniel W. Lozier and F. W. J. Olver",
title = "{Airy} and {Bessel} Functions by Parallel Integration
of {ODEs}",
crossref = "Sincovec:1993:PSS",
pages = "530--538",
year = "1993",
bibdate = "Fri Jul 09 06:36:27 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Mathai:1993:HGS,
author = "A. M. Mathai",
title = "A handbook of generalized special functions for
statistical and physical sciences",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xi + 235",
year = "1993",
ISBN = "0-19-853595-3",
ISBN-13 = "978-0-19-853595-9",
LCCN = "QA351 .M35 1993",
bibdate = "Sat Oct 30 18:57:40 MDT 2010",
bibsource = "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Oxford science publications",
URL = "http://www.loc.gov/catdir/enhancements/fy0635/92036065-d.html;
http://www.loc.gov/catdir/enhancements/fy0635/92036065-t.html",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Handbooks, manuals, etc",
tableofcontents = "I Mathematical preliminaries \\
1.1 The gamma function 1 \\
1.2 Bernoulli polynomials 6 \\
1.3 Asymptotic expansions of gamma functions 9 \\
1.4 The psi function 11 \\
1.5 The generalized zeta functions 12 \\
1.6 The beta function 15 \\
1.7 Calculation of residues for gamma functions 16 \\
1.8 The Mellin transform 23 \\
1.9 Density functions 24 \\
1.10 Methods of deriving distributions 49 \\
2 The G-function \\
2.1 The G-function 60 \\
2.2 Some basic properties of the G-function 69 \\
2.3 The Mellin transform of a G-function 78 \\
2.4 Properties connected with the derivatives of a
G-function 94 \\
2.5 Series representations for a G-function 96 \\
2.6 G-functions as multiple integrals or as solutions
of integral equations 106 \\
2.7 Differential equation for a G-function 111 \\
2.8 Asymptotic expansions for a G-function 112 \\
3 Elementary special functions and the G-function \\
3.1 Gamma and related functions: notations and
definitions 117 \\
3.2 Hypergeometric functions: notations and special
cases 118 \\
3.3 Confluent hypergeometric function and related
functions 119 \\
3.4 Exponential integral and related functions 121 \\
3.5 Bessel functions and associated functions 121 \\
3.6 Other special functions 122 \\
3.7 Orthogonal polynomials 124 \\
3.8 Elementary special functions expressed in terms of
G-functions 127 \\
3.9 G-functions expressed in terms of elementary
special functions 129 \\
3.10 Some integrals involving G-functions 132 \\
3.11 The H-function 140 \\
3.12 Computational aspects of G- and H-functions 144
\\
3.13 Orders of the special functions for small and
large values of the argument 145 \\
4 Generalizations to matrix variables \\
4.1 Scalar functions of a symmetric positive definite
matrix 152 \\
4.2 Scalar functions of matrix arguments 158 \\
4.3 Laplace transform 160 \\
4.4 Hypergeometric functions of matrix arguments 171
\\
4.5 Generalized matrix transform or M-transform 177 \\
4.6 Zonal polynomial 194 \\
4.7 Matrix variate Dirichlet distribution 197 \\
4.8 Hypergeometric functions of many scalar variables
205 \\
4.9 Hypergeometric functions of many matrix arguments
215 \\
4.10 G- and H-functions of two variables 217 \\
Bibliography 227 \\
Glossary of symbols 231 \\
Author index 233 \\
Subject index 234",
}
@Article{Mazenc:1993:CFU,
author = "Christophe Mazenc and Xavier Merrheim and Jean-Michel
Muller",
title = "Computing functions $ \cos^{-1} $ and $ \sin^{-1} $
using {Cordic}",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "1",
pages = "118--122",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.192222",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{McQuillan:1993:NAV,
author = "S. E. McQuillan and J. V. McCanny and R. Hamill",
booktitle = "Proceedings of the 11th Symposium on Computer
Arithmetic, 2 July 1993",
title = "New algorithms and {VLSI} architectures for {SRT}
division and square root",
crossref = "Swartzlander:1993:SCA",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "80--86",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-11",
summary = "Radix two algorithms for SRT division and
square-rooting are developed. For these schemes, the
result digits and the residuals are computed
concurrently and the computations in adjacent rows are
overlapped. Consequently, their performance should
\ldots{}",
}
@Article{Montuschi:1993:RIT,
author = "P. Montuschi and L. Ciminiera",
title = "Reducing iteration time when result digit is zero for
radix $2$ {SRT} division and square root with redundant
remainders",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "2",
pages = "239--246",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.204797",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Montuschi:1995:RRI}.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A new architecture is presented for shared radix 2
division and square root whose main characteristic is
the ability to avoid any addition/subtraction, when the
digit 0 has been selected. The solution presented uses
a redundant representation of the \ldots{}",
}
@TechReport{Morris:1993:NLM,
author = "Alfred H. {Morris, Jr.}",
title = "{NSWC} Library of Mathematics Subroutines",
type = "Report",
number = "NSWCDD/TR-92/425",
institution = "Naval Surface Warfare Center",
address = "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
20903-5000, USA",
pages = "464",
month = jan,
year = "1993",
bibdate = "Tue Jun 13 08:47:19 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
note = "See also earlier edition \cite{Morris:1990:NLM}.",
URL = "https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA261511.xhtml",
abstract = "The NSWC library is a library of general purpose
Fortran subroutines that provide a basic computational
capability for a variety of mathematical activities.
Emphasis has been placed on the transportability of the
codes. Subroutines are available in the following
areas: elementary operations, geometry, special
functions, polynomials, vectors, matrices, large dense
systems of linear equations, banded matrices, sparse
matrices, eigenvalues and eigenvectors, l1 solution of
linear equations, least-squares solution of linear
equations, optimization, transforms, approximation of
functions, curve fitting, surface fitting, manifold
fitting, numerical integration, integral equations,
ordinary differential equations, partial differential
equations, and random number generation.",
acknowledgement = ack-nhfb,
remark = "[13-Jun-2023] Despite several Web searches, a
machine-readable freely downloadable copy of this
report, and its associated software, has not yet been
located. The entry for the earlier edition
[Morris:1993:NLM] has links to a PDF file and the
Fortran 90 source code. Another entry [Miller:2004:AMF]
has links to some of the source code, without
indication of software version dates.",
}
@Article{Muller:1993:NAC,
author = "J{\"u}rgen M{\"u}ller",
title = "On numerical analytic continuation and convergence
acceleration by summability methods",
journal = "Analysis",
volume = "13",
number = "3",
pages = "279--291",
year = "1993",
ISSN = "0174-4747",
MRclass = "40G10 (40A30 41A25 65B10)",
MRnumber = "1245757 (94j:40013)",
MRreviewer = "S. Sridhar",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Analysis. International Mathematical Journal of
Analysis and its Applications",
keywords = "convergence acceleration",
}
@Article{Perger:1993:NEG,
author = "Warren F. Perger and Atul Bhalla and Mark Nardin",
title = "A numerical evaluator for the generalized
hypergeometric series",
journal = j-COMP-PHYS-COMM,
volume = "77",
number = "2",
pages = "249--254",
month = oct,
year = "1993",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(93)90008-Z",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Dec 01 09:22:29 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "Uses extended precision complex arithmetic.",
}
@Article{Petkovic:1993:SII,
author = "Miodrag S. Petkovi{\'c} and Carsten Carstensen",
title = "Some improved inclusion methods for polynomial roots
with {Weierstrass}' corrections",
journal = j-COMPUT-MATH-APPL,
volume = "25",
number = "3",
pages = "59--67",
month = feb,
year = "1993",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:11 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219390143J",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Book{Povolotskii:1993:OFR,
author = "A. I. Povolotski{\u\i} and G. A. Sviridyuk",
title = "{{\cyr Odnomerny{\u\i} matematicheski{\u\i} analiz
{\`e}lementarnykh funktsi{\u\i}}}. ({Russian})
[One-dimensional mathematical analysis of elementary
functions] {{\cyr Nepreryvnye funktsii.
Differentsiruemye funktsii. Integriruemye funktsii}}.
[Continuous functions. Differentiable functions.
Integrable functions]",
publisher = "Chelyabinsk. Gos. Univ.",
address = "Chelyabinsk, USSR",
pages = "92",
year = "1993",
ISBN = "5-230-17764-0",
ISBN-13 = "978-5-230-17764-7",
MRclass = "26-01 (00A05)",
MRnumber = "94e:26001",
MRreviewer = "J{\'o}zef Kalinowski",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Ratis:1993:CCH,
author = "Yu. L. Ratis and P. Fern{\'a}ndez de C{\'o}rdoba",
title = "A code to calculate (high order) {Bessel} functions
based on the continued fractions method",
journal = j-COMP-PHYS-COMM,
volume = "76",
number = "3",
pages = "381--388",
month = aug,
year = "1993",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(93)90062-H",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:29:39 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/001046559390062H",
abstract = "We have developed a fast code to calculate Bessel
functions of integer and fractional order based on the
continued fractions method. This algorithm is specially
useful in the case of Bessel functions of high order
because it does not require any recalculation using
normalization relations.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Book{Saurer:1993:BSF,
author = "Josef Saurer",
title = "Bases of special functions and their domains of
convergence",
volume = "73",
publisher = "Akademie Verlag GmbH",
address = "Berlin, Germany",
pages = "158",
year = "1993",
ISBN = "3-05-501613-0",
ISBN-13 = "978-3-05-501613-4",
ISSN = "0138-3019",
LCCN = "QA351 .S28 1993",
bibdate = "Sat Oct 30 18:53:24 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematical research",
acknowledgement = ack-nhfb,
remark = "Revised version of the author's
thesis--Universit{\"a}t Essen, 1992.",
subject = "Functions, Special; Analytic functions; Eigenfunction
expansions; Convergence; Mathematical physics",
tableofcontents = "Introduction 9 \\
1 Foundations of the theory 15 \\
1.1 Holomorphic operator functions in Frechet spaces 15
\\
1.2 Floquet eigenvalue problems (with a regular
singular point) 22 \\
1.3 Relationships between differential operators
corresponding to Floquet eigenvalue problems for
systems of differential equations and scalar
differential equations 26 \\
1.4 Biholomorphic images of functions 30 \\
1.5 An expansion theorem 37 \\
2 First order differential systems with a regular
singular point 43 \\
2.1 Fundamental properties 44 \\
2.2 Construction of fundamental systems depending
holomorphically on parameters 46 \\
2.3 A family of second order differential equations 55
\\
2.4 Differential equations and special functions of
mathematical physics 57 \\
2.4.1 Bessel equation, Bessel function 57 \\
2.4.2 Whittaker equation, Whittaker function 58 \\
2.4.3 Hypergeometric equation, hypergeometric function
60 \\
2.4.4 Generalised spherical function 61 \\
3 Floquet eigenvalue problems for first order
differential systems with a regular singular point 63
\\
3.1 Construction of biorthogonal canonical systems of
eigen- and associated vectors of the operator functions
$T$ and $T^*$ 67 \\
3.2 A general expansion theorem 73 \\
3.3 Floquet eigenvalue problems and expansion theorems
for a family of second order differential equations 75
\\
4 Domains of convergence of the eigenfunction
expansions 83 \\
4.1 The Bessel and Whittaker case 85 \\
4.2 The hypergeometric case 95 \\
4.3 Typical domains of convergence 105 \\
5 Examples of expansions in series of special functions
109 \\
5.1 Expansions in series of Bessel functions 109 \\
5.2 Expansions in series of Whittaker functions 115 \\
5.3 Expansions in series of hypergeometric functions
119 \\
6 First order differential systems for products of
vector-valued functions 127 \\
6.1 Products of vectors and sums of matrices of
different dimensions 128 \\
6.2 Construction of the first order differential system
132 \\
7 Floquet eigenvalue problems and expansions in series,
of m - fold products of special functions 135 \\
7.1 Construction of biorthogonal canonical systems of
eigen- and associated vectors of the operator functions
$T$ and $T^*$ 142 \\
7.2 Application 145 \\
References 151 \\
Notation index 154 \\
Index 157",
}
@InProceedings{Schulte:1993:ERC,
author = "M. Schulte and E. Swartzlander",
title = "Exact rounding of certain elementary functions",
crossref = "Swartzlander:1993:SCA",
bookpages = "xii + 284",
pages = "138--145",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf",
abstract = "An algorithm is described which produces exactly
rounded results for the functions of reciprocal, square
root, 2/sup x/, and log 2/sup x/. Hardware designs
based on this algorithm are presented for floating
point numbers with 16- and 24-b significands. These
designs use a polynomial approximation in which
coefficients are originally selected based on the
Chebyshev series approximation and are then adjusted to
ensure exactly rounded results for all inputs. To
reduce the number of terms in the approximation, the
input interval is divided into subintervals of equal
size and different coefficients are used for each
subinterval. For floating point numbers with 16-b
significands, the exactly rounded value of the function
can be computed in 51 ns on a 20-mm/sup 2/ chip. For
floating point numbers with 24-b significands, the
functions can be computed in 80 ns on a 98-mm/sup 2/
chip.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Electr. and Comput. Eng., Texas Univ.,
Austin, TX, USA",
classification = "C4120 (Functional analysis); C5230 (Digital
arithmetic methods)",
confdate = "29 June--2 July 1993",
conflocation = "Windsor, Ont., Canada",
confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
Natural Sci. and Eng. Res.; Council of Canada",
keywords = "Elementary functions; Exact rounding; Floating point
numbers; Polynomial approximation; Reciprocal; Rounded
results; Square root",
thesaurus = "Floating point arithmetic; Function evaluation",
}
@Article{Schulte:1993:PHD,
author = "Michael J. Schulte and Earl E. {Swartzlander, Jr.}",
title = "Parallel hardware designs for correctly rounded
elementary functions",
journal = j-INTERVAL-COMP,
volume = "4",
pages = "65--88",
year = "1993",
ISSN = "0135-4868",
MRclass = "65G10 (65C20)",
MRnumber = "1 305 859",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the International Conference on
Numerical Analysis with Automatic Result Verification
(Lafayette, LA, 1993)",
acknowledgement = ack-nhfb,
fjournal = "Interval Computations = Interval'nye vychisleniia",
}
@TechReport{Schwarz:1993:HRAa,
author = "E. Schwarz",
title = "High-radix algorithms for high-order arithmetic
operations",
type = "Technical Report",
number = "CSL-TR-93-559",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jan,
year = "1993",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@PhdThesis{Schwarz:1993:HRAb,
author = "Eric Mark Schwarz",
title = "High-radix algorithms for high-order arithmetic
operations",
type = "Thesis ({Ph.D.})",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "224",
month = apr,
year = "1993",
bibdate = "Mon Jan 07 22:38:06 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Many common algorithms for high-order arithmetic
operations require an initial approximation. The
Newton--Raphson algorithm starts with an approximation
and then quadratically converges on the solution. The
initial approximation determines the number of
iterations of the algorithm and is typically
implemented as a look-up table in the form of a ROM or
PLA. A novel method is suggested which describes
high-order arithmetic operations with a partial product
array. This method applies to the operations of
division, reciprocal, square root, natural logarithm,
exponential, and trigonometric functions. The partial
product array of Boolean elements which describes the
operation can be summed on an existing floating-point
multiplier. The hardware needed is only the logic gates
to create the Boolean elements in the array and a
multiplexor, and the latency is that of the multiplier.
Thus, by reusing a floating-point multiplier, a
high-precision approximation to a high-order arithmetic
operation can be implemented with a low marginal
cost.\par
This dissertation describes the implementation and
shows a method for deriving partial product arrays to
approximate arithmetic operations. Then the proposed
method is applied and evaluated for several operations.
The proposed method yields a minimum approximation of
twelve bits correct for the reciprocal operation and
sixteen bits for the square root operation. The
proposed method is shown to be as small as 0.05\% the
size (in gates) of an equivalent precision look-up
table and has up to four times the accuracy (in bits)
as an equivalent latency polynomial approximation.
Also, three new iterative algorithms to increase the
precision of the approximations and a theoretical
analysis of the partial product array representation
are detailed. Thus, high-radix algorithms of many
arithmetic operations are possible at low cost.",
acknowledgement = ack-nhfb,
keywords = "division; elementary functions; exponential;
logarithm; PPA (partial product array); reciprocal
square root; square root",
remark = "AAT 9317816. ProQuest document ID 746798521.",
}
@InProceedings{Schwarz:1993:HSA,
author = "E. M. Schwarz and M. J. Flynn",
booktitle = "Proceedings of the 11th Symposium on Computer
Arithmetic, 2 July 1993",
title = "Hardware starting approximation for the square root
operation",
crossref = "Swartzlander:1993:SCA",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "103--111",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
summary = "A method for obtaining high-precision approximations
of high-order arithmetic operations is presented. These
approximations provide an accurate starting
approximation for high-precision iterative algorithms,
which translates into few iterations and \ldots{}",
}
@TechReport{Schwarz:1993:UFM,
author = "Eric Mark Schwarz and M. J. (Michael J.) Flynn",
title = "Using a floating-point multiplier's internals for
high-radix division and square root",
type = "Technical report",
number = "CSL-TR-93-554",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
pages = "iv + 45",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.",
remark = "``January 1993.'' Abstract: ``A method for obtaining
high-precision approximations of high-order arithmetic
operations at low-cost is presented in this study.
Specifically, high-precision approximations of the
reciprocal (12 bits worst case) and square root (16
bits) operations are obtained using the internal
hardware of a floating-point multiplier without the use
of look-up tables. The additional combinatorial logic
necessary is very small due to the reuse of existing
hardware. These low-cost high-precision approximations
are used by iterative algorithms to perform the
operations of division and square root. The method
presented also applies to several other high-order
arithmetic operations. Thus, high-radix algorithms for
high-order arithmetic operations such as division and
square root are possible at low-cost.''",
}
@Article{Sellers:1993:CDC,
author = "H. Sellers",
title = "The {C$^2$-DIIS} Convergence Acceleration Algorithm",
journal = j-IJQC,
volume = "45",
number = "1",
pages = "31--??",
year = "1993",
CODEN = "IJQCB2",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Wed Jan 3 14:24:13 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
keywords = "convergence acceleration",
}
@Article{Shishkov:1993:RDB,
author = "Dimit{\cdprime}r Shishkov",
title = "Reduction of domains of basic elementary functions to
arbitrary small intervals",
journal = "Annuaire Univ. Sofia Fac. Math. Inform.",
volume = "87",
number = "1--2",
pages = "3--32 (1999)",
year = "1993",
ISSN = "0205-0808",
MRclass = "65D20",
MRnumber = "MR1745336",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Godishnik na Sofi\u\i skiya Universitet ``Sv. Kliment
Okhridski''. Fakultet po Matematika i Informatika.
Annuaire de l'Universit\'e de Sofia ``St. Kliment
Ohridski''. Facult\'e de Math\'ematiques et
Informatique",
}
@Article{Snyder:1993:AFI,
author = "W. Van Snyder",
title = "{Algorithm 723}: {Fresnel} Integrals",
journal = j-TOMS,
volume = "19",
number = "4",
pages = "452--456",
month = dec,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/168173.168193",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Apr 29 15:24:56 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See remarks \cite{Snyder:1996:RAF,Snyder:2021:CRA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p452-van_snyder/",
abstract = "An implementation of approximations for Fresnel
integrals and associated functions is described. The
approximations were originally developed by W. J. Cody,
but a Fortran implementation using them has not
previously been published.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; special functions",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Rational approximation. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing.",
}
@Article{Thompson:1993:CCQ,
author = "William J. Thompson",
title = "Cutting Corners: Quick Square Roots and Trig
Functions",
journal = j-COMPUT-PHYS,
volume = "7",
number = "1",
pages = "18--??",
month = jan,
year = "1993",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4823136",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:39 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4823136",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Vedder:1993:IAN,
author = "John D. Vedder",
title = "An invertible approximation to the normal distribution
function",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "16",
number = "1",
pages = "119--123",
month = jun,
year = "1993",
CODEN = "CSDADW",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
bibdate = "Fri Feb 6 11:39:39 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/016794739390248R",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Article{Zaitsev:1993:IMM,
author = "A. V. Zaitsev",
title = "Implementation of {Miller}'s method for evaluation of
{Bessel} functions of first kind",
journal = j-J-SOV-MATH,
volume = "63",
number = "5",
pages = "558--560",
month = feb,
year = "1993",
CODEN = "JSOMAR",
DOI = "https://doi.org/10.1007/bf01142530",
ISSN = "0090-4104 (print), 2376-5798 (electronic)",
ISSN-L = "0090-4104",
bibdate = "Wed Mar 1 09:29:38 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Soviet Mathematics",
journal-URL = "http://link.springer.com/journal/10958",
}
@Article{Anonymous:1994:C,
author = "Anonymous",
title = "Corrigenda",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "553--553",
month = dec,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 14 16:17:03 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Hull:1994:ICE}",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Bajard:1994:BNH,
author = "Jean-Claude Bajard and Sylvanus Kla and Jean-Michel
Muller",
title = "{BKM}: a new hardware algorithm for complex elementary
functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "955--963",
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295857",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68M07",
MRnumber = "1 294 301",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bender:1994:DAS,
author = "Carl M. Bender and Stefan Boettcher",
title = "Determination of $ f(\infty) $ from the asymptotic
series for $ f(x) $ about $ x = 0 $",
journal = j-J-MATH-PHYS,
volume = "35",
number = "4",
pages = "1914--1921",
month = apr,
year = "1994",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.530577",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "41A60 (41A21 65D15 81Q15)",
MRnumber = "95d:41063",
bibdate = "Tue Nov 1 08:58:10 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v35/i4/p1914_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "8",
}
@Article{Brown:1994:CAS,
author = "Barry W. Brown and Lawrence Levy",
title = "Certification of {Algorithm 708}: Significant Digit
Computation of the Incomplete Beta",
journal = j-TOMS,
volume = "20",
number = "3",
pages = "393--397",
month = sep,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 19 12:53:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{DiDonato:1992:ASD}.",
URL = "http://doi.acm.org/10.1145/192115.192155;
http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; continued fractions; F-distribution",
subject = "G.1.2 [Numerical Analysis]: Approximation",
}
@Article{Bruno:1994:AAF,
author = "Oscar P. Bruno and Fernando Reitich",
title = "Approximation of analytic functions: a method of
enhanced convergence",
journal = j-MATH-COMPUT,
volume = "63",
number = "207",
pages = "195--213",
month = jul,
year = "1994",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "30B10 (41A21 41A25)",
MRnumber = "94m:30003",
MRreviewer = "A. Edrei",
bibdate = "Tue Mar 25 15:38:13 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math., Georgia Inst. of Technol., Atlanta, GA,
USA",
ajournal = "Math. Comput.",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Sch. of Math., Georgia Inst. of Technol., Atlanta, GA,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "analytic functions; approximation; conformal;
conformal maps; convergence of numerical methods;
convergence rates; enhanced convergence; Euler
transform; function approximation; Pad{\'e};
perturbation methods; perturbation techniques; power;
series; series (mathematics); series expansions;
Stieltjes-type functions; Taylor expansion;
transformations; truncated enhanced",
treatment = "T Theoretical or Mathematical",
}
@Article{Carlson:1994:AAS,
author = "B. C. Carlson and J. L. Gustafson",
title = "Asymptotic Approximations for Symmetric Elliptic
Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "25",
number = "2",
pages = "288--303",
month = mar,
year = "1994",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33E05 (41A60)",
MRnumber = "95b:33056",
MRreviewer = "Bruce C. Berndt",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/25/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/22847",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Chaudhry:1994:GIG,
author = "M. Aslam Chaudhry and S. M. Zubair",
title = "Generalized incomplete gamma functions with
applications",
journal = j-J-COMPUT-APPL-MATH,
volume = "55",
number = "1",
pages = "99--123",
day = "31",
month = oct,
year = "1994",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:24:33 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042794901872",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Chen:1994:ABB,
author = "Yang Chen and Mourad E. H. Ismail and K. A. Muttalib",
title = "Asymptotics of basic {Bessel} functions and
$q$-{Laguerre} polynomials",
journal = j-J-COMPUT-APPL-MATH,
volume = "54",
number = "3",
pages = "263--272",
day = "20",
month = oct,
year = "1994",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:24:33 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279200128V",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Chen:1994:EDU,
author = "Sau-Gee Chen and Chieh-Chih Li",
booktitle = "{Proceedings of TENCON '94. IEEE Region 10's Ninth
Annual International Conference. Theme: `Frontiers of
Computer Technology'}",
title = "Efficient designs of unified $2$'s complement division
and square root algorithm and architecture",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "943--947",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Efficient unified 2's complement division and square
root algorithm, and their architectures are proposed in
this work. The designs are high speed, small area and
high compatibility. The architectures provide bit level
pipelined operation, as well \ldots{}",
}
@Article{Cortadella:1994:HRD,
author = "J. Cortadella and T. Lang",
title = "High-Radix Division and Square-Root with Speculation",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "919--931",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295854",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
summary = "The speed of high-radix digit-recurrence dividers and
square-root units is mainly determined by the
complexity of the result-digit selection. We present a
scheme in which a simpler function speculates the
result digit, and, when this speculation is \ldots{}",
}
@Article{Damnjanovic:1994:EFL,
author = "Zlatan Damnjanovic",
title = "Elementary functions and loop programs",
journal = j-NOTRE-DAME-J-FORM-LOG,
volume = "35",
number = "4",
pages = "496--522",
year = "1994",
CODEN = "NDJFAM",
ISSN = "0029-4527 (print), 1939-0726 (electronic)",
ISSN-L = "0029-4527",
MRclass = "03D20 (68Q15)",
MRnumber = "96i:03036",
MRreviewer = "John P. Helm",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Notre Dame journal of formal logic",
journal-URL = "http://projecteuclid.org/all/euclid.ndjfl",
}
@Article{Das:1994:ATE,
author = "Mrinal Kanti Das",
title = "Analysis of two elementary functions",
journal = j-INT-J-MATH-EDU-SCI-TECH,
volume = "25",
number = "1",
pages = "17--24",
year = "1994",
CODEN = "IJMEBM",
ISSN = "0020-739X (print), 1464-5211 (electronic)",
ISSN-L = "0020-739X",
MRclass = "26-01 (33B10)",
MRnumber = "1 257 731",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematical Education in
Science and Technology",
journal-URL = "http://www.tandfonline.com/loi/tmes20",
}
@TechReport{Dunham:1994:PMAa,
author = "Charles B. Dunham",
title = "Provably Monotone Approximations, {IV}",
type = "Technical report",
number = "TR-417",
institution = "Department of Computer Science, University of Western
Ontario",
address = "London, Ontario, Canada",
day = "8",
month = mar,
year = "1994",
bibdate = "Tue Apr 12 11:26:47 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.csd.uwo.ca/tech-reports/",
acknowledgement = ack-nhfb,
}
@TechReport{Dunham:1994:PMAb,
author = "Charles B. Dunham",
title = "Provably Monotone Approximations, {IV}, Revised",
type = "Technical report",
number = "TR-422",
institution = "Department of Computer Science, University of Western
Ontario",
address = "London, Ontario, Canada",
day = "4",
month = apr,
year = "1994",
bibdate = "Tue Apr 12 11:26:47 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.csd.uwo.ca/tech-reports/",
acknowledgement = ack-nhfb,
}
@Article{Dunkl:1994:AHI,
author = "Charles F. Dunkl and Donald E. Ramirez",
title = "{Algorithm 736}: Hyperelliptic Integrals and the
Surface Measure of Ellipsoids",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "427--435",
month = dec,
year = "1994",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/198429.198431",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D30",
MRnumber = "1 368 025",
bibdate = "Tue Mar 14 16:16:51 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "elliptic integral; expected radius; Lauricella's
hypergeometric function; optimal designs; surface
measure",
subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical
Differentiation -- multiple quadrature; G.3
[Mathematics of Computing]: Probability and
Statistics",
}
@Article{Dunkl:1994:CHI,
author = "Charles F. Dunkl and Donald E. Ramirez",
title = "Computing Hyperelliptic Integrals for Surface Measure
of Ellipsoids",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "413--426",
month = dec,
year = "1994",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/198429.198430",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D30",
MRnumber = "1 368 024",
bibdate = "Tue Mar 14 16:16:49 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "elliptic integral; expected radius; Lauricella's
hypergeometric function; optimal designs; surface
measure",
subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical
Differentiation -- multiple quadrature; G.3
[Mathematics of Computing]: Probability and
Statistics",
}
@Book{Ercegovac:1994:DSR,
author = "Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang",
title = "Division and Square Root: Digit-recurrence Algorithms
and Implementations",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "x + 230",
year = "1994",
ISBN = "0-7923-9438-0",
ISBN-13 = "978-0-7923-9438-9",
LCCN = "QA76.9.C62 E73 1994",
bibdate = "Fri Mar 27 09:46:24 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / 1 \\
1. General Comments / 5 \\
2. Division by Digit Recurrence / 5 \\
3. Theory of Digit-Recurrence Division / 19 \\
4. Division With Scaling and Prediction /65 \\
5. Higher Radix Division / 91 \\
6. On-The-Fly Conversion and Round / 121 \\
7. Square Root by Digit Recurrence / 135 \\
8. Implementations of Square Root / 153 \\
A: Restoring and Non-Restoring Division / 182 \\
B: Evaluation of Some Implementations / 182 \\
Bibliography / 207 \\
Index / 227",
}
@Article{Everitt:1994:GBF,
author = "W. N. Everitt and C. Markett",
title = "On a generalization of {Bessel} functions satisfying
higher-order differential equations",
journal = j-J-COMPUT-APPL-MATH,
volume = "54",
number = "3",
pages = "325--349",
day = "20",
month = oct,
year = "1994",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:24:33 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042794902550",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Fukushima:1994:NCI,
author = "Toshio Fukushima and Hideharu Ishizaki",
title = "Numerical computation of incomplete elliptic integrals
of a general form",
journal = j-CELEST-MECH-DYN-ASTR,
volume = "59",
number = "3",
pages = "237--251",
month = jul,
year = "1994",
CODEN = "CLMCAV",
DOI = "https://doi.org/10.1007/BF00692874",
ISSN = "0923-2958 (print), 1572-9478 (electronic)",
ISSN-L = "0923-2958",
MRclass = "33E05 65R20 65D32 (33E30 70-08 70E15)",
MRnumber = "1285916 (95c:65041)",
bibdate = "Wed Oct 20 21:26:45 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/0923-2958/",
ZMnumber = "Zbl 0818.33013",
abstract = "We present an algorithm to compute the incomplete
elliptic integral of a general form. The algorithm
efficiently evaluates some linear combinations of
incomplete elliptic integrals of all kinds to a high
precision. Some numerical examples are given as
illustrations. This enables us to numerically calculate
the values and the partial derivatives of incomplete
elliptic integrals of all kinds, which are essential
when dealing with many problems in celestial mechanics,
including the analytic solution of the torque-free
rotational motion of a rigid body around its
barycenter.",
acknowledgement = ack-nhfb,
fjournal = "Celestial Mechanics \& Dynamical Astronomy. An
International Journal of Space Dynamics",
keywords = "Incomplete elliptic integrals; numerical computation",
}
@Article{Hahn:1994:UDF,
author = "H. Hahn and D. Timmermann and B. J. Hosticka and B.
Rix",
title = "A unified and division-free {CORDIC} argument
reduction method with unlimited convergence domain
including inverse hyperbolic functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "11",
pages = "1339--1344",
month = nov,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.324568",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Homeier:1994:NCA,
author = "Herbert H. H. Homeier",
editor = "Ralf Gruber and Marco Tomassini",
booktitle = "Proceedings of the 6th {Joint EPS-APS International
Conference} on {Physics Computing, Physics Computing}
'94",
title = "Nonlinear convergence acceleration for orthogonal
series",
publisher = "European Physical Society, Boite Postale 69, CH-1213
Petit-Lancy, Geneva, Switzerland",
address = "Lugano",
pages = "47--50",
year = "1994",
ISBN = "2-88270-011-3",
ISBN-13 = "978-2-88270-011-7",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA942",
keywords = "convergence acceleration",
tech = "Technical Report TC-NA-94-2, Institut f{\"u}r
{Physikalische} und {Theoretische Chemie,
Universit{\"a}t Regensburg, D-93040 Regensburg}, 1994",
}
@Article{Hull:1994:ICE,
author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
Tang",
title = "Implementing Complex Elementary Functions Using
Exception Handling",
journal = j-TOMS,
volume = "20",
number = "2",
pages = "215--244",
month = jun,
year = "1994",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/178365.178404",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 21 15:10:29 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See correction \cite{Anonymous:1994:C}, and improved
analysis, tightened bounds, and exhibition of worst
cases for complex square roots
\cite{Jeannerod:2017:REC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/",
abstract = "Algorithms are developed for reliable and accurate
evaluations of the complex elementary functions
required in Fortran 77 and Fortran 90, namely cabs,
csqrt, cexp, clog, csin, and ccos. The algorithms are
presented in a pseudocode that has a convenient
exception-handling facility. A tight error bound is
derived for each algorithm. Corresponding Fortran
programs for an IEEE environment have also been
developed to illustrate the practicality of the
algorithms, and these programs have been tested very
carefully to help confirm the correctness of the
algorithms and their error bounds. The results are of
these tests are included in the paper, but the Fortran
programs are not; the programs are available from
Fairgrieve, (tff@cs.toronto.edu).",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; complex elementary functions; design;
implementation",
subject = "G.1.0 [Numerical Analysis]: General--error analysis;
numerical algorithms; G.1.2 [Numerical Analysis]:
Approximation--elementary function approximation; G.4
[Mathematics of Computing]: Mathematical
Software--algorithm analysis; reliability and
robustness; verification",
}
@Article{Iserles:1994:CAD,
author = "A. Iserles",
title = "Convergence acceleration as a dynamical system",
journal = j-APPL-NUM-MATH,
volume = "15",
number = "2",
pages = "101--121",
day = "13",
month = sep,
year = "1994",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "58F23 (30D05 58F08 65D99 65H99)",
MRnumber = "95i:58155",
MRreviewer = "Peter M. Makienko",
bibdate = "Wed Jul 28 14:35:48 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=15&issue=2;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Innovative methods in numerical analysis (Bressanone,
1992).",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=15&issue=2&aid=496",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@Article{Jablonski:1994:NES,
author = "Aleksander Jablonski",
title = "Numerical Evaluation of Spherical {Bessel} Functions
of the First Kind",
journal = j-J-COMPUT-PHYS,
volume = "111",
number = "2",
pages = "256--259",
month = apr,
year = "1994",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1994.1060",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:54:54 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999184710606",
abstract = "Calculations of cross sections for elastic scattering
of electrons require frequent evaluations of the
spherical Bessel functions, $ j_l(x) $ and $ n_l(x) $,
in a wide range of the argument $x$ and the order $l$.
It turns out that the usual algorithms providing the
values of the spherical Bessel function of the first
kind, $ j_l(x) $, have a rather limited range of
stability. It is shown that there is no algorithm
implementing a single method which can be used in
calculations associated with the theory of elastic
scattering of electrons. An attempt is made to select
different areas of stability from different algorithms
in order to create a relatively fast and universal
algorithm.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@InProceedings{Jain:1994:SRR,
author = "V. K. Jain and Lei Lin",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP-94, 19--22} April 1994",
title = "Square-root, reciprocal, sine\slash cosine, arctangent
cell for signal and image processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II/521--II/524",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This paper discusses an efficient interpolation method
for nonlinear function generation. Based on this, a 24
bit VLSI cell, capable of computing the (1) square
root, (2) reciprocal, (3) sine/cosine, and (4)
arctangent functions, is presented for \ldots{}",
}
@Misc{Karp:1994:FPA,
author = "Alan H. Karp and Peter Markstein and Dennis
Brzezinski",
title = "Floating point arithmetic unit using modified
{Newton--Raphson} technique for division and square
root",
howpublished = "US Patent 5,341,321",
day = "23",
month = aug,
year = "1994",
bibdate = "Thu Oct 17 10:20:52 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Patent filed 5 May 1993, granted to Hewlett-Packard
Company on 23 August 1994. Patent expired 5-May-2013.
See criticism in \cite{Zimmermann:2005:XXX}.",
URL = "http://patft.uspto.gov/netahtml/PTO/search-bool.html;
https://patents.google.com/patent/US5341321A",
abstract = "A floating point processing system which uses a
multiplier unit and an adder unit to perform floating
point division and square root operations using both a
conventional and a modified form of the Newton--Raphson
method. The modified form of the Newton--Raphson method
is used in place of the final iteration of the
conventional Newton--Raphson so as to compute high
precision approximated results with a substantial
improvement in speed. The invention computes
approximated results faster and simplifies hardware
requirements because no multiplications of numbers of
the precision of the result are required.",
acknowledgement = ack-nhfb,
}
@Article{Kearfott:1994:AIP,
author = "R. B. Kearfott and M. Dawande and K. Du and C. Hu",
title = "Algorithm 737: {INTLIB}: a Portable {Fortran}-77
Elementary Function Library",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "447--459",
month = dec,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat May 20 15:54:18 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
accepted = "December 1993",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "BLAS; Fortran 77; Fortran 90; interval arithmetic;
operator overloading; standard functions",
subject = "D.2.2 [Software Engineering]: Tools and Techniques --
software libraries; D.2.7 [Software Engineering]:
Distribution and Maintenance -- documentation;
portability; G.1.0 [Numerical Analysis]: General --
computer arithmetic; G.1.2 [Numerical Analysis]:
Approximation -- elementary function approximation",
}
@Article{Khajah:1994:UHP,
author = "H. G. Khajah and E. L. Ortiz",
title = "Ultra-high precision computations",
journal = j-COMPUT-MATH-APPL,
volume = "27",
number = "7",
pages = "41--57",
month = apr,
year = "1994",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(94)90148-1",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Mon Jun 13 22:03:39 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122194901481",
abstract = "We describe a machine independent Fortran subroutine
which performs the four basic arithmetic operations
with a degree of accuracy prescribed by the user.
Tables of Chebyshev expansions of orders 48 and 50 for
some basic mathematical functions are obtained as a
result of applying this subroutine in conjunction with
the recursive formulation of the Tau Method. A recently
devised technique for the sharp determination of upper
and lower error bounds for Tau Method approximations
enables us to find the degree $n$ required to achieve a
prescribed accuracy $ \epsilon $ over a given interval
$ [a, b] $. A number of practical illustrations are
given.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Imperial Coll. of Sci., Technol. and
Med., London, UK",
classification = "C6140D (High level languages); C7310 (Mathematics)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "$\cos(\pi x)$; $\erf(x) / x$; $\exp(-x^2)$; $\exp(x)$;
$\sin(\pi x)$; $x \exp(x^2) erfc(x)$; $z \exp(z)
\Ei(-z)$; Arithmetic operations; Chebyshev expansions;
Lower error bounds; Machine independent Fortran
subroutine; Mathematical functions; Tau method; Upper
error bounds",
pubcountry = "UK",
thesaurus = "FORTRAN; Mathematics computing",
}
@Article{Lewanowicz:1994:SAS,
author = "Stanis{\l}aw Lewanowicz",
title = "A simple approach to the summation of certain slowly
convergent series",
journal = j-MATH-COMPUT,
volume = "63",
number = "208",
pages = "741--745",
month = oct,
year = "1994",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65B10",
MRnumber = "95a:65010",
MRreviewer = "Thomas A. Atchison",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Litvinov:1994:ACR,
author = "Grigori L. Litvinov",
title = "Approximate construction of rational approximations
and the effect of error autocorrection",
journal = j-RUSS-J-MATH-PHYS,
volume = "1",
number = "3",
pages = "313--352",
month = "????",
year = "1994",
CODEN = "RJMPEL",
ISSN = "1061-9208 (print), 1555-6638 (electronic)",
ISSN-L = "1061-9208",
bibdate = "Tue Mar 24 20:54:11 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arxiv.org/abs/math/0101042",
abstract = "Several construction methods for rational
approximations to functions of one real variable are
described in the present paper; the computational
results that characterize the comparative accuracy of
these methods are presented; an effect of error
autocorrection is considered. This effect occurs in
efficient methods of rational approximation (e.g.,
Pad{\'e} approximations, linear and nonlinear Pad{\'e}
Chebyshev approximations) where very significant errors
in the coefficients do not affect the accuracy of the
approximation. The matter of import is that the errors
in the numerator and the denominator of a fractional
rational approximant compensate each other. This effect
is related to the fact that the errors in the
coefficients of a rational approximant are not
distributed in an arbitrary way but form the
coefficients of a new approximant to the approximated
function. Understanding of the error autocorrection
mechanism allows to decrease this error by varying the
approximation procedure depending on the form of the
approximant. Some applications are described in the
paper. In particular, a method of implementation of
basic calculations on decimal computers that uses the
technique of rational approximations is described in
the Appendix.\par
To a considerable extent the paper is a survey and the
exposition is as elementary as possible.",
acknowledgement = ack-nhfb,
fjournal = "Russian Journal of Mathematical Physics",
}
@TechReport{Lozier:1994:NESa,
author = "D. W. Lozier and F. W. J. Olver",
title = "Numerical evaluation of special functions",
type = "Report",
number = "NISTIR 5383",
institution = "Computing and Applied Mathematics Laboratory, U. S.
Department of Commerce",
address = "Washington, DC, USA",
pages = "47",
month = mar,
year = "1994",
MRclass = "65D20 (33-00)",
bibdate = "Thu Nov 16 07:52:34 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://math.nist.gov/~DLozier/publications/nistir5383.pdf",
abstract = "Higher transcendental functions continue to play
varied and important roles in investigations by
engineers, mathematicians, scientists and
statisticians. The purpose of this paper is to assist
in locating useful approximations and software for the
numerical generation of these functions, and to offer
some suggestions for future developments in this
field.",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
tableofcontents = "1. Introduction / 3 \\
2. Mathematical Developments / 5 \\
3. Packages, Libraries and Systems / 6 \\
3.1. Software Packages / 6 \\
3.2. Intermediate Libraries / 8 \\
3.3. Comprehensive Libraries / 8 \\
3.4. Interactive Systems / 12 \\
4. Functions of One Variable / 15 \\
4.1. Airy Functions / 15 \\
4.2. Error Functions, Dawson's Integral, Fresnel
Integrals, Goodwin--Staton Integral / 15 \\
4.3. Exponential Integrals, Logarithmic Integral, Sine
and Cosine Integrals / 16 \\
4.4. Gamma, Psi, and Polygamma Functions / 16 \\
4.5. Landau Density and Distribution Functions / 16 \\
4.6. Polylogarithms, Clausen Integral / 16 \\
4.7. Zeta Function / 17 \\
4.8. Additional Functions of One Variable / 17 \\
5. Functions of Two or More Variables / 17 \\
5.1. Bessel Functions / 17 \\
5.2. Coulomb Wave Functions / 18 \\
5.3. Elliptic Integrals and Functions / 18 \\
5.4. Fermi--Dirac, Bose--Einstein, and Debye Integrals
/ 19 \\
5.5. Hypergeometric and Concuent Hypergeometric
Functions / 19 \\
5.6. Incomplete Bessel Functions, Incomplete Beta
Function / 19 \\
5.7. Incomplete Gamma Functions, Generalized
Exponential Integrals / 20 \\
5.8. Legendre Functions and Associated Legendre
Functions / 20 \\
5.9. Mathieu, Lam{\'e}, and Spheroidal Wave Functions /
20 \\
5.10. Orthogonal Polynomials / 21 \\
5.11. Polylogarithms (Generalized) / 21 \\
5.12. Struve and Anger--Weber Functions / 21 \\
5.13. Weber Parabolic Cylinder Functions / 21 \\
5.14. Zeta Function (Generalized) / 21 \\
5.15. Additional Functions of Two or More Variables /
21 \\
6. Testing and Library Construction / 22 \\
7. Future Trends / 22 \\
Acknowledgments / 23 \\
A Note on the Reference Acronyms / 23 \\
References / 23--47",
}
@InProceedings{Lozier:1994:NESb,
author = "D. W. Lozier and F. W. J. Olver",
title = "Numerical evaluation of special functions",
crossref = "Gautschi:1994:MCH",
volume = "48",
pages = "79--125",
year = "1994",
DOI = "https://doi.org/10.1090/psapm/048/1314844",
MRclass = "65D20 (30-04 33-04 41-04)",
MRnumber = "95m:65036 (1314844)",
MRreviewer = "John P. Coleman",
bibdate = "Fri Jul 9 05:44:10 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
series = "Proc. Sympos. Appl. Math.",
URL = "http://math.nist.gov/mcsd/Reports/2001/nesf/",
abstract = "Higher transcendental functions continue to play
varied and important roles in investigations by
engineers, mathematicians, scientists, and
statisticians. The purpose of this paper is to assist
in locating useful approximations and software for the
numerical generation of these functions, and to offer
some suggestions for future developments in the
field.",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
remark = "The references list contains about 400 entries which
should ultimately be incorporated in this BibTeX
bibliography collection.",
}
@TechReport{Lozier:1994:SNS,
author = "Daniel W. Lozier",
title = "Software Needs in Special Functions",
type = "Technical Report",
number = "NISTIR 5490",
institution = pub-NIST,
address = pub-NIST:adr,
pages = "16",
month = aug,
year = "1994",
bibdate = "Fri Jul 09 05:47:26 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Lozier:1996:SNS}.",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps",
acknowledgement = ack-nhfb,
}
@Article{MacLeod:1994:CIA,
author = "Allan J. MacLeod",
title = "Computation of inhomogeneous {Airy} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "53",
number = "1",
pages = "109--116",
day = "29",
month = jul,
year = "1994",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:24:31 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042794901961",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{MacLeod:1994:TBT,
author = "Allan J. MacLeod",
title = "Table-based tests for {Bessel} function software",
journal = j-ADV-COMPUT-MATH,
volume = "2",
number = "2",
pages = "251--260",
month = mar,
year = "1994",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/BF02521111",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
MRclass = "65-04 (33-04 33C10 65D20)",
MRnumber = "1269384",
bibdate = "Sat Feb 3 18:21:41 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/BF02521111",
acknowledgement = ack-nhfb,
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
}
@InProceedings{Magnus:1994:ASA,
author = "Alphonse P. Magnus",
title = "Asymptotics and super asymptotics of best rational
approximation error norms for the exponential function
(the `$ 1 / 9 $' problem) by the
{Carath{\'e}odory--Fej{\'e}r} method",
crossref = "Cuyt:1994:NNM",
pages = "173--185",
year = "1994",
bibdate = "Mon Nov 24 21:30:41 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "809.41015",
acknowledgement = ack-nhfb,
}
@Article{Marsaglia:1994:REI,
author = "George Marsaglia and Arif Zaman and John C. W.
Marsaglia",
title = "Rapid evaluation of the inverse of the normal
distribution function",
journal = j-STAT-PROB-LETT,
volume = "19",
number = "4",
pages = "259--266",
day = "15",
month = mar,
year = "1994",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/0167-7152(94)90174-0",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "65U05",
MRnumber = "1 278 658",
bibdate = "Thu Dec 22 07:42:24 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
MathSciNet database",
ZMnumber = "0798.65132",
abstract = "This is an interesting article with direct application
in generating normal random variable by computer
programs. The suggested applications are related to
Monte Carlo simulation based on massively parallel
systems or supercomputers. The idea is to replace
larger programs with complicated computations and with
difficulties in accuracy controlling by simpler
arithmetic programs that use tabled constants. These
seem to be the normal evolution since memory becomes
cheaper and cheaper.\par
The authors compute the inverse of the cPhi function $$
c P h i(x) = (2 / \pi)^{1 / 2} \int^\infty_x \exp ( -
t^2 / 2) d t = u, $$ using a uniform random variable as
input and the truncated Taylor series development of
it. In order to increase the speed the coefficients of
the truncated Taylor series $$ x(u_0 + h) = x(u_0) +
x'(u_0) \cdot h + {1 \over 2} x''(u_0) \cdot h^2 + {1
\over 6} x'''(u_0) \cdot h^3, $$ are predetermined for
1024 points. And here comes another bright idea: the
1024 points are chosen based on the representation of
the uniform random variable in modern computers as
floating point variable of the form: $ u = 2^{-k} ((1 /
2) + (j / 64)) + 2^{-k} \cdot (m / 2^{24}) $ with $ 0
\le k & l t; 32 $, $ 0 \le j & l t; 32 $ and $ 0 \le m
& l t; 2^{18} $ and considering 32 bit
representation.\par
With this assumptions and the truncation to the third
power of $h$ of the Taylor series, the authors show
that the error does not exceed the limit of single
precision accuracy. Furthermore the calculations are
speeded up based on reducing multiplications. A number
of FORTRAN programs are also presented in order to
evaluate the complementary normal distribution function
cPhi (several versions) with great accuracy, create the
constant tables, and generate the normal distribution
variable. These simple programs give the user the
possibility to completely control the accuracy.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "cPhi function; FORTRAN programs; massive parallel
systems; Monte Carlo simulation; normal distribution
function; normal random variable; supercomputers;
truncated Taylor series",
ZMclass = "*65C99 Numerical simulation 65C05 Monte Carlo methods
60-04 Machine computation, programs (probability
theory) 60E05 General theory of probability
distributions 62E17 Approximations to statistical
distributions (nonasymptotic)",
ZMreviewer = "A. Pasculescu (Bucuresti)",
}
@Article{Merrheim:1994:CEF,
author = "X. Merrheim",
title = "The computation of elementary functions in radix $ 2^p
$",
journal = j-COMPUTING,
volume = "53",
number = "3--4",
pages = "219--232",
year = "1994",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68M07",
MRnumber = "95j:68028",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "International Symposium on Scientific Computing,
Computer Arithmetic and Validated Numerics (Vienna,
1993).",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Narayanaswami:1994:AE,
author = "Chandrasekhar Narayanaswami and William Luken",
title = "Approximating $ x^n $ efficiently",
journal = j-INFO-PROC-LETT,
volume = "50",
number = "4",
pages = "205--210",
day = "25",
month = may,
year = "1994",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "65D20 (41-04 65B99)",
MRnumber = "95b:65031",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "Compendex database;
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
affiliation = "IBM Advanced Workstations and Systems Div",
affiliationaddress = "Austin, TX, USA",
classification = "721.1; 723.2; 723.5; 741.2; 921.1; 921.6; B0290F
(Interpolation and function approximation); C4130
(Interpolation and function approximation); C6130B
(Graphics techniques)",
corpsource = "IBM Adv. Workstations and Syst. Div., Austin, TX,
USA",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
journalabr = "Inf Process Lett",
keywords = "$x^n$ approximation; approximation theory;
Approximation theory; Color computer graphics;
Computational complexity; Computational methods;
computer graphics; elementary functions; floating-point
arithmetic; Function evaluation; graphics modeling;
Image quality; Light intensity computation; look-up
tables; performance requirements; Polynomial
evaluation; Polynomials; polynomials; power function;
scientific applications; Semiconducting silicon; Table
lookup",
treatment = "T Theoretical or Mathematical",
}
@Article{Nishioka:1994:EFB,
author = "Keiji Nishioka",
title = "Elementary functions based on elliptic curves",
journal = j-TOKYO-J-MATH,
volume = "17",
number = "2",
pages = "439--446",
year = "1994",
ISSN = "0387-3870",
MRclass = "12H05",
MRnumber = "96b:12011",
MRreviewer = "Alexandru Buium",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Tokyo journal of mathematics",
}
@Article{Ohta:1994:INP,
author = "Shigemi Ohta and Eiichi Goto and Weng Fai Wong and
Nobuaki Yoshida",
title = "Improvement and new proposal on fast evaluation of
elementary functions. ({Japanese})",
journal = j-TRANS-INFO-PROCESSING-SOC-JAPAN,
volume = "35",
number = "5",
pages = "926--933",
month = may,
year = "1994",
CODEN = "JSGRD5",
ISSN = "0387-5806",
ISSN-L = "0387-5806",
MRclass = "65D20",
MRnumber = "95f:65045",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp.
1570-1579, 1993) introduced fast methods for numerical
evaluation of elementary functions based on table
lookup. They are called ATA (add/table-lookup/add) and
ATA-M (add/table-lookup/add and multiply) methods for
single- and double-precision calculations respectively.
In this paper, an improvement to these methods that
shrinks the size of the table by a factor of about 3/16
is presented. Another method called the `split parallel
multiplication method', which is characterized by
simpler table lookup than ATA-M and by split and
parallel use of double-precision floating point
circuitry, is also introduced, These new methods fit on
to integrated circuits of a size comparable with
commercially available floating-point accelerators.
Methods for accelerating double-precision division,
generating uniform pseudo-random numbers in
double-precision, and accelerating the multiplication
of single-precision complex numbers using the same
circuitry are proposed.",
acknowledgement = ack-nhfb,
affiliation = "RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan",
classification = "C4120 (Functional analysis); C5230 (Digital
arithmetic methods); C6130 (Data handling techniques)",
fjournal = "Transactions of the Information Processing Society of
Japan",
keywords = "Add/table-lookup/add method;
Add/table-lookup/add/multiply method; ATA method; ATA-M
method; Double-precision calculations; Double-precision
division; Double-precision floating point circuitry;
Elementary functions evaluation; Floating-point
accelerators; Integrated circuits; Numerical
evaluation; Single-precision calculations;
Single-precision complex number multiplication; Split
parallel multiplication method; Table size; Uniform
pseudo-random number generation",
language = "Japanese",
pubcountry = "Japan",
thesaurus = "Digital arithmetic; Function evaluation; Random number
generation; Table lookup",
}
@InProceedings{Olver:1994:GEI,
author = "F. W. J. Olver",
title = "The generalized exponential integral",
crossref = "Zahar:1994:ACF",
pages = "497--510",
year = "1994",
MRclass = "33B20 (34E05 41A60)",
MRnumber = "1333639",
MRreviewer = "Richard B. Paris",
bibdate = "Sat Feb 18 15:02:52 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "International Series of Numerical Mathematics",
acknowledgement = ack-nhfb,
}
@Article{Osada:1994:CAM,
author = "Naoki Osada",
title = "Convergence acceleration methods",
journal = "S\=urikaisekikenky\=usho K\=oky\=uroku",
volume = "880",
number = "??",
pages = "28--43",
month = "????",
year = "1994",
MRclass = "65B05",
MRnumber = "1366233",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "The state of the art of scientific computing and its
prospects (Japanese) (Kyoto, 1993)",
acknowledgement = ack-nhfb,
fjournal = "S\=urikaisekikenky\=usho K\=oky\=uroku",
keywords = "convergence acceleration",
}
@InProceedings{Rappoport:1994:TMC,
author = "Juri M. Rappoport",
title = "The {Tau-Method} and the Computation of the {Bessel}
Functions of the Complex Order",
crossref = "Brown:1994:PCL",
pages = "353--355",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Schulte:1994:HDE,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "Hardware Design for Exactly Rounded Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "964--973",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295858",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This paper presents hardware designs that produce
exactly rounded results for the functions of
reciprocal, square-root, 2/sup x/, and log/sub 2/(x).
These designs use polynomial approximation in which the
terms in the approximation are generated in parallel,
and then summed by using a multi-operand adder. To
reduce the number of terms in the approximation, the
input interval is partitioned into subintervals of
equal size, and different coefficients are used for
each subinterval. The coefficients used in the
approximation are initially determined based on the
Chebyshev series approximation. They are then adjusted
to obtain exactly rounded results for all inputs.
Hardware designs are presented, and delay and area
comparisons are made based on the degree of the
approximating polynomial and the accuracy of the final
result. For single-precision floating point numbers, a
design that produces exactly rounded results for all
four functions has an estimated delay of 80 ns and a
total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS
technology. Allowing the results to have a maximum
error of one unit in the last place reduces the
computational delay by 5\% to 30\% and the area
requirements by 33\% to 77\%.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Dept. of Electr. and Comput. Eng., Texas Univ.,
Austin, TX, USA",
ajournal = "IEEE Trans. Comput.",
classification = "B0290F (Interpolation and function approximation);
B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C4130 (Interpolation and function
approximation); C5120 (Logic and switching circuits);
C5230 (Digital arithmetic methods)",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "1 Micron; 1.0-Micron CMOS technology; Argument
reduction; Chebyshev series approximation; Chip area;
Computational delay; Computer arithmetic; Exact
rounding; Exactly rounded elementary functions;
Hardware designs; Multi-operand adder; Parallel
multiplier; Polynomial approximation; Reciprocal;
Single-precision floating point numbers;
Special-purpose hardware; Square-root",
numericalindex = "Size 1.0E-06 m",
pubcountry = "USA",
thesaurus = "Approximation theory; Chebyshev approximation; CMOS
integrated circuits; Digital arithmetic; Multiplying
circuits; Polynomials; Summing circuits",
}
@InProceedings{Skaf:1994:LHI,
author = "Ali Skaf and Jean-Michel Muller and Alain Guyot",
editor = "Anonymous",
booktitle = "{ESSCIRC '94: Twentieth European Solid-State Circuits
Conference. Ulm, Germany. September 20--22, 1994}",
title = "On-Line Hardware Implementation for Complex
Exponential and Logarithm",
publisher = "{\'E}ditions Fronti{\`e}res",
address = "B. P. 33. 91192 Gif-sur-Yvette Cedex, France",
pages = "252--255",
year = "1994",
ISBN = "2-86332-160-9",
ISBN-13 = "978-2-86332-160-7",
bibdate = "Fri Sep 29 10:32:36 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Sorenson:1994:TFG,
author = "J. Sorenson",
title = "Two Fast {GCD} Algorithms",
journal = j-J-ALG,
volume = "16",
number = "1",
pages = "110--144",
month = jan,
year = "1994",
CODEN = "JOALDV",
DOI = "https://doi.org/10.1006/jagm.1994.1006",
ISSN = "0196-6774 (print), 1090-2678 (electronic)",
ISSN-L = "0196-6774",
bibdate = "Tue Dec 11 09:15:38 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jalg.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0196677484710066",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms",
journal-URL = "http://www.sciencedirect.com/science/journal/01966774",
}
@Article{Spouge:1994:CGD,
author = "John L. Spouge",
title = "Computation of the Gamma, Digamma, and Trigamma
Functions",
journal = j-SIAM-J-NUMER-ANAL,
volume = "31",
number = "3",
pages = "931--944",
month = jun,
year = "1994",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "33B15 (30E10 33-04 40-04 65D20)",
MRnumber = "95g:33002",
MRreviewer = "E. Kaucher",
bibdate = "Mon Jan 20 15:27:00 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@InProceedings{Temme:1994:CAI,
author = "N. M. Temme",
title = "Computational aspects of incomplete gamma functions
with large complex parameters",
crossref = "Zahar:1994:ACF",
pages = "551--562",
year = "1994",
bibdate = "Sat Feb 18 15:02:52 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "International Series of Numerical Mathematics",
acknowledgement = ack-nhfb,
}
@Article{Temme:1994:SAI,
author = "N. M. Temme",
title = "A Set of Algorithms for the Incomplete Gamma
Functions",
journal = j-PROBAB-ENGRG-INFORM-SCI,
volume = "8",
number = "2",
pages = "291--307",
month = apr,
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1017/S0269964800003417",
ISSN = "0269-9648 (print), 1469-8951 (electronic)",
ISSN-L = "0269-9648",
bibdate = "Thu Aug 24 08:18:58 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/probab-engrg-inform-sci.bib",
URL = "https://www.cambridge.org/core/product/F5677268895A0805A0BDF31E4B20A106",
acknowledgement = ack-nhfb,
ajournal = "Probab. Engrg. Inform. Sci.",
fjournal = "Probability in the Engineering and Informational
Sciences",
journal-URL = "http://www.journals.cambridge.org/jid_PES",
onlinedate = "01 July 2009",
}
@Article{Timmermann:1994:CFV,
author = "D. Timmermann and B. Rix and H. Hahn and B. J.
Hosticka",
title = "A {CMOS} floating-point vector-arithmetic unit",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "29",
number = "5",
pages = "634--639",
month = may,
year = "1994",
CODEN = "IJSCBC",
DOI = "https://doi.org/10.1109/4.284719",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This work describes a floating-point arithmetic unit
based on the CORDIC algorithm. The unit computes a full
set of high level arithmetic and elementary functions:
multiplication, division, (co)sine, hyperbolic
(co)sine, square root, natural logarithm, inverse
(hyperbolic) tangent, vector norm, and phase. The chip
has been integrated in 1.6 mu m double-metal n-well
CMOS technology and achieves a normalized peak
performance of 220 MFLOPS.",
acknowledgement = ack-nhfb,
affiliation = "Fraunhofer Inst. of Microelectron. Circuits and Syst.,
Duisburg, Germany",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C5120 (Logic and switching circuits); C5220P
(Parallel architecture); C5230 (Digital arithmetic
methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine;
Division; Double-metal n-well CMOS technology;
Floating-point vector-arithmetic unit; Hyperbolic sine;
Inverse tangent; Multiplication; Natural logarithm;
Phase; Sine; Square root; Vector norm",
numericalindex = "Size 1.6E-06 m; Computer speed 2.2E+08 FLOPS",
pubcountry = "USA",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Integrated logic circuits; Parallel architectures;
Pipeline processing; Vector processor systems",
}
@Article{Turner:1994:SRM,
author = "Stephen M. Turner",
title = "Square roots mod $p$",
journal = j-AMER-MATH-MONTHLY,
volume = "101",
number = "5",
pages = "443--449",
month = may,
year = "1994",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11A07",
MRnumber = "95c:11004",
MRreviewer = "David Lee Hilliker",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{Watanabe:1994:MSP,
author = "T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu
Oguni",
title = "Mathematical Software for the {P.C.} and Work
Stations: a Collection of {Fortran 77} Programs",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xiv + 387",
month = jun,
year = "1994",
ISBN = "0-444-82000-0",
ISBN-13 = "978-0-444-82000-6",
LCCN = "QA 76.73 F25 F6813 1994",
bibdate = "Sun Sep 28 10:42:07 MDT 1997",
bibsource = "http://www.amazon.com/exec/obidos/ISBN=0444820000/wholesaleproductA/;
http://www.cbooks.com/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translation of: FORTRAN 77 ni yoru suchi keisan
sofutowea.",
price = "US\$178.50",
URL = "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0444820000",
acknowledgement = ack-nhfb,
alttitle = "{Fortran 77} ni yoru suchi keisan sofutowea.
English.",
keywords = "Fortran 77 (computer program language); Numerical
analysis --- Use of --- Computers; {Fortran 77}
(Computer program language)",
}
@InProceedings{Wong:1994:FEE,
author = "W. F. Wong and E. Goto",
title = "Fast evaluation of the elementary functions in double
precision",
crossref = "Mudge:1994:PTS",
bookpages = "xi + 621",
pages = "349--358",
year = "1994",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "One of the most spectacular development in computer
technology is the growth in memory density and speed.
It is with this development in mind that we intend to
tackle the old problem of computing the elementary
functions. Since the dawn of computing, the fast and
accurate computation of the elementary functions has
been a constant concern of numerical computing. It now
seems possible to use tables of sizes in the range of
megabits to aid in such computation. To this end, in
this paper, we propose a method called ATA-M (Add-Table
Lookup-Add with Multiplication) for evaluating
polynomials with the aid of tables. When applied to the
elementary functions, we obtained a set of algorithms
which computes the reciprocal, square root,
exponential, sine, cosine, logarithm, are tangent and
the hyperbolic functions in about 3 to 4 double
precision floating point multiplication time and
utilizing about 2 Mbyte of tables.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
Singapore, Singapore",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods)",
confdate = "4-7 Jan. 1994",
conflocation = "Wailea, HI, USA",
confsponsor = "IEEE; ACM; Univ. Hawaii; Univ. Hawaii Coll. Bus.
Admin",
keywords = "Add-Table Lookup-Add with Multiplication; ATA-M;
Double precision; Elementary functions; Floating point
multiplication time; Hyperbolic functions; Memory
density; Memory speed; Numerical computing;
Polynomials",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Polynomials; Table lookup",
}
@Article{Wong:1994:FHB,
author = "W. F. Wong and E. Goto",
title = "Fast Hardware-Based Algorithms for Elementary Function
Computations Using Rectangular Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "3",
pages = "278--294",
month = mar,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.272429",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:54 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429",
abstract = "As the name suggests, elementary functions play a
vital role in scientific computations. Yet due to their
inherent nature, they are a considerable computing task
by themselves. Not surprisingly, since the dawn of
computing, the goal of speeding up elementary function
computation has been pursued. This paper describes new
hardware based algorithms for the computation of the
common elementary functions, namely division,
logarithm, reciprocal square root, arc tangent, sine
and cosine. These algorithms exploit microscopic
parallelism using specialized hardware with heavy use
of truncation based on detailed accuracy analysis. The
contribution of this work lies in the fact that these
algorithms are very fast and yet are accurate. If we
let the time to perform an IEEE Standard 754 double
precision floating point multiplication be $
\tau_\times $, our algorithms to achieve roughly $ 3.68
\tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times
$, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $
6.5 \tau_\times $, for division, logarithm, square
root, exponential, are tangent and complex exponential
(sine and cosine) respectively. The trade-off is the
need for tables and some specialized hardware. The
total amount of tables required, however, is less than
128 Kbytes. We discuss the hardware, algorithmic and
accuracy aspects of these algorithms.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
Singapore, Singapore",
ajournal = "IEEE Trans. Comput.",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Arc tangent; Common elementary functions; Cosine;
Elementary function computations; Floating point
multiplication; Hardware-based algorithms; Microscopic
parallelism; Reciprocal square root; Rectangular
multipliers; Scientific computations; Sine",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Error analysis",
}
@Article{Xu:1994:VPC,
author = "Guo Liang Xu and Jia Kai Li",
title = "Variable precision computation of elementary
functions. ({Chinese})",
journal = j-J-NUMER-METHODS-COMPUT-APPL,
volume = "15",
number = "3",
pages = "161--171",
year = "1994",
ISSN = "1000-3266",
MRclass = "65D20 (65Y20)",
MRnumber = "MR1357336 (96i:65013)",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal on Numerical Methods and Computer
Applications. Shuzhi Jisuan yu Jisuanji Yingyong",
}
@Article{Abad:1995:CRC,
author = "Julio Abad and Javier Sesma",
title = "Computation of the Regular Confluent Hypergeometric
Function",
journal = j-MATHEMATICA-J,
volume = "5",
number = "4",
pages = "??--??",
month = "Fall",
year = "1995",
CODEN = "????",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
ISSN-L = "1047-5974",
bibdate = "Sat Nov 6 13:34:06 MDT 2010",
bibsource = "http://www.mathematica-journal.com/issue/v5i4/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html",
acknowledgement = ack-nhfb,
fjournal = "Mathematica Journal",
journal-URL = "http://www.mathematica-journal.com/",
}
@Article{Amos:1995:RAP,
author = "D. E. Amos",
title = "A Remark on {Algorithm 644}: a Portable Package for
{Bessel} Functions of a Complex Argument and
Nonnegative Order",
journal = j-TOMS,
volume = "21",
number = "4",
pages = "388--393",
month = dec,
year = "1995",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/212066.212078",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 09 10:24:54 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See
\cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "complex Airy Functions; complex Bessel functions;
derivatives of Airy functions; H, I, J, K, and Y Bessel
functions; log gamma function",
subject = "G.1.0 [Numerical Analysis]: General -- numerical
algorithms; G.1.m [Numerical Analysis]: Miscellaneous;
G.m [Mathematics of Computing]: Miscellaneous",
}
@Article{Bagby:1995:CNP,
author = "Richard J. Bagby",
title = "Calculating normal probabilities",
journal = j-AMER-MATH-MONTHLY,
volume = "102",
number = "1",
pages = "46--48",
month = jan,
year = "1995",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65D20",
MRnumber = "96f:65021",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "http://www.jstor.org/journals/00029890.htm;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Baratchart:1995:RIE,
author = "L. Baratchart and E. B. Saff and F. Wielonsky",
title = "Rational interpolation of the exponential function",
journal = j-CAN-J-MATH,
volume = "47",
number = "??",
pages = "1121--1147",
month = "????",
year = "1995",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1995-058-6",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:39:05 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v47/;
https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
}
@TechReport{Borwein:1995:EARa,
author = "Peter Borwein",
title = "An Efficient Algorithm for the {Riemann} Zeta
Function",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "9",
day = "20",
month = jan,
year = "1995",
bibdate = "Thu Sep 01 18:09:22 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://docserver.carma.newcastle.edu.au/107",
abstract = "A very simple class of algorithms for the computation
of the Riemann-zeta function to arbitrary precision in
arbitrary domains is proposed. These algorithms out
perform the standard methods based on Euler--Maclaurin
summation, are easier to implement and are easier to
analyse.",
acknowledgement = ack-nhfb,
author-dates = "10 May 1953--23 August 2020",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1995:EARb,
author = "P. Borwein",
editor = "????",
booktitle = "{CMS} Conference Proceedings",
title = "An efficient algorithm for the {Riemann} zeta
function",
volume = "27",
publisher = "Canadian Mathematical Society",
address = "616 Cooper Street, Ottawa, ON, K1R 5J2, Canada",
pages = "29--34",
month = jan,
year = "1995",
bibdate = "Wed Jun 28 08:27:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://web.archive.org/web/20140602151514/http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
acknowledgement = ack-nhfb,
xxURL = "http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
}
@Article{Carlson:1995:NCR,
author = "B. C. Carlson",
title = "Numerical computation of real or complex elliptic
integrals",
journal = j-NUMER-ALGORITHMS,
volume = "10",
number = "1--2",
pages = "13--26",
month = jul,
year = "1995",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/BF02198293",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "33Exx (33-04 65D20)",
MRnumber = "1 345 407",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Special functions (Torino, 1993)",
abstract = "Algorithms for numerical computation of symmetric
elliptic integrals of all three kinds are improved in
several ways and extended to complex values of the
variables (with some restrictions in the case of the
integral of the third kind). Numerical check values,
consistency checks, and relations to Legendre's
integrals and Bulirsch's integrals are included.",
acknowledgement = ack-nhfb,
classification = "B0290R (Integral equations); C4180 (Integral
equations)",
conflocation = "Torino, Italy; 14-15 Oct. 1993",
conftitle = "International Joint Symposium on Special Functions and
Artificial Intelligence",
corpsource = "Ames Lab., Iowa State Univ., Ames, IA, USA",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Bulirsch's integrals; complex elliptic integrals;
complex values; consistency checks; elliptic equations;
integral equations; Legendre's integrals; numerical
analysis; numerical check values; numerical computation
algorithms; real elliptic integrals",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{Chaudhry:1995:DGI,
author = "M. Aslam Chaudhry and S. M. Zubair",
title = "On the decomposition of generalized incomplete gamma
functions with applications to {Fourier} transforms",
journal = j-J-COMPUT-APPL-MATH,
volume = "59",
number = "3",
pages = "253--284",
day = "30",
month = may,
year = "1995",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:24:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704279400026W",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Chen:1995:UCA,
author = "San-Gee Chen and Chieh-Chih Li",
booktitle = "{IEEE} Signal Processing Society Workshop on {VLSI}
Signal Processing, {VIII, 1995}",
title = "A unified cellular array for multiplication, division
and square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "533--541",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A unified fast, small-area processor capable of
executing multiplication, division and square-root
operations, all starting from MSD is proposed. Unlike
the existing designs which require both addition and
subtraction operations, and complicated \ldots{}",
}
@Article{Das:1995:IFC,
author = "D. Das and K. Mukhopadhyaya and B. P. Sinha",
title = "Implementation of four common functions on an {LNS}
co-processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "1",
pages = "155--161",
month = jan,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.367997",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "We propose a scheme for evaluating four commonly used
functions namely, (1) inverse trigonometric functions,
(2) trigonometric functions, (3) the exponential
function, and (4) the logarithmic function with the
help of a logarithmic number system (\ldots{}).",
}
@Article{Daumas:1995:MRR,
author = "Marc Daumas and Christophe Mazenc and Xavier Merrheim
and Jean-Michel Muller",
title = "Modular range reduction: a new algorithm for fast and
accurate computation of the elementary functions",
journal = j-J-UCS,
volume = "1",
number = "3",
pages = "162--175 (electronic)",
year = "1995",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
MRclass = "68M07 (68Q20)",
MRnumber = "1 390 003",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@Article{Doman:1995:SAP,
author = "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
title = "A Set of {Ada} Packages for High Precision
Calculations",
journal = j-TOMS,
volume = "21",
number = "4",
pages = "416--431",
month = dec,
year = "1995",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Nov 14 09:57:55 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accuracy; Ada; arithmetic elementary-function
evaluation; floating-point; multiple-precision portable
software",
subject = "G.1.0 [Numerical Analysis]: General -- computer
arithmetic; G.1.2 [Numerical Analysis]: Approximation
-- elementary function approximation; G.4 [Mathematics
of Computing]: Mathematical Software -- algorithm
analysis; efficiency; portability",
}
@Article{Driver:1995:NQH,
author = "Kathy Driver",
title = "Nondiagonal quadratic {Hermite--Pad{\'e}}
approximation to the exponential function",
journal = j-J-COMPUT-APPL-MATH,
volume = "65",
number = "1--3",
pages = "125--134",
day = "29",
month = dec,
year = "1995",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:02:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042795001069",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Goano:1995:ACC,
author = "Michele Goano",
title = "{Algorithm 745}: Computation of the Complete and
Incomplete {Fermi--Dirac} Integral",
journal = j-TOMS,
volume = "21",
number = "3",
pages = "221--232",
month = sep,
year = "1995",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/210089.210090",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 09 10:19:43 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Goano:1997:RA7}",
URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "asymptotic expansions; confluent hypergeometric
functions; convergence acceleration; e[k] transforms;
epsilon algorithm; Euler transformation; Fermi--Dirac
integral; incomplete Fermi--Dirac integral; incomplete
gamma function; Levin's u transform; Riemann's zeta
function",
subject = "G.1.2 [Mathematics of Computing]: Approximation; G.4
[Mathematics of Computing]: Mathematical Software; J.2
[Computer Applications]: Physical Sciences and
Engineering",
}
@Article{Hobson:1995:EMR,
author = "R. F. Hobson and M. W. Fraser",
title = "An efficient maximum-redundancy radix-$8$ {SRT}
division and square-root method",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "30",
number = "1",
pages = "29--38",
month = jan,
year = "1995",
CODEN = "IJSCBC",
DOI = "https://doi.org/10.1109/4.350197",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A new approach to integrating hardware multiplication,
division, and square-root is presented. We use a fully
integrated control path which simultaneously reduces
part of the redundant partial-remainder and performs a
truncated multiplication of the next quotient or
square-root digit by the divisor or square-root value.
A separate (parallel) full precision iterative
multiplier is used for partial remainder production.
Strategic details of a radix-8 implementation are
discussed. It is shown that a maximally redundant digit
set is a viable choice for high performance in this
case.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC,
Canada",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
floating point algorithm; Integrated control path;
Maximally redundant digit set; Maximum-redundancy
radix-8 SRT algorithm; Multiplication; Parallel
iterative multiplier; Partial remainder production;
Redundant partial-remainder; Square-root method; Table
lookup",
numericalindex = "Size 1.2E-06 m",
pubcountry = "USA",
summary = "A new approach to integrating hardware multiplication,
division, and square-root is presented. We use a fully
integrated control path which simultaneously reduces
part of the redundant partial-remainder and performs a
truncated multiplication of the \ldots{}",
thesaurus = "Adders; CMOS digital integrated circuits; Digital
arithmetic; Dividing circuits; Floating point
arithmetic; Multiplying circuits",
}
@InProceedings{Ito:1995:EIA,
author = "M. Ito and N. Takagi and S. Yajima",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "Efficient Initial Approximation and Fast Converging
Methods for Division and Square Root",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2--9",
month = jul,
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-sfo # " and " # ack-nhfb,
summary = "Efficient initial approximations and fast converging
algorithms are important to achieve the desired
precision faster at lower hardware cost in
multiplicative division and square root. In this paper,
a new initial approximation method for division,
\ldots{}",
}
@Book{Jeffrey:1995:HMF,
author = "Alan Jeffrey",
title = "Handbook of Mathematical Formulas and Integrals",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xxiv + 410",
year = "1995",
ISBN = "0-08-052301-3, 0-12-382580-6 (e-book), 1-4832-9514-1
(e-book)",
ISBN-13 = "978-0-08-052301-9, 978-0-12-382580-3 (e-book),
978-1-4832-9514-5 (e-book)",
LCCN = "QA47 .J38 1995",
bibdate = "Wed Jun 12 14:33:38 MDT 2024",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/book/9780123825803",
abstract = "If there is a formula to solve a given problem in
mathematics, you will find it in Alan Jeffrey's
\booktitle{Handbook of Mathematical Formulas and
Integrals}. Thanks to its unique thumb-tab indexing
feature, answers are easy to find based upon the type
of problem they solve. The Handbook covers important
formulas, functions, relations, and methods from
algebra, trigonometric and exponential functions,
combinatorics, probability, matrix theory, calculus and
vector calculus, both ordinary and partial differential
equations, Fourier series, orthogonal polynomials, and
Laplace transforms. Based on Gradshteyn and Ryzhik's
Table of Integrals, Series, and Products, Fifth Edition
(edited by Jeffrey), but far more accessible and
written with particular attention to the needs of
students and practicing scientists and engineers, this
book is an essential resource. Affordable and
authoritative, it is the first place to look for help
and a rewarding place to browse.",
acknowledgement = ack-nhfb,
subject = "Mathematics; Tables; Formulae; Math{\'e}matiques;
Formules; formulas (algorithms); Mathematics.",
tableofcontents = "0: Quick Reference List of Frequently Used Data \\
0.1: Useful Identities / 1 \\
0.2: Complex Relationships / 2 \\
0.3: Constants / 2 \\
0.4: Derivatives of Elementary Functions / 3 \\
0.5: Rules of Differentiation and Integration / 3 \\
0.6: Standard Integrals / 4 \\
0.7: Standard Series / 11 \\
0.8: Geometry / 13 \\
1: Numerical, Algebraic, and Analytical Results for
Series and Calculus \\
1.1: Algebraic Results Involving Real and Complex
Numbers / 25 \\
1.2: Finite Sums / 29 \\
1.3: Bernoulli and Euler Numbers and Polynomials 37 \\
1.4: Determinants / 47 \\
1.5: Matrices / 55 \\
1.6: Permutations and Combinations / 62 \\
1.7: Partial Fraction Decomposition / 63 \\
1.8: Convergence of Series / 66 \\
1.9: Infinite Products / 71 \\
1.10: Functional Series / 73 \\
1.11: Power Series / 74 \\
1.12: Taylor Series / 79 \\
1.13: Fourier Series / 81 \\
1.14: Asymptotic Expansions / 85 \\
1.15: Basic Results from the Calculus / 86 \\
2: Functions and Identities \\
2.1: Complex Numbers and Trigonometric and Hyperbolic
Functions / 101 \\
2.2: Logarithms and Exponentials / 112 \\
2.3: The Exponential Function / 114 \\
2.4: Trigonometric Identities / 115 \\
2.5: Hyperbolic Identities / 121 \\
2.6: The Logarithm / 126 \\
2.7: Inverse Trigonometric and Hyperbolic Functions /
128 \\
2.8: Series Representations of Trigonometric and
Hyperbolic Functions / 133 \\
2.9: Useful Limiting Values and Inequalities Involving
Elementary Functions / 136 \\
3: Derivatives of Elementary Functions \\
3.1: Derivatives of Algebraic, Logarithmic, and
Exponential Functions / 139 \\
3.2: Derivatives of Trigonometric Functions / 140 \\
3.3: Derivatives of Inverse Trigonometric Functions /
140 \\
3.4: Derivatives of Hyperbolic Functions / 141 \\
3.5: Derivatives of Inverse Hyperbolic Functions 142
\\
4: Indefinite Integrals of Algebraic Functions \\
4.1: Algebraic and Transcendental Functions / 145 \\
4.2: Indefinite Integrals of Rational Functions 146 \\
4.3: Nonrational Algebraic Functions / 158 \\
5: Indefinite Integrals of Exponential Functions \\
5.1: Basic Results / 167 \\
6: Indefinite Integrals of Logarithmic Functions \\
6.1: Combinations of Logarithms and Polynomials 173 \\
7: Indefinite Integrals of Hyperbolic Functions \\
7.1: Basic Results / 179 \\
7.2: Integrands Involving Powers of sinh(bx) or
cosh(bx) / 180 \\
7.3: Integrands Involving (a [plus or minus]
bx)[superscript m] sinh(cx) or (a + bx)[superscript m]
cosh(cx) / 181 \\
7.4: Integrands Involving x[superscript m]
sinh[superscript n] x or x[superscript m]
cosh[superscript n] x / 183 \\
7.5: Integrands Involving x[superscript m]
sinh[superscript -n] x or x[superscript m]
cosh[superscript -n] x / 183 \\
7.6: Integrands Involving (1 [plus or minus] cosh
x)[superscript -m] / 185 \\
7.7: Integrands Involving sinh(ax)cosh[superscript -n]
x or cosh(ax)sinh[superscript -n] x / 185 \\
7.8: Integrands Involving sinh(ax + b) and cosh(cx + d)
/ 186 \\
7.9: Integrands Involving tanh kx and coth kx 188 \\
7.10: Integrands Involving (a + bx)[superscript m] sinh
kx or (a + bx)[superscript m] cosh kx / 189 \\
8: Indefinite Integrals Involving Inverse Hyperbolic
Functions \\
8.1: Basic Results / 191 \\
8.2: Integrands Involving x[superscript -n]
arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 \\
8.3: Integrands Involving x[superscript n] arctanh(x/a)
or x[superscript n] arccoth(x/a) 194 \\
8.4: Integrands Involving x[superscript -n]
arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195
\\
9: Indefinite Integrals of Trigonometric Functions \\
9.1: Basic Results / 197 \\
9.2: Integrands Involving Powers of x and Powers of sin
x or cos x / 197 \\
9.3: Integrands Involving tan x and/or cot x 205 \\
9.4: Integrands Involving sin x and cos x / 207 \\
9.5: Integrands Involving Sines and Cosines with Linear
Arguments and Powers of x / 211 \\
10: Indefinite Integrals of Inverse Trigonometric
Functions \\
10.1: Integrands Involving Powers of x and Powers of
Inverse Trigonometric Functions / 215 \\
11: The Gamma, Beta, Pi, and Psi Functions \\
11.1: The Euler Integral and Limit and Infinite Product
Representations for [Gamma] (x) / 221 \\
12: Elliptic Integrals and Functions \\
12.1: Elliptic Integrals / 229 \\
12.2: Jacobian Elliptic Functions / 235 \\
12.3: Derivatives and Integrals / 237 \\
12.4: Inverse Jacobian Elliptic Functions / 237 \\
13: Probability Integrals and the Error Function \\
13.1: Normal Distribution / 239 \\
13.2: The Error Function / 242 \\
14: Fresnel Integrals, Sine and Cosine Integrals \\
14.1: Definitions, Series Representations, and Values
at Infinity / 245 \\
14.2: Definitions, Series Representations, and Values
at Infinity / 247 \\
15: Definite Integrals \\
15.1: Integrands Involving Powers of x / 249 \\
15.2: Integrands Involving Trigonometric Functions 251
\\
15.3: Integrands Involving the Exponential Function /
254 \\
15.4: Integrands Involving the Hyperbolic Function 256
\\
15.5: Integrands Involving the Logarithmic Function /
256 \\
16: Different Forms of Fourier Series \\
16.1: Fourier Series for f(x) on -[pi] [less than or
equal] x [less than or equal] [pi] / 257 \\
16.2: Fourier Series for f(x) on -L [less than or
equal] x [less than or equal] L / 258 \\
16.3: Fourier Series for f(x) on a [less than or equal]
x [less than or equal] b / 258 \\
16.4: Half-Range Fourier Cosine Series for f(x) on 0
[less than or equal] x [less than or equal] [pi] 259
\\
16.5: Half-Range Fourier Cosine Series for f(x) on 0
[less than or equal] x [less than or equal] L 259 \\
16.6: Half-Range Fourier Sine Series for f(x) on 0
[less than or equal] x [less than or equal] [pi] 260
\\
16.7: Half-Range Fourier Sine Series for f(x) on 0
[less than or equal] x [less than or equal] L 260 \\
16.8: Complex (Exponential) Fourier Series for f(x) on
-[pi] [less than or equal] x [less than or equal] [pi]
/ 260 \\
16.9: Complex (Exponential) Fourier Series for f(x) on
-L [less than or equal] x [less than or equal] L 261
\\
16.10: Representative Examples of Fourier Series 261
\\
16.11: Fourier Series and Discontinuous Functions 265
\\
17: Bessel Functions \\
17.1: Bessel's Differential Equation / 269 \\
17.2: Series Expansions for J[subscript v](x) and
Y[subscript v](x) / 270 \\
17.3: Bessel Functions of Fractional Order / 272 \\
17.4: Asymptotic Representations for Bessel Functions /
273 \\
17.5: Zeros of Bessel Functions / 273 \\
17.6: Bessel's Modified Equation / 274 \\
17.7: Series Expansions for I[subscript v](x) and
K[subscript v](x) / 276 \\
17.8: Modified Bessel Functions of Fractional Order /
277 \\
17.9: Asymptotic Representations of Modified Bessel
Functions / 278 \\
17.10: Relationships between Bessel Functions 278 \\
17.11: Integral Representations of J[subscript n](x),
I[subscript n](x), and K[subscript n](x) / 281 \\
17.12: Indefinite Integrals of Bessel Functions 281 \\
17.13: Definite Integrals Involving Bessel Functions /
282 \\
17.14: Spherical Bessel Functions / 283 \\
18: Orthogonal Polynomials \\
18.2: Legendre Polynomials P[subscript n](x) 286 \\
18.3: Chebyshev Polynomials T[subscript n](x) and
U[subscript n](x) / 290 \\
18.4: Laguerre Polynomials L[subscript n](x) 294 \\
18.5: Hermite Polynomials H[subscript n](x) / 296 \\
19: Laplace Transformation \\
20: Fourier Transforms \\
21: Numerical Integration \\
21.1: Classical Methods / 315 \\
22: Solutions of Standard Ordinary Differential
Equations \\
22.2: Separation of Variables / 323 \\
22.3: Linear First-Order Equations / 323 \\
22.4: Bernoulli's Equation / 324 \\
22.5: Exact Equations / 325 \\
22.6: Homogeneous Equations / 325 \\
22.7: Linear Differential Equations / 326 \\
22.8: Constant Coefficient Linear Differential
Equations \\
Homogeneous Case / 327 \\
22.9: Linear Homogeneous Second-Order Equation 330 \\
22.10: Constant Coefficient Linear Differential
Equations \\
Inhomogeneous Case / 331 \\
22.11: Linear Inhomogeneous Second-Order Equation 333
\\
22.12: Determination of Particular Integrals by the
Method of Undetermined Coefficients / 334 \\
22.13: The Cauchy-Euler Equation / 336 \\
22.14: Legendre's Equation / 337 \\
22.15: Bessel's Equations / 337 \\
22.16: Power Series and Frobenius Methods / 339 \\
22.17: The Hypergeometric Equation / 344 \\
22.18: Numerical Methods / 345 \\
23: Vector Analysis \\
23.1: Scalars and Vectors / 353 \\
23.2: Scalar Products / 358 \\
23.3: Vector Products / 359 \\
23.4: Triple Products / 360 \\
23.5: Products of Four Vectors / 361 \\
23.6: Derivatives of Vector Functions of a Scalar t /
361 \\
23.7: Derivatives of Vector Functions of Several Scalar
Variables / 362 \\
23.8: Integrals of Vector Functions of a Scalar
Variable t / 363 \\
23.9: Line Integrals / 364 \\
23.10: Vector Integral Theorems / 366 \\
23.11: A Vector Rate of Change Theorem / 368 \\
23.12: Useful Vector Identities and Results / 368 \\
24: Systems of Orthogonal Coordinates \\
24.1: Curvilinear Coordinates / 369 \\
24.2: Vector Operators in Orthogonal Coordinates 371
\\
24.3: Systems of Orthogonal Coordinates / 371 \\
25: Partial Differential Equations and Special
Functions \\
25.1: Fundamental Ideas / 381 \\
25.2: Method of Separation of Variables / 385 \\
25.3: The Sturm--Liouville Problem and Special
Functions / 387 \\
25.4: A First-Order System and the Wave Equation 390
\\
25.5: Conservation Equations (Laws) / 391 \\
25.6: The Method of Characteristics / 392 \\
25.7: Discontinuous Solutions (Shocks) / 396 \\
25.8: Similarity Solutions / 398 \\
25.9: Burgers's Equation, the KdV Equation, and the
KdVB Equation / 400 \\
26: The z-Transform \\
26.1: The z-Transform and Transform Pairs / 403 \\
27: Numerical Approximation \\
27.2: Economization of Series / 411 \\
27.3: Pade Approximation / 413 \\
27.4: Finite Difference Approximations to Ordinary and
Partial Derivatives / 415",
}
@Article{Krattenthaler:1995:HHM,
author = "C. Krattenthaler",
title = "{HYP} and {HYPQ}: {Mathematica} packages for the
manipulation of binomial sums and hypergeometric
series, respectively $q$-binomial sums and basic
hypergeometric series",
journal = j-J-SYMBOLIC-COMP,
volume = "20",
number = "5--6",
pages = "737--744",
month = nov # "--" # dec,
year = "1995",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "05Axx (11Bxx 33-04 33Cxx 33Dxx)",
MRnumber = "1 395 424",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Symbolic computation in combinatorics $ \Delta_1 $
(Ithaca, NY, 1993).",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics computing); C1100 (Mathematical
techniques)",
corpsource = "Inst. fur Math., Wien Univ., Austria",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "basic hypergeometric; binomial sums; HYP;
hypergeometric series; HYPQ; Mathematica packages;
mathematics computing; packages; q-binomial sums;
series; series (mathematics); software; symbol
manipulation",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kwan:1995:CII,
author = "H. Kwan and R. L. {Nelson, Jr.} and E. E.
{Swartzlander, Jr.}",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "Cascaded Implementation of an Iterative
Inverse-Square-Root Algorithm, with Overflow
Lookahead",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "115--122",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
summary = "We present an unconventional method of computing the
inverse of the square root. It implements the
equivalent of two iterations of a well-known
multiplicative method to obtain 24-bit mantissa
accuracy. We implement each ``iteration'' as a
\ldots{}",
}
@InProceedings{Lang:1995:VHR,
author = "T. Lang and P. Montuschi",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "Very-High Radix Combined Division and Square Root with
Prescaling and Selection by Rounding",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "124--131",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
summary = "An algorithm for square root with prescaling is
developed and combined with a similar scheme for
division. An implementation is described, evaluated and
compared with other combined div/sqrt \ldots{}",
}
@Book{Lau:1995:NLC,
author = "H. T. (Hang Tong) Lau",
title = "A Numerical Library in {C} for Scientists and
Engineers",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xvii + 795",
year = "1995",
ISBN = "0-8493-7376-X",
ISBN-13 = "978-0-8493-7376-3",
LCCN = "QA76.73.C15 L38 1995",
bibdate = "Fri Sep 26 14:29:10 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html",
acknowledgement = ack-nhfb,
shorttableofcontents = "Introduction \\
1 Elementary Procedures \\
2 Algebraic Evaluations \\
3 Linear Algebra \\
4 Analytic Evaluations \\
5 Analytic Problems \\
6 Special Functions \\
7 Interpolation and Approximation",
subject = "C (Computer program language)",
tableofcontents = "1. Elementary Procedures \\
1.1. Real vector and matrix Initialization \\
1.2. Real vector and matrix Duplication \\
1.3. Real vector and matrix Multiplication \\
1.4. Real vector vector products \\
1.5. Real matrix vector products \\
1.6. Real matrix matrix products \\
1.7. Real vector and matrix Elimination \\
1.8. Real vector and matrix Interchanging \\
1.9. Real vector and matrix Rotation \\
1.10. Real vector and matrix Norms \\
1.11. Real vector and matrix Scaling \\
1.12. Complex vector and matrix Multiplication \\
1.13. Complex vector and matrix Scalar products \\
1.14. Complex vector and matrix Elimination \\
1.15. Complex vector and matrix Rotation \\
1.16. Complex vector and matrix Norms \\
1.17. Complex vector and matrix Scaling \\
1.18. Complex monadic operations \\
1.19. Complex dyadic operations \\
1.20. Long integer arithmetic \\
2. Algebraic Evaluations \\
2.1. Evaluation of polynomials in Grunert form \\
2.2. Evaluation of general orthogonal polynomials \\
2.3. Evaluation of Chebyshev polynomials \\
2.4. Evaluation of Fourier series \\
2.5. Evaluation of continued fractions \\
2.6. Transformation of polynomial representation \\
2.7. Operations on orthogonal polynomials \\
3. Linear Algebra \\
3.1. Full real general matrices \\
3.2. Real Symmetric positive definite matrices \\
3.3. General real symmetric matrices \\
3.4. Real full rank overdetermined systems \\
3.5. Other real matrix problems \\
3.6. Real sparse non-symmetric band matrices \\
3.7. Real sparse non-symmetric tridiagonal matrices \\
3.8. Sparse symmetric positive definite band matrices
\\
3.9. Symmetric positive definite tridiagonal matrices
\\
3.10. Sparse real matrices \\
Iterative methods \\
3.11. Similarity transformation \\
3.12. Other transformations \\
3.13. The (ordinary) eigenvalue problem \\
3.14. The generalized eigenvalue problem \\
3.15. Singular values \\
3.16. Zeros of polynomials \\
4. Analytic Evaluations \\
4.1. Evaluation of an infinite series \\
4.2. Quadrature \\
4.3. Numerical differentiation \\
5. Analytic Problems \\
5.1. Non-linear equations \\
5.2. Unconstrained optimization \\
5.3. Overdetermined nonlinear systems \\
5.4. Differential equations \\
Initial value problems \\
5.5. Two point boundary value problems \\
5.6. Two-dimensional boundary value problems \\
5.7. Parameter estimation in differential equations \\
6. Special Functions \\
6.1. Elementary functions \\
6.2. Exponential integral \\
6.3. Gamma function \\
6.4. Error function \\
6.5. Bessel functions of integer order \\
6.6. Bessel functions of real order \\
7. Interpolation and Approximation \\
7.1. Real data in one dimension \\
Appendix B: Prototype Declarations \\
Appendix C: Procedure Descriptions \\
Appendix D: Memory Management Utilities",
}
@InProceedings{Leeser:1995:VSR,
author = "M. Leeser and J. O'Leary",
booktitle = "Proceedings of the {IEEE} International Conference on
Computer Design: {VLSI} in Computers and Processors,
{ICCD '95}",
title = "Verification of a subtractive radix-$2$ square root
algorithm and implementation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "526--531",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Many modern microprocessors implement floating point
square root hardware using subtractive algorithms. Such
processors include the HP PA7200, the MIPS R4400, and
the Intel Pentium. The Intel Pentium division bug
highlights the importance of \ldots{}",
}
@Article{Lether:1995:MAZ,
author = "F. G. Lether and P. R. Wenston",
title = "Minimax approximations to the zeros of {$ P_n(x) $}
and {Gauss--Legendre} quadrature",
journal = j-J-COMPUT-APPL-MATH,
volume = "59",
number = "2",
pages = "245--252",
day = "19",
month = may,
year = "1995",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:24:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042794000305",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Lewanowicz:1995:AMC,
author = "Stanis{\l}aw Lewanowicz and Stefan Paszkowski",
title = "An analytic method for convergence acceleration of
certain hypergeometric series",
journal = j-MATH-COMPUT,
volume = "64",
number = "210",
pages = "691--713",
month = apr,
year = "1995",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2153446",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33C45 (65B10 65D20)",
MRnumber = "1277769 (95h:33006)",
MRreviewer = "Anton Hut'a",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Comput. Sci., Wroclaw Univ., Poland",
classcodes = "B0290 (Numerical analysis); C4100 (Numerical
analysis)",
corpsource = "Inst. of Comput. Sci., Wroclaw Univ., Poland",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "analytic method; convergence acceleration; convergence
of numerical methods; fast converging expansions;
hypergeometric; iterated transformation; mathematical
constants; series; series (mathematics)",
treatment = "T Theoretical or Mathematical",
}
@Article{Liu:1995:SRV,
author = "S.-I. Liu",
title = "Square-rooting and vector summation circuits using
current conveyors",
journal = "IEE Proceedings on Circuits, Devices and Systems [see
also IEE Proceedings G - Circuits, Devices and
Systems]",
volume = "142",
number = "4",
pages = "223--226",
month = aug,
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "New analogue squaring, square-rooting and vector
summation circuits using current conveyors (CCIIs) are
presented. They consist of MOS transistors biased in
the triode region, a buffered unity-gain inverting
amplifier, resistors and CCIIs. A general \ldots{}",
}
@Article{Louie:1995:VPS,
author = "Marianne E. Louie and Milo{\v{s}} D. Ercegovac",
title = "A Variable-Precision Square Root Implementation for
Field Programmable Gate Arrays",
journal = j-J-SUPERCOMPUTING,
volume = "9",
number = "3",
pages = "315--336",
month = sep,
year = "1995",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/BF01212874",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Wed Jul 6 11:13:09 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3;
http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315;
http://www.wkap.nl/oasis.htm/95692",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., California Univ., Los Angeles,
CA, USA",
classification = "C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
corpsource = "Dept. of Comput. Sci., California Univ., Los Angeles,
CA, USA",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
keywords = "digital arithmetic; field programmable gate arrays;
square root; square root implementation;
variable-precision; Xilinx XC4010",
treatment = "P Practical",
}
@Article{Lucas:1995:EII,
author = "S. K. Lucas and H. A. Stone",
title = "Evaluating infinite integrals involving {Bessel}
functions of arbitrary order",
journal = j-J-COMPUT-APPL-MATH,
volume = "64",
number = "3",
pages = "217--231",
year = "1995",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(95)00142-5",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Thu Jul 8 13:22:49 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/B6TYH-4002HHC-J/2/54f1e67d9bea3e951acc3c39556ab452",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "$\varepsilon$-algorithm; Bessel functions; Bessel
zeros; infinite integration; mW transform; quadrature",
remark = "This paper examines several methods for accurately
integrating oscillatory functions, such as products of
$ f(x) $ with a trigonometric function or a Bessel
function. It also discusses finding zeros of Bessel
functions, and sequence acceleration techniques.",
}
@Article{Luther:1995:HAT,
author = "Wolfram Luther",
title = "Highly accurate tables for elementary functions",
journal = j-BIT-NUM-MATH,
volume = "35",
number = "3",
pages = "352--360",
month = sep,
year = "1995",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01732609",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D20 (68U05)",
MRnumber = "97h:65024",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit35.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=3&spage=352",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "elementary functions",
}
@InProceedings{Lynch:1995:KTF,
author = "T. Lynch and A. Ahmed and M. Schulte and T. Callaway",
title = "The {K5} Transcendental Functions",
crossref = "Knowles:1995:PSC",
pages = "163--171",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
URL = "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf",
acknowledgement = ack-nhfb,
}
@Article{Maroni:1995:IRB,
author = "P. Maroni",
title = "An integral representation for the {Bessel} form",
journal = j-J-COMPUT-APPL-MATH,
volume = "57",
number = "1--2",
pages = "251--260",
day = "20",
month = feb,
year = "1995",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:24:35 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042793E0249L",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Matsubara:1995:NBS,
author = "G. Matsubara and N. Ide and H. Tago and S. Suzuki and
N. Goto",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "30-ns 55-b Shared Radix $2$ Division and Square Root
Using a Self-Timed Circuit",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "98--105",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
summary = "A shared radix 2 division and square root
implementation using a self-timed circuit is presented.
The same execution time for division and square root is
achieved by using an on-the-fly digit decoding and a
root multiple generation technique. Most \ldots{}",
}
@Article{Miller:1995:RCF,
author = "A. R. Miller and I. S. Moskowitz",
title = "Reduction of a class of {Fox--Wright} psi functions
for certain rational parameters",
journal = j-COMPUT-MATH-APPL,
volume = "30",
number = "11",
pages = "73--82",
month = dec,
year = "1995",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219500165U",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From the abstract: ``The Fox--Wright Psi function is a
special case of Fox's $H$-function and a generalization
of the generalized hypergeometric function. In the
present paper, we show that the Psi function reduces to
a single generalized hypergeometric function when
certain of its parameters are integers and to a finite
sum of generalized hypergeometric functions when these
parameters are rational numbers.''",
}
@Article{Montuschi:1995:RRI,
author = "P. Montuschi and L. Ciminiera",
title = "A remark on {``Reducing iteration time when result
digit is zero for radix-$2$ SRT division and square
root with redundant remainders''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "1",
pages = "144--146",
month = jan,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.368000",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Montuschi:1993:RIT}.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "In a previous paper by P. Montuschi and L. Ciminiera
(ibid., vol. 42, no.2 p239-246, Feb 1993), an
architecture for shared radix 2 division and square
root has been presented whose main characteristic is
the ability to avoid any addition/subtraction,
\ldots{}",
}
@Article{Muldoon:1995:EZB,
author = "Martin E. Muldoon",
title = "Electrostatics and zeros of {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "65",
number = "1--3",
pages = "299--308",
day = "29",
month = dec,
year = "1995",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:02:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042795001182",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{OLeary:1995:NRI,
author = "J. O'Leary and M. Leeser and J. Hickey and M.
Aagaard",
title = "Non-Restoring Integer Square Root: a Case Study in
Design by Principled Optimization",
journal = j-LECT-NOTES-COMP-SCI,
volume = "901",
pages = "52--??",
year = "1995",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat May 11 13:45:32 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Paszkowski:1995:QHS,
author = "S. Paszkowski",
title = "Quasipower and hypergeometric series---construction
and evaluation",
journal = j-NUMER-ALGORITHMS,
volume = "10",
number = "3--4",
pages = "337--361",
month = oct,
year = "1995",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "41A58 (33-04 65B99)",
MRnumber = "96k:41042",
MRreviewer = "Walter Schempp",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
B0290Z (Other numerical methods); C4130 (Interpolation
and function approximation); C4190 (Other numerical
methods)",
corpsource = "Inst. for Low Temp. and Structure Res., Polish Acad.
of Sci., Wroclaw, Poland",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "approximation theory; Euler's dilogarithm;
Hermite-Pade approximation; hypergeometric series;
Levin's transforms; Pade approximants; power series;
quasipower; recurrence relations; series (mathematics);
transforms",
pubcountry = "Switzerland",
treatment = "P Practical; T Theoretical or Mathematical",
}
@InProceedings{Prabhu:1995:MRD,
author = "J. A. Prabhu and G. B. Zyner",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, 19--21 July 1995",
title = "{167 MHz} Radix-$8$ Divide and Square Root Using
Overlapped Radix-$2$ Stages",
crossref = "Knowles:1995:PSC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "155--162",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
summary = "UltraSPARC's IEEE-754 compliant floating point divide
and square root implementation is presented. Three
overlapping stages of SRT radix-$2$ quotient selection
logic enable an effective radix-$8$ calculation at 167
MHz while only a single radix-$2$ \ldots{}",
}
@InProceedings{Schwarz:1995:RQC,
author = "E. M. Schwarz",
booktitle = "Conference Record of the Twenty-Ninth Asilomar
Conference on Signals, Systems and Computers, 1995",
title = "Rounding for quadratically converging algorithms for
division and square root",
crossref = "Singh:1995:CRT",
volume = "1",
pages = "600--603",
month = oct,
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
summary = "Exactly rounded results are necessary for many
architectures such as IEEE 754 standard. For division
and square root, rounding is easy to perform if a
remainder is available. But for quadratically
converging algorithms, the remainder is not \ldots{}",
}
@Article{Sidhu:1995:EIF,
author = "Satinder S. Sidhu",
title = "Elliptic Integrals and Functions",
journal = j-COMPUT-PHYS,
volume = "9",
number = "3",
pages = "268--276",
month = may # "\slash " # jun,
year = "1995",
CODEN = "CPHYE2",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Thu Feb 02 18:05:53 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers in Physics",
}
@Article{Smith:1995:CFA,
author = "Roger Alan Smith",
title = "A Continued-Fraction Analysis of Trigonometric
Argument Reduction",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "11",
pages = "1348--1351",
month = nov,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.475133",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Dec 08 10:21:28 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The calculation of a trigonometric function of a large
argument x is effectively carried out by finding the
integer $N$ and $ 0 \leq \alpha < 1 $ such that $ x =
(N + \alpha) \pi / 4 $. This reduction modulo $ \pi / 4
$ makes it possible to calculate a trigonometric
function of a reduced argument, either $ \alpha \pi / 4
$ or $ (1 - \alpha) \pi / 4 $, which lies in the
interval $ (0, \pi / 4) $. Payne and Hanek [1]
described an efficient algorithm for computing $ \alpha
$ to a predetermined level of accuracy. They noted that
if $x$ differs only slightly from an integral multiple
$ \pi / 2 $, the reduction must be carried out quite
accurately to avoid loss of significance in the reduced
argument. We present a simple method using continued
fractions for determining, for all numbers $x$ for
which the greatest number of insignificant leading bits
occur. Applications are made IEEE single-precision and
double-precision formats and two extended-precision
formats.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "argument reduction; computer arithmetic; continued
fractions; nonlinear optimization; Payne/Hanek radian
reduction; range reduction; trigonometric functions",
}
@InProceedings{Soderquist:1995:APC,
author = "Peter Soderquist and Miriam Leeser",
title = "An Area\slash Performance Comparison of Subtractive
and Multiplicative Divide\slash Square Root
Implementations",
crossref = "Knowles:1995:PSC",
pages = "132--139",
month = jul,
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-12",
}
@Book{Varchenko:1995:MHF,
author = "A. N. (Aleksandr Nikolaevich) Varchenko",
title = "Multidimensional Hypergeometric Functions and
Representation Theory of {Lie} Algebras and Quantum
Groups",
volume = "21",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "ix + 371",
year = "1995",
ISBN = "981-02-1880-X",
ISBN-13 = "978-981-02-1880-5",
LCCN = "QA353.H9 V37 1995",
bibdate = "Sat Oct 30 21:12:24 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Advanced series in mathematical physics",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions; Kac-Moody algebras;
Representations of Lie algebras; Representations of
quantum groups",
tableofcontents = "1. Introduction \\
2. Construction of complexes calculating homology of
the complement of a configuration \\
3. Construction of homology complexes for
discriminantal configuration \\
4. Algebraic interpretation of chain complexes of a
discriminantal configuration \\
5. Quasiisomorphism of two-sided Hochschild complexes
to suitable one-sided Hochschild complexes \\
6. Bundle properties of a discriminantal configuration
\\
7. R-matrix for the two-sided Hochschild complexes \\
8. Monodromy \\
9. R-matrix operator as the canonical element, quantum
doubles \\
10. Hypergeometric integrals \\
11. Kac--Moody Lie algebras without Serre's relations
and their doubles \\
12. Hypergeometric integrals of a discriminantal
configuration \\
13. Resonances at infinity \\
14. Degenerations of discriminantal configurations \\
15. Remarks on homology groups of a configuration with
coefficients in local systems more general than complex
one-dimensional",
}
@Book{Vilenkin:1995:RLG,
author = "N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii
Ulsianovich) Klimyk",
title = "Representation of {Lie} Groups and Special Functions:
Recent Advances",
volume = "316",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xvi + 497",
year = "1995",
ISBN = "0-7923-3210-5",
ISBN-13 = "978-0-7923-3210-7",
LCCN = "QA176 .V55 1995",
bibdate = "Sat Oct 30 16:43:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematics and its applications",
URL = "http://www.loc.gov/catdir/enhancements/fy0823/95108075-d.html;
http://www.loc.gov/catdir/enhancements/fy0823/95108075-t.html",
acknowledgement = ack-nhfb,
remark = "Translated to English from Russian by V. A. Groza and
A. A. Groza.",
subject = "Representations of Lie groups; Functions, Special;
Integral transforms",
tableofcontents = "Preface / xiii \\
1. $h$-Harmonic Polynomials, $h$-Hankel Transform, and
Coxeter Groups / 1 \\
2. Symmetric Polynomials and Symmetric Functions / 67
\\
3. Hypergeometric Functions Related to Jack Polynomials
/ 185 \\
4. Clebsch--Gordan Coefficients and Racah Coefficients
of Finite Dimensional Representations / 265 \\
5. Clebsch--Gordan Coefficients of the Group $U(n)$ and
Related Generalizations of Hypergeometric Functions /
317 \\
6. Gel'fand Hypergeometric Functions / 393 \\
Bibliography / 463 \\
Supplementary Bibliography / 484 \\
Bibliography Notes / 488 \\
Subject Index / 494",
}
@Article{Vrahatis:1995:RPP,
author = "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
Zafiropoulos and T. N. Grapsa",
title = "{RFSFNS}: a portable package for the numerical
determination of the number and the calculation of
roots of {Bessel} functions",
journal = j-COMP-PHYS-COMM,
volume = "92",
number = "2--3",
pages = "252--266",
month = dec,
year = "1995",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(95)00115-9",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:01 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See erratum \cite{Vrahatis:1999:ESP}.",
URL = "http://www.sciencedirect.com/science/article/pii/0010465595001159",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Book{Watson:1995:TTB,
author = "G. N. (George Neville) Watson",
title = "A Treatise on the Theory of {Bessel} Functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "vi + 804",
year = "1995",
ISBN = "0-521-48391-3 (paperback), 0-521-06743-X (hardcover)",
ISBN-13 = "978-0-521-48391-9 (paperback), 978-0-521-06743-0
(hardcover)",
LCCN = "QA408 .W2 1995",
bibdate = "Sat Apr 19 09:15:26 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
series = "Cambridge mathematical library",
URL = "http://www.loc.gov/catdir/description/cam028/96139881.html;
http://www.loc.gov/catdir/toc/cam029/96139881.html",
acknowledgement = ack-nhfb,
remark = "First published 1922. Second edition 1944. Reprinted
1966.",
subject = "Bessel functions",
tableofcontents = "1. Bessel functions before 1826 \\
2. The Bessel coefficients \\
3. Bessel functions \\
4. Differential equations \\
5. Miscellaneous properties of Bessel functions \\
6. Integral representations of Bessel functions \\
7. Asymptotic expansions of Bessel functions \\
8. Bessel functions of large order \\
9. Polynomials associated with Bessel functions \\
10. Functions associated with Bessel functions \\
11. Addition theorems \\
12. Definite integrals \\
13. Infinitive integrals \\
14. Multiple integrals \\
15. The zeros of Bessel functions \\
16. Neumann series and Lommel's functions of two
variables \\
17. Kapteyn series \\
18. Series of Fourier-Bessel and Dini \\
19. Schl{\"o}mlich series \\
20. The tabulation of Bessel functions \\
Tables of Bessel functions \\
Bibliography \\
Indices",
xxauthor = "G. N. Watson",
}
@Article{Wong:1995:EHS,
author = "W. F. Wong and Yoshio Oyanagi and Eiichi Goto",
title = "Evaluation of the {Hitachi S-3800} Supercomputer Using
Six Benchmarks",
journal = j-IJSAHPC,
volume = "9",
number = "1",
pages = "58--70",
month = "Spring",
year = "1995",
CODEN = "IJSAE9",
ISSN = "0890-2720",
bibdate = "Tue Feb 18 09:07:32 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The S-3000 series is the third generation of Hitachi's
supercomputers. It is claimed to be currently the
fastest single processor supercomputer. In this paper,
we introduce the S-3000 and, using six benchmarks we
designed, evaluate a member of this series of
supercomputer, the top of the range S-3800, against its
predecessor, the Hitachi HITAC S-820. Our purpose is to
determine in what areas the S-3800 is an improvement
over its predecessor. The suite of benchmarks include
kernels for random number generation, elementary
function computation, FFT, dense matrix operations,
SOR, and list vector (scatter\slash gather) operations.
The use of small-to medium-sized kernels, as opposed to
large application benchmarks, help to better understand
the behavior of the machine. Our findings support the
claim that the S-3000 series is at least twice as fast
as the previous generation of Hitachi supercomputers.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
Singapore",
affiliationaddress = "Singapore",
classification = "722.4; 921.3; 921.6; 922.2",
fjournal = "International Journal of Supercomputer Applications
and High Performance Computing",
journal-URL = "http://hpc.sagepub.com/content/by/year",
journalabr = "Int J Supercomput Appl High Perform Comput",
keywords = "Benchmarks; Computer selection and evaluation;
Computer testing; Fast Fourier transforms; Fastest
single processor; Hitachi supercomputer; Matrix
algebra; Medium sized kernels; Performance; Random
number generation; Supercomputers; Vectors",
}
@Article{Wong:1995:FEE,
author = "W. F. Wong and E. Goto",
title = "Fast evaluation of the elementary functions in single
precision",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "3",
pages = "453--457",
month = mar,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.372037",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In this paper we introduce a new method for the fast
evaluation of the elementary functions in single
precision based on the evaluation of truncated Taylor
series using a difference method. We assume the
availability of large and fast (at least for read
purposes) memory. We call this method the ATA
(Add-Table lookup-Add) method. As the name implies, the
hardware required for the method are adders (both two/
and multi/operand adders) and fast tables. For IEEE
single precision numbers our initial estimates indicate
that we can calculate the basic elementary functions,
namely reciprocal, square root, logarithm, exponential,
trigonometric and inverse trigonometric functions,
within the latency of two to four floating point
multiplies.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
Singapore, Singapore",
ajournal = "IEEE Trans. Comput.",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Difference method; Elementary functions; Fast
evaluation; Floating point multiplies; Inverse
trigonometric functions; Logarithm functions;
Reciprocal; Single precision; Square root; Truncated
Taylor series",
pubcountry = "USA",
thesaurus = "Error analysis; Floating point arithmetic",
}
@Article{Ypma:1995:HDN,
author = "Tjalling J. Ypma",
title = "Historical Development of the {Newton--Raphson}
Method",
journal = j-SIAM-REVIEW,
volume = "37",
number = "4",
pages = "531--551",
month = dec,
year = "1995",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1037125",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "01A05 (65-03)",
MRnumber = "97b:01003",
MRreviewer = "M. Z. Nashed",
bibdate = "Sat Mar 29 09:55:35 MDT 2014",
bibsource = "Compendex database;
http://epubs.siam.org/toc/siread/37/4;
http://www.siam.org/journals/sirev/sirev374.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/23425.htm;
http://link.aip.org/link/?SIR/37/531/1",
abstract = "This expository paper traces the development of the
Newton--Raphson method for solving nonlinear algebraic
equations through the extant notes, letters, and
publications of Isaac Newton, Joseph Raphson, and
Thomas Simpson. It is shown how Newton's formulation
differed from the iterative process of Raphson, and
that Simpson was the first to give a general
formulation, in terms of fluxional calculus, applicable
to nonpolynomial equations. Simpson's extension of the
method to systems of equations is exhibited.",
acknowledgement = ack-nhfb,
affiliation = "Western Washington Univ",
affiliationaddress = "Bellingham, WA, USA",
classification = "921.1; 921.2; 921.6",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "Algebra; Algorithms; Approximation theory;
Differentiation (calculus); Finite difference method;
Fluxional calculus; Isaac Newton; Iterative methods;
Joseph Raphson; Linearization; Newton--Raphson method;
Nonlinear algebraic equations; Nonlinear equations;
Nonpolynomial equation; Polynomials; Secant method;
Thomas Simpson",
onlinedate = "December 1995",
}
@Article{Zhang:1995:TMAa,
author = "J. Zhang and J. A. Belward",
title = "Tau-method approximations for the {Bessel} function {$
Y_0 (z) $}",
journal = j-COMPUT-MATH-APPL,
volume = "30",
number = "7",
pages = "5--14",
month = oct,
year = "1995",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(95)00120-N",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Sun Jun 12 08:33:42 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219500120N",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Zhang:1995:TMAb,
author = "J. Zhang",
title = "Tau-method approximations for the {Bessel} function {$
Y_1 (z) $}",
journal = j-COMPUT-MATH-APPL,
volume = "30",
number = "7",
pages = "15--19",
month = oct,
year = "1995",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(95)00121-E",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Sun Jun 12 09:26:01 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219500121E",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From p. 18 (conclusions section), ``We may use this
method to approximate the Bessel functions of other
integer orders. \ldots{} It is therefore advisable to
use the recurrence relations of the Bessel functions to
compute function values for $ n > 1 $ \ldots''. [This
is a similar limitation as with Chebyshev and minimax
polynomial approximations: they are valid only for a
single order the Bessel function.]",
}
@InProceedings{Ahrendt:1996:FHC,
author = "Timm Ahrendt",
title = "Fast High-Precision Computations of Complex Square
Roots",
crossref = "LakshmanYN:1996:IPI",
pages = "142--149",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; measurement;
SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Models of Computation, Bounded-action devices.
{\bf G.1.5} Mathematics of Computing, NUMERICAL
ANALYSIS, Roots of Nonlinear Equations, Iterative
methods. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
xxtitle = "Fast high-precision computation of complex square
roots",
}
@Article{Balla:1996:SCB,
author = "K. Balla and V. H. Linh",
title = "The simultaneous computation of {Bessel} functions of
first and second kind",
journal = j-COMPUT-MATH-APPL,
volume = "31",
number = "4--5",
pages = "87--97",
month = feb # "\slash " # mar,
year = "1996",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:26 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122195002200",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Cappuccino:1996:DDH,
author = "G. Cappuccino and P. Corsonello and G. Cocorullo",
title = "Design and demonstration of high throughput square
rooting circuit",
journal = j-ELECT-LETTERS,
volume = "32",
number = "5",
pages = "434",
month = "????",
year = "1996",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "Not \ldots{}",
}
@Article{Chaudhry:1996:ACF,
author = "M. A. Chaudhry and N. M. Temme and E. J. M. Veling",
title = "Asymptotics and closed form of a generalized
incomplete gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "67",
number = "2",
pages = "371--379",
day = "29",
month = mar,
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:27:48 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042795000186",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Guyot:1996:STD,
author = "A. Guyot and M. Renaudin and B. {El Hassan} and V.
Levering",
booktitle = "Proceedings of the Ninth International Conference on
{VLSI} Design, 1996",
title = "Self timed division and square-root extraction",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "376--381",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This paper describes a self-timed integrated circuit
for division and square-root extraction. First it
concentrates on the development and the proof of a new
mathematical algorithm. Then the design methodology and
the architecture of a self-timed \ldots{}",
}
@Article{Heinrich:1996:AAF,
author = "Peter Heinrich",
title = "Algorithm Alley: a Fast Integer Square Root",
journal = j-DDJ,
volume = "21",
number = "4",
pages = "113--114, 130",
month = apr,
year = "1996",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@TechReport{Hickey:1996:FSP,
author = "Timothy J. Hickey and Qun Ju",
title = "Fast, Sound, and Precise Narrowing of the Exponential
Function",
type = "Technical report",
institution = "Computer Science Department, Brandeis University",
address = "Waltham, MA, USA 02254",
month = mar,
year = "1996",
bibdate = "Sat Nov 05 15:42:23 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
acknowledgement = ack-nhfb,
}
@Article{Homeier:1996:CAI,
author = "H. H. H. Homeier",
title = "On Convergence Acceleration for the Iterative Solution
of the Inverse {Dyson} Equation",
journal = j-J-MOL-STRUCT-THEOCHEM,
volume = "368",
pages = "81--91",
year = "1996",
CODEN = "THEODJ",
ISSN = "0166-1280 (print), 1872-7999 (electronic)",
ISSN-L = "0166-1280",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the 2nd {Electronic Computational
Chemistry Conference}.",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954",
fjournal = "Journal of molecular structure. Theochem",
journal-URL = "http://www.sciencedirect.com/science/journal/01661280",
keywords = "convergence acceleration",
tech = "Technical Report TC-QM-95-4, Institut f{\"u}r
{Physikalische} und {Theoretische Chemie,
Universit{\"a}t Regensburg, D-93040 Regensburg}, 1995",
}
@TechReport{Homeier:1996:KMP,
author = "H. H. H. Homeier",
title = "{Zur Konvergenzverbesserung der M{\o}ller--Plesset
St{\"o}rungsreihe} ({English}: {On} Convergence
Acceleration of the {M{\o}ller--Plesset} Perturbation
Series)",
number = "Homeier:1996:KMP",
institution = inst-IPTC,
address = inst-IPTC:adr,
year = "1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Poster CP 14.77, {Fr{\"u}hjahrstagung des
Arbeitskreises Festk{\"o}rperphysik bei der DPG,
Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31,
2165-2166 (1996).",
URL = "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962",
keywords = "convergence acceleration",
}
@Article{Ito:1996:SRI,
author = "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
title = "Square rooting by iterative multiply-additions",
journal = j-INFO-PROC-LETT,
volume = "60",
number = "5",
pages = "267--269",
day = "8",
month = dec,
year = "1996",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68M07",
MRnumber = "97i:68014",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods)",
corpsource = "Dept. of Inf. Sci., Kyoto Univ., Japan",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "computer arithmetic; convergence of numerical methods;
digital arithmetic; iterative methods; iterative
multiply-additions; linear converging ratio;
multiplicative methods; Newton--Raphson method;
read-only storage; ROM sizes; square root algorithm",
treatment = "T Theoretical or Mathematical",
}
@Article{Jeffrey:1996:UBL,
author = "D. J. Jeffrey and D. E. G. Hare and Robert M.
Corless",
title = "Unwinding the branches of the {Lambert $W$} function",
journal = j-MATH-SCI,
volume = "21",
number = "1",
pages = "1--7",
month = jun,
year = "1996",
ISSN = "0312-3685 (print), 1475-6080 (electronic)",
ISSN-L = "0312-3685",
bibdate = "Sat Oct 06 09:02:19 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.appliedprobability.org/data/files/TMS%20articles/21_1_1.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Scientist",
journal-URL = "http://www.appliedprobability.org/content.aspx?Group=tms&Page=allissues",
}
@Unpublished{Kahan:1996:TCR,
author = "W. Kahan",
title = "A Test for Correctly Rounded {SQRT}",
pages = "4",
year = "1996",
bibdate = "Mon Apr 25 05:47:38 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Lecture notes.",
URL = "http://www.cs.berkeley.edu/~wkahan/SQRTest.ps",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Kalantari:1996:HOI,
author = "B. Kalantari and I. Kalantari",
title = "High order iterative methods for approximating square
roots",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "2",
pages = "395--399",
month = jun,
year = "1996",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01731991",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D15 (65H99)",
MRnumber = "97k:65039",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Kantabutra:1996:HCE,
author = "V. Kantabutra",
title = "On hardware for computing exponential and
trigonometric functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "3",
pages = "328--339",
month = mar,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.485571",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kolbig:1996:PF,
author = "K. S. K{\"o}lbig",
title = "The polygamma function $ \psi^{(k)}(x) $ for $ x = 1 /
4 $ and $ x = 3 / 4 $",
journal = j-J-COMPUT-APPL-MATH,
volume = "75",
number = "1",
pages = "43--46",
day = "12",
month = nov,
year = "1996",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(96)00055-6",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:35:58 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042796000556",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Lang:1996:BPU,
author = "T. Lang and R. Wong",
title = "``{Best} possible'' upper bounds for the first two
positive zeros of the {Bessel} function {$ J_v(x) $}:
the infinite case",
journal = j-J-COMPUT-APPL-MATH,
volume = "71",
number = "2",
pages = "311--329",
day = "27",
month = jul,
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:35:56 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042795002200",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Lehoucq:1996:CEU,
author = "R. B. Lehoucq",
title = "The Computation of Elementary Unitary Matrices",
journal = j-TOMS,
volume = "22",
number = "4",
pages = "393--400",
month = dec,
year = "1996",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The construction of elementary unitary matrices that
transform a complex vector to a multiple of $ e_1 $,
the first column of the identity matrix, is studied. We
present four variants and their software
implementation, including a discussion on the {LAPACK}
subroutine {CLARFG}. Comparisons are also given.",
accepted = "June 1996",
acknowledgement = ack-rfb # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf F.2}: Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf G.1.3}:
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis.",
}
@Article{Lether:1996:RAF,
author = "Frank G. Lether",
title = "Rational approximation formulas for computing the
positive zeros of {$ J_0 (x) $}",
journal = j-J-COMPUT-APPL-MATH,
volume = "67",
number = "1",
pages = "167--172",
day = "20",
month = feb,
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:27:48 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042795002197",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Li:1996:NNR,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the {IEEE} International Conference on
Computer Design: {VLSI} in Computers and Processors:
{ICCD '96}",
title = "A new non-restoring square root algorithm and its
{VLSI} implementations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "538--544",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We present a new non-restoring square root algorithm
that is very efficient to implement. The new algorithm
presented here has the following features unlike other
square root algorithms. First, the focus of the
``non-restoring'' is on the {\&} \ldots{}",
}
@Article{Lorch:1996:BPU,
author = "Lee Lorch and Riccardo Uberti",
title = "``{Best} possible'' upper bounds for the first
positive zeros of {Bessel} functions --- the finite
part",
journal = j-J-COMPUT-APPL-MATH,
volume = "75",
number = "2",
pages = "249--258",
day = "28",
month = nov,
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:35:58 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042796000659",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@TechReport{Lozier:1996:PST,
author = "Daniel W. Lozier",
title = "A Proposed Software Test Service for Special
Functions",
type = "Technical Report",
number = "NISTIR 5916",
institution = pub-NIST,
address = pub-NIST:adr,
pages = "11",
month = oct,
year = "1996",
bibdate = "Fri Jul 09 06:02:16 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Lozier:1997:PST}.",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps",
acknowledgement = ack-nhfb,
}
@Article{Lozier:1996:SNS,
author = "Daniel W. Lozier",
title = "Software Needs in Special Functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "66",
number = "??",
pages = "345--358",
month = "????",
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Fri Jul 09 05:51:55 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
remark = "See preprint \cite{Lozier:1994:SNS}.",
}
@Article{Macleod:1996:AMS,
author = "Allan J. Macleod",
title = "{Algorithm 757}: {MISCFUN}, a software package to
compute uncommon special functions",
journal = j-TOMS,
volume = "22",
number = "3",
pages = "288--301",
month = sep,
year = "1996",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 31 16:07:02 MDT 1996",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://doi.acm.org/10.1145/232826.232846;
http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/",
abstract = "MISCFUN (MISCellaneous FUNctions) is a Fortran package
for the evaluation of several special functions, which
are not used often enough to have been included in the
standard libraries or packages. The package uses
Chebyshev expansions as the underlying method of
approximation, with the Chebyshev coefficients given to
20D. A wide variety of functions are included, and the
package is designed so that other functions can be
added in a standard manner.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev
approximation and theory. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Certification and
testing.",
}
@Article{Oleksy:1996:CAM,
author = "Cz. Oleksy",
title = "A convergence acceleration method of {Fourier}
series",
journal = j-COMP-PHYS-COMM,
volume = "96",
number = "1",
pages = "17--26",
year = "1996",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(96)00044-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
MRclass = "65B05",
MRnumber = "1396682 (97c:65012)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
keywords = "convergence acceleration",
}
@Article{Panteliou:1996:DII,
author = "S. D. Panteliou and A. D. Dimarogonas and I. N. Katz",
title = "Direct and inverse interpolation for {Jacobian}
elliptic functions, zeta function of {Jacobi} and
complete elliptic integrals of the second kind",
journal = j-COMPUT-MATH-APPL,
volume = "32",
number = "8",
pages = "51--57",
month = oct,
year = "1996",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:33 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122196001666",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Book{Patel:1996:HND,
author = "Jagdish K. Patel and Campbell B. Read",
title = "Handbook of the Normal Distribution",
volume = "150",
publisher = pub-DEKKER,
address = pub-DEKKER:adr,
edition = "Second revised and expanded",
pages = "ix + 431",
year = "1996",
ISBN = "0-8247-9342-0 (hardcover)",
ISBN-13 = "978-0-8247-9342-5 (hardcover)",
LCCN = "QA273.6 .P373 1996",
bibdate = "Sat Dec 16 17:22:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Statistics, textbooks and monographs",
URL = "http://www.loc.gov/catdir/enhancements/fy0647/95049404-d.html",
acknowledgement = ack-nhfb,
subject = "Gaussian distribution",
tableofcontents = "Genesis: an historical background \\
Basic properties \\
Expansions and algorithms \\
Characterizations \\
Sampling distributions \\
Limit theorems and expansions \\
Normal approximations to distributions \\
Order statistics from normal samples \\
The bivariate normal distribution \\
Bivariate normal sampling distributions \\
Point estimation \\
Statistical intervals",
}
@Article{Plofker:1996:ESM,
author = "Kim Plofker",
title = "An Example of the Secant Method of Iterative
Approximation in a {Fifteenth-Century Sanskrit} Text",
journal = j-HIST-MATH,
volume = "23",
number = "3",
pages = "246--256",
month = aug,
year = "1996",
CODEN = "HIMADS",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Jun 26 06:19:07 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086096900269",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860",
}
@Article{Qiu:1996:SEC,
author = "S.-L. Qiu and M. K. Vamanamurthy",
title = "Sharp Estimates for Complete Elliptic Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "27",
number = "3",
pages = "823--834",
month = may,
year = "1996",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "33E05",
MRnumber = "97f:33033",
MRreviewer = "G. D. Anderson",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@InProceedings{Rao:1996:RTS,
author = "V. M. Rao and B. Nowrouzian",
booktitle = "Canadian Conference on Electrical and Computer
Engineering. 26--29 May 1996",
title = "Rounding techniques for signed binary arithmetic",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "294--297",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This paper is concerned with the derivation of the
relationship that exists between the number truncation
in two's complement (TC) arithmetic and the
corresponding truncation in signed-binary (SB)
arithmetic. The resulting relationship is subsequently
exploited and applied to the development of a pair of
novel techniques for SB rounding. These techniques are
then translated into algorithm suitable for two-level
logic implementation. Finally, the resulting algorithms
are applied to the design and implementation of a
high-speed SB-kernel based TC multiply-accumulate
arithmetic architecture.",
acknowledgement = ack-nhfb,
}
@Article{Schatzman:1996:ADF,
author = "James C. Schatzman",
title = "Accuracy of the discrete {Fourier} transform and the
fast {Fourier} transform",
journal = j-SIAM-J-SCI-COMP,
volume = "17",
number = "5",
pages = "1150--1166",
month = sep,
year = "1996",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827593247023",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65T20 (42A65 42C10 68Q25)",
MRnumber = "97e:65155",
bibdate = "Fri Dec 4 14:47:53 MST 1998",
bibsource = "http://epubs.siam.org/toc/sjoce3/17/5;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/24702",
acknowledgement = ack-nhfb,
ajournal = "SIAM J. Sci. Comput.",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
remark = "This article analyzes errors in computing
one-dimensional Fourier transforms, the fast way (FFT)
and the slow way. The author identifies two main causes
of accuracy loss in the computed transforms: (1)
inaccurate sine and cosine functions, and (2) failure
to use accurate summation methods, such as Kahan's
compensated summation.",
}
@Article{Schwarz:1996:HSA,
author = "Eric M. Schwarz and Michael J. Flynn",
title = "Hardware Starting Approximation Method and Its
Application to the Square Root Operation",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "12",
pages = "1356--1369",
month = dec,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.545966",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "Quadratically converging algorithms for high-order
arithmetic operations typically are accelerated by a
starting approximation. The higher the precision of the
starting approximation, the less number of iterations
required for convergence. \ldots{}",
}
@Article{Sinclair:1996:ORS,
author = "R. Sinclair",
title = "Optimization of reciprocals and square roots on the
{i860} microprocessor",
journal = j-INT-J-HIGH-SPEED-COMPUTING,
volume = "8",
number = "1",
pages = "57--64",
year = "1996",
CODEN = "IHSCEZ",
ISSN = "0129-0533",
bibdate = "Mon Feb 25 11:19:22 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Article1st database",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Speed Computing
(IJHSC)",
journal-URL = "http://www.worldscientific.com/worldscinet/ijhsc",
}
@Article{Snyder:1996:RAF,
author = "W. Van Snyder",
title = "Remark on {Algorithm 723}: {Fresnel} Integrals",
journal = j-TOMS,
volume = "22",
number = "4",
pages = "498--500",
month = dec,
year = "1996",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/235815.235825",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Snyder:1993:AFI}.",
abstract = "{\it Algorithm 723: Fresnel Integrals} has been
improved to provide more precise results for $ x \gg 0
$.",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms, performance",
subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Rational
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Certification and testing.",
}
@Book{Temme:1996:SFI,
author = "N. M. Temme",
title = "Special Functions: an Introduction to the Classical
Functions of Mathematical Physics",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 374",
year = "1996",
DOI = "https://doi.org/10.1002/9781118032572",
ISBN = "0-471-11313-1",
ISBN-13 = "978-0-471-11313-3",
LCCN = "QC20.7.F87 T46 1996",
bibdate = "Mon Nov 24 21:41:54 MST 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.bibsys.no:2100/BIBSYS;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
shorttableofcontents = "Bernoulli, Euler and Stirling numbers \\
Useful methods and techniques \\
The gamma function \\
Differential equations \\
Hypergeometric functions \\
Orthogonal polynomials \\
Confluent hypergeometric functions \\
Legendre functions \\
Bessel functions \\
Separating the wave equation \\
Special statistical distribution functions \\
Elliptic integrals and elliptic functions \\
Numerical aspects of special functions",
subject = "functions, special; mathematical physics; boundary
value problems",
tableofcontents = "1 Bernoulli, Euler and Stirling Numbers / 1 \\
1.1. Bernoulli Numbers and Polynomials / 2 \\
1.1.1. Definitions and Properties / 3 \\
1.1.2. A Simple Difference Equation / 6 \\
1.1.3. Euler's Summation Formula / 9 \\
1.2. Euler Numbers and Polynomials / 14 \\
1.2.1. Definitions and Properties / 15 \\
1.2.2. Boole's Summation Formula / 17 \\
1.3. Stirling Numbers / 18 \\
1.4. Remarks and Comments for Further Reading / 21 \\
1.5. Exercises and Further Examples / 22 \\
2 Useful Methods and Techniques / 29 \\
2.1. Some Theorems from Analysis / 29 \\
2.2. Asymptotic Expansions of Integrals / 31 \\
2.2.1. Watson's Lemma / 32 \\
2.2.2. The Saddle Point Method / 34 \\
2.2.3. Other Asymptotic Methods / 38 \\
2.3. Exercises and Further Examples / 39 \\
3 The Gamma Function / 41 \\
3.1. Introduction / 41 \\
3.1.1. The Fundamental Recursion Property / 42 \\
3.1.2. Another Look at the Gamma Function / 42 \\
3.2. Important Properties / 43 \\
3.2.1. Prym's Decomposition / 43 \\
3.2.2. The Cauchy--Saalsch{\"u}tz Representation / 44
\\
3.2.3. The Beta Integral / 45 \\
3.2.4. The Multiplication Formula / 46 \\
3.2.5. The Reflection Formula / 46 \\
3.2.6. The Reciprocal Gamma Function / 48 \\
3.2.7. A Complex Contour for the Beta Integral / 49 \\
3.3. Infinite Products / 50 \\
3.3.1. Gauss' Multiplication Formula / 52 \\
3.4. Logarithmic Derivative of the Gamma Function / 53
\\
3.5. Riemann's Zeta Function / 57 \\
3.6. Asymptotic Expansions / 61 \\
3.6.1. Estimations of the Remainder / 64 \\
3.6.2. Ratio of Two Gamma Functions / 66 \\
3.6.3. Application of the Saddle Point Method / 69 \\
3.7. Remarks and Comments for Further Reading / 71 \\
3.8. Exercises and Further Examples / 72 \\
4 Differential Equations / 79 \\
4.1. Separating the Wave Equation / 79 \\
4.1.1. Separating the Variables / 81 \\
4.2. Differential Equations in the Complex Plane / 83
\\
4.2.1. Singular Points / 83 \\
4.2.2. Transformation of the Point at Infinity / 84 \\
4.2.3. The Solution Near a Regular Point / 85 \\
4.2.4. Power Series Expansions Around a Regular Point /
90 \\
4.2.5. Power Series Expansions Around a Regular
Singular Point / 92 \\
4.3. Sturm's Comparison Theorem / 97 \\
4.4. Integrals as Solutions of Differential Equations /
98 \\
4.5. The Liouville Transformation / 103 \\
4.6. Remarks and Comments for Further Reading / 104 \\
4.7. Exercises and Further Examples / 104 \\
5 Hypergeometric Functions / 107 \\
5.1. Definitions and Simple Relations / 107 \\
5.2. Analytic Continuation / 109 \\
5.2.1. Three Functional Relations / 110 \\
5.2.2. A Contour Integral Representation / 111 \\
5.3. The Hypergeometric Differential Equation / 112 \\
5.4. The Singular Points of the Differential Equation /
114 \\
5.5. The Riemann--Papperitz Equation / 116 \\
5.6. Barnes' Contour Integral for $F(a, b; c; z)$ / 119
\\
5.7. Recurrence Relations / 121 \\
5.8. Quadratic Transformations / 122 \\
5.9. Generalized Hypergeometric Functions / 124 \\
5.9.1. A First Introduction to g-functions / 125 \\
5.10. Remarks and Comments for Further Reading / 127
\\
5.11. Exercises and Further Examples / 128 \\
6 Orthogonal Polynomials / 133 \\
6.1. General Orthogonal Polynomials / 133 \\
6.1.1. Zeros of Orthogonal Polynomials / 137 \\
6.1.2. Gauss Quadrature / 138 \\
6.2. Classical Orthogonal Polynomials / 141 \\
6.3. Definitions by the Rodrigues Formula / 142 \\
6.4. Recurrence Relations / 146 \\
6.5. Differential Equations / 149 \\
6.6. Explicit Representations / 151 \\
6.7. Generating Functions / 154 \\
6.8. Legendre Polynomials / 156 \\
6.8.1. The Norm of the Legendre Polynomials / 156 \\
6.8.2. Integral Expressions for the Legendre
Polynomials / 156 \\
6.8.3. Some Bounds on Legendre Polynomials / 157 \\
6.8.4. An Asymptotic Expansion as n is Large / 158 \\
6.9. Expansions in Terms of Orthogonal Polynomials /
160 \\
6.9.1. An Optimal Result in Connection with Legendre
Polynomials / 160 \\
6.9.2. Numerical Aspects of Chebyshev Polynomials / 162
\\
6.10. Remarks and Comments for Further Reading / 164
\\
6.11. Exercises and Further Examples / 164 \\
7 Confluent Hypergeometric Functions / 171 \\
7.1. The $M$-function / 172 \\
7.2. The $U$-function / 175 \\
7.3. Special Cases and Further Relations / 177 \\
7.3.1. Whittaker Functions / 178 \\
7.3.2. Coulomb Wave Functions / 178 \\
7 3.3. Parabolic Cylinder Functions / 179 \\
7 3.4. Error Functions / 180 \\
7.3.5. Exponential Integrals / 180 \\
7.3.6. Fresnel Integrals / 182 \\
7.3.7. Incomplete Gamma Functions / 185 \\
7.3.8. Bessel Functions / 186 \\
7.3.9. Orthogonal Polynomials / 186 \\
7.4. Remarks and Comments for Further Reading / 186 \\
7.5. Exercises and Further Examples / 187 \\
8 Legendre Functions / 193 \\
8.1. The Legendre Differential Equation / 194 \\
8.2. Ordinary Legendre Functions / 194 \\
8.3. Other Solutions of the Differential Equation / 196
\\
8.4. A Few More Series Expansions / 198 \\
8.5. The function $Q_n(z)$ / 200 \\
8.6. Integral Representations / 202 \\
8.7. Associated Legendre Functions / 209 \\
8.8. Remarks and Comments for Further Reading / 213 \\
8.9. Exercises and Further Examples / 214 \\
9 Bessel Functions / 219 \\
9.1. Introduction / 219 \\
9.2. Integral Representations / 220 \\
9.3. Cylinder Functions / 223 \\
9.4. Further Properties / 227 \\
9.5. Modified Bessel Functions / 232 \\
9.6. Integral Representations for the $I$- and
$K$-Functions / 234 \\
9.7. Asymptotic Expansions / 238 \\
9.8. Zeros of Bessel Functions / 241 \\
9.9. Orthogonality Relations, Fourier--Bessel Series /
244 \\
9.10. Remarks and Comments for Further Reading / 247
\\
9.11. Exercises and Further Examples / 247 \\
10 Separating the Wave Equation / 257 \\
10.1. General Transformations / 258 \\
10.2. Special Coordinate Systems / 259 \\
10.2.1. Cylindrical Coordinates / 259 \\
10.2.2. Spherical Coordinates / 261 \\
10.2.3. Elliptic Cylinder Coordinates / 263 \\
10.2.4. Parabolic Cylinder Coordinates / 264 \\
10.2.5. Oblate Spheroidal Coordinates / 266 \\
10.3. Boundary Value Problems / 268 \\
10.3.1. Heat Conduction in a Cylinder / 268 \\
10.3.2. Diffraction of a Plane Wave Due to a Sphere /
270 \\
10.4. Remarks and Comments for Further Reading / 271
\\
10.5. Exercises and Further Examples / 272 \\
11 Special Statistical Distribution Functions / 275 \\
11.1. Error Functions / 275 \\
11.1.1. The Error Function and Asymptotic Expansions /
276 \\
11.2. Incomplete Gamma Functions / 277 \\
11.2.1. Series Expansions / 279 \\
11.2.2. Continued Fraction for $\Gamma(a, z)$ / 280 \\
11.2.3. Contour Integral for the Incomplete Gamma
Functions / 282 \\
11.2.4. Uniform Asymptotic Expansions / 283 \\
11.2.5. Numerical Aspects / 286 \\
11.3. Incomplete Beta Functions / 288 \\
11.3.1. Recurrence Relations / 289 \\
11.3.2. Contour Integral for the Incomplete Beta
Function / 290 \\
11.3.3. Asymptotic Expansions / 291 \\
11.3.4. Numerical Aspects / 297 \\
11.4. Non-Central Chi-Squared Distribution / 298 \\
11.4.1. A Few More Integral Representations / 300 \\
11.4.2. Asymptotic Expansion; $m$ Fixed, $j$ Large /
302 \\
11.4.3. Asymptotic Expansion; $j$ Large, $m$ Arbitrary
/ 303 \\
11.4.4. Numerical Aspects / 305 \\
11.5. An Incomplete Bessel Function / 308 \\
11.6. Remarks and Comments for Further Reading / 309
\\
11.7. Exercises and Further Examples / 310 \\
12 Elliptic Integrals and Elliptic Functions / 319 \\
12.1. Complete Integrals of the First and Second Kind /
315 \\
12.1.1. The Simple Pendulum / 316 \\
12.1.2. Arithmetic Geometric Mean / 318 \\
12.2. Incomplete Elliptic Integrals / 321 \\
12.3. Elliptic Functions and Theta Functions / 322 \\
12.3.1. Elliptic Functions / 323 \\
12.3.2. Theta Functions / 324 \\
12.4. Numerical Aspects / 328 \\
12.5. Remarks and Comments for Further Reading / 329
\\
12.6. Exercises and Further Examples / 330 \\
13 Numerical Aspects of Special Functions / 333 \\
13.1. A Simple Recurrence Relation / 334 \\
13.2. Introduction to the General Theory / 335 \\
13.3. Examples / 338 \\
13.4. Miller's Algorithm / 343 \\
13.5. How to Compute a Continued Fraction / 347 \\
Bibliography / 349 \\
Notations and Symbols / 361 \\
Index / 365",
}
@Article{Temme:1996:UAI,
author = "N. M. Temme",
title = "Uniform asymptotics for the incomplete gamma functions
starting from negative values of the parameters",
journal = j-METHODS-APPL-ANAL,
volume = "3",
number = "3",
pages = "335--344",
year = "1996",
DOI = "https://doi.org/10.4310/MAA.1996.v3.n3.a3",
ISSN = "1073-2772 (print), 1945-0001 (electronic)",
ISSN-L = "1073-2772",
MRclass = "33B20 (41A60)",
MRnumber = "1421474",
MRreviewer = "Richard B. Paris",
bibdate = "Sat Feb 18 15:19:00 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Methods and Applications of Analysis",
journal-URL = "http://www.intlpress.com/MAA/",
}
@Article{Waissi:1996:SAS,
author = "Gary R. Waissi and Donald F. Rossin",
title = "A sigmoid approximation of the standard normal
integral",
journal = j-APPL-MATH-COMP,
volume = "77",
number = "1",
pages = "91--95",
month = jun,
year = "1996",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/0096-3003(95)00190-5",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Nov 20 21:02:39 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0096300395001905",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Book{Walz:1996:AE,
author = "Guido Walz",
title = "Asymptotics and Extrapolation",
volume = "88",
publisher = pub-AKADEMIE-VERLAG,
address = pub-AKADEMIE-VERLAG:adr,
pages = "330",
year = "1996",
ISBN = "3-05-501732-3",
ISBN-13 = "978-3-05-501732-2",
LCCN = "QA281 .W349 1996",
bibdate = "Thu Dec 1 10:25:13 MST 2011",
bibsource = "catalog.princeton.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematical research",
acknowledgement = ack-nhfb,
subject = "Extrapolation; Asymptotic expansions",
tableofcontents = "Part I: Asymptotic Expansions \\
1. Asymptotic Systems and Expansions / 15 \\
2. Geometric Asymptotic Expansions / 21 \\
3. Logarithmic Asymptotic Expansions / 39 \\
Part II: Linear Extrapolation Methods \\
4. Fundamental Concepts and General Philosophy / 193
\\
5. Error Bounds, Stopping Rules and Monotonicity / 244
\\
6. Generalizations and Final Remarks / 289 \\
Historical Notes / 303 \\
References / 308\\
Index / 329",
}
@Article{Weniger:1996:CWF,
author = "Ernst Joachim Weniger",
title = "Computation of the {Whittaker} function of the second
kind by summing its divergent asymptotic series with
the help of nonlinear sequence transformations",
journal = j-COMPUT-PHYS,
volume = "10",
number = "5",
pages = "496--??",
month = sep,
year = "1996",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.168579",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:46:03 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.168579",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Williams:1996:TMF,
author = "K. B. Williams",
title = "Testing Math Functions: When requirements are tight,
we must carefully examine all potential sources of
error. {Make} sure your math library isn't the weak
link in the chain",
journal = j-CCCUJ,
volume = "14",
number = "12",
pages = "49--54, 58--65",
month = dec,
year = "1996",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Thu Nov 14 06:34:33 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Describes a package that extends the
Cody-Waite-Plauger work on the ELEFUNT package for the
testing of the elementary functions, including the
inverse hyperbolic functions, cube root, and Bessel
functions of the first and second kinds. The C++
package implements 192-bit extended precision versions
of all of the functions, so that accurate results are
available for comparison with the normal
double-precision results.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@Article{Zahle:1996:FDW,
author = "M. Z{\"a}hle and H. Ziezold",
title = "Fractional derivatives of {Weierstrass}-type
functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "76",
number = "1--2",
pages = "265--275",
day = "17",
month = dec,
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:35:58 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042796001100",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Book{Zhang:1996:CSF,
author = "Shanjie Zhang and Jianming Jin",
title = "Computation of Special Functions",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xxvi + 717",
year = "1996",
ISBN = "0-471-11963-6",
ISBN-13 = "978-0-471-11963-0",
LCCN = "QA351.C45 1996",
bibdate = "Wed Mar 22 14:39:04 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
price = "US\$94.00",
acknowledgement = ack-nhfb,
shorttableofcontents = "Preface / xi \\
Acknowledgments / xvii \\
List of Computer Programs / xix \\
1: Bernoulli and Euler Numbers / 1 \\
2: Orthogonal Polynomials / 12 \\
3: Gamma, Beta, and Psi Functions / 44 \\
4: Legendre Functions / 77 \\
5: Bessel Functions / 126 \\
6: Modified Bessel Functions / 202 \\
7: Integrals of Bessel Functions / 252 \\
8: Spherical Bessel Functions / 273 \\
9: Kelvin Functions / 307 \\
10: Airy Functions / 325 \\
11: Struve Functions / 341 \\
12: Hypergeometric and Confluent Hypergeometric / 366
\\
13: Parabolic Cylinder Functions / 425 \\
14: Mathieu Functions / 475 \\
15: Spheroidal Wave Functions / 536 \\
16: Error Function and Fresnel Integrals / 620 \\
17: Cosine and Sine Integrals / 644 \\
18: Elliptic Integrals and Jacobian Elliptic Functions
19: Exponential Integrals / 680 \\
20: Summary of Methods for Computing Special Functions
Appendix A: Derivation of Some Special Differential
Appendix B: Root-Finding Methods / 704 \\
Reference / 706 \\
Appendix C: About the Software / 707 \\
Index / 709 \\
Index of Computer Programs / 715",
tableofcontents = "Preface / xi \\
Acknowledgments / xvii \\
List of Computer Programs / xix \\
1: Bernoulli and Euler Numbers / 1 \\
1.1 Bernoulli Numbers / 1 \\
1.2 Euler Numbers / 6 \\
1.3 Mathematical Table / 10 \\
References / 11 \\
2: Orthogonal Polynomials / 12 \\
2.1 Introduction / 12 \\
2.2 Chebyshev Polynomials / 13 \\
2.3 Laguerre Polynomials / 18 \\
2.4 Hermite Polynomials / 20 \\
2.5 Numerical Computation / 23 \\
2.6 Application in Numerical Integration / 27 \\
References / 43 \\
3: Gamma, Beta, and Psi Functions / 44 \\
3.1 Gamma Function / 44 \\
3.2 Beta Function / 53 \\
3.3 Psi Function / 55 \\
3.4 Incomplete Gamma Function / 61 \\
3.5 Incomplete Beta Function / 64 \\
3.6 Mathematical Tables / 66 \\
References and Further Reading / 76 \\
4: Legendre Functions / 77 \\
4.1 Introduction / 77 \\
4.2 Legendre Functions of the First Kind / 78 \\
4.3 Legendre Functions of the Second Kind / 83 \\
4.4 Associated Legendre Functions of the First Kind /
89 \\
4.5 Associated Legendre Functions of the Second Kind /
96 \\
4.6 Legendre Functions with an Arbitrary Degree / 104
\\
4.7 Mathematical Tables / 113 \\
References and Further Reading / 125 \\
5: Bessel Functions / 126 \\
5.1 Introduction / 126 \\
5.2 Computation of $J_0(x)$, $J_1(x)$, $Y_0(x)$, and
$Y_1(x)$ / 131 \\
5.3 Computation of $J_n(x)$ and $Y_n(x)$ with Real
Arguments / 140 \\
5.4 Computation of $Y_n(z)$ and$ Y_n(z)$ with Complex
Arguments / 149 \\
5.5 Computation of $J_\nu(z)$ and $J_\nu(z)$ with an
Arbitrary Order / 161 \\
5.6 Assessment of Validity and Accuracy of Computation
/ 175 \\
5.7 Zeros of Bessel Functions / 180 \\
5.8 Lambda Functions / 182 \\
5.9 Mathematical Tables / 184 \\
References and Further Reading / 201 \\
6: Modified Bessel Functions / 202 \\
6.1 Introduction / 202 \\
6.2 Computation of $I_0(x)$, $I_1(x)$, $K_0(x)$, and
$K_1(x)$ / 207 \\
6.3 Computation of $I_n(x)$ and $K_n(x)$ with Real
Arguments / 213 \\
6.4 Computation of $I_n(z)$ and $K_n(z)$ with Complex
Arguments / 217 \\
6.5 Computation of $I_\nu(z)$ and $K_\nu(z)$ with an
Arbitrary Order / 225 \\
6.6 Computation of $H_\nu^{(1)}(z)$ and
$H_\nu^{(2)}(z)$ for Complex Arguments / 235 \\
6.7 Mathematical Tables / 239 \\
References and Further Reading / 251 \\
7: Integrals of Bessel Functions / 252 \\
7.1 Simple Integrals of Bessel Functions / 252 \\
7.2 Simple Integrals of Modified Bessel Functions / 261
\\
7.3 Curves and Tables / 268 \\
References / 272 \\
8: Spherical Bessel Functions / 273 \\
8.1 Spherical Bessel Functions / 273 \\
8.2 Riccati--Bessel Functions / 283 \\
8.3 Modified Spherical Bessel Functions / 286 \\
8.4 Mathematical Tables / 295 \\
References and Further Reading / 306 \\
9: Kelvin Functions / 307 \\
9.1 Introduction / 307 \\
9.2 Mathematical Properties / 311 \\
9.3 Asymptotic Expansions / 312 \\
9.4 Numerical Computation / 315 \\
9.5 Zeros of Kelvin Functions / 321 \\
9.6 Mathematical Tables / 321 \\
Reference / 324 \\
10: Airy Functions / 325 \\
10.1 Introduction / 325 \\
10.2 Numerical Computation / 329 \\
10.3 Mathematical Tables / 336 \\
References / 340 \\
11: Struve Functions / 341 \\
11.1 Struve Functions / 341 \\
11.2 Modified Struve Functions / 353 \\
11.3 Mathematical Tables / 362 \\
References / 365 \\
12: Hypergeometric and Confluent Hypergeometric
Functions / 366 \\
12.1 Definition of Hypergeometric Functions / 366 \\
12.2 Properties of Hypergeometric Functions / 368 \\
12.3 Linear Transformation Formulas / 369 \\
12.4 Recurrence Relations for Hypergeometric Functions
/ 372 \\
12.5 Special Functions Expressed as Hypergeometric
Functions / 373 \\
12.6 Numerical Computation of Hypergeometric Functions
/ 374 \\
12.7 Definition of Confluent Hypergeometric Functions /
385 \\
12.8 Properties of Confluent Hypergeometric Functions /
387 \\
12.9 Recurrence Relations for Confluent Hypergeometric
Functions / 389 \\
12.10 Special Functions Expressed as Confluent
Hypergeometric Functions / 394 \\
12.11 Definition of Whittaker Functions / 395 \\
12.12 Numerical Computation of Confluent Hypergeometric
Functions / 398 \\
12.13 Mathematical Tables / 411 \\
References and Further Reading / 424 \\
13: Parabolic Cylinder Functions / 425 \\
13.1 Introduction / 425 \\
13.2 Definitions of Parabolic Cylinder Functions / 428
\\
13.3 Basic Properties / 432 \\
13.4 Series and Asymptotic Expansions / 437 \\
13.5 Numerical Computation / 438 \\
13.6 Mathematical Tables / 455 \\
References and Further Reading / 474 \\
14: Mathieu Functions / 475 \\
14.1 Definition of Mathieu Functions / 475 \\
14.2 Determination of Expansion Coefficients and
Characteristic Values / 477 \\
14.3 Approximate Calculation of Characteristic Values /
482 \\
14.4 Expansion of Mathieu Functions When $|q| < 1$ /
485 \\
14.5 Properties of Mathieu Functions / 487 \\
14.6 Definition of Modified Mathieu Functions / 489 \\
14.7 Properties of Modified Mathieu Functions / 496 \\
14.8 Numerical Computation: Algorithms and Computer
Programs / 501 \\
14.9 Mathematical Tables / 520 \\
References and Further Reading / 535 \\
15: Spheroidal Wave Functions / 536 \\
15.1 Spheroidal Coordinate Systems / 536 \\
15.2 Wave Equation and Its Solution in Spheroidal
Coordinates / 540 \\
15.3 Definitions of Angular and Radial Prolate
Spheroidal Wave Functions / 542 \\
15.4 Determination of Characteristic Values and
Expansion Coefficients / 550 \\
15.5 Evaluation of Prolate Radial Wave Functions of the
Second Kind for Small $c \xi$ / 556 \\
15.6 Definitions of Angular and Radial Oblate
Spheroidal Wave Functions / 559 \\
15.7 Evaluation of Oblate Radial Wave Functions of the
Second Kind for Small $c \xi$ / 561 \\
15.8 Numerical Computation: Algorithms and Computer
Programs / 569 \\
15.9 Mathematical Tables / 594 \\
References / 619 \\
16: Error Function and Fresnel Integrals / 620 \\
16.1 Introduction to Error Function / 620 \\
16.2 Numerical Computation of Error Function / 621 \\
16.3 Gaussian Probability Integral / 624 \\
16.4 Introduction to Fresnel Integrals / 625 \\
16.5 Series and Asymptotic Expansions of Fresnel
Integrals / 629 \\
16.6 Numerical Computation of Fresnel Integrals / 630
\\
16.7 Zeros of Error Function and Fresnel Integrals /
635 \\
16.8 Mathematical Tables / 636 \\
References and Further Reading / 643 \\
17: Cosine and Sine Integrals / 644 \\
17.1 Introduction / 644 \\
17.2 Series and Asymptotic Expansions / 646 \\
17.3 Numerical Computation / 647 \\
17.4 Mathematical Table / 651 \\
References and Further Readings / 653 \\
18: Elliptic Integrals and Jacobian Elliptic Functions
/ 654 \\
18.1 Introduction to Elliptic Integrals / 654 \\
18.2 Series Expansion of Elliptic Integrals / 659 \\
18.3 Numerical Computation of Elliptic Integrals / 661
\\
18.4 Introduction to Jacobian Elliptic Functions / 666
\\
18.5 Numerical Computation of Jacobian Elliptic
Functions / 670 \\
18.6 Mathematical Tables / 672 \\
References and Further Reading / 679 \\
19: Exponential Integrals / 680 \\
19.1 Introduction / 680 \\
19.2 Series, Asymptotic, and Continued Fraction
Expressions / 682 \\
19.3 Rational Approximations / 683 \\
19.4 Numerical Computation / 684 \\
19.5 Mathematical Tables / 688 \\
References / 693 \\
20: Summary of Methods for Computing Special Functions
/ 694 \\
Appendix A: Derivation of Some Special Differential
Equations / 697 \\
A.1 Helmholtz Equation and Separation of Variables /
697 \\
A.2 Circular Cylindrical Coordinates / 698 \\
A.3 Elliptic Cylindrical Coordinates / 700 \\
A.4 Parabolic Cylindrical Coordinates / 700 \\
A.5 Spherical Coordinates / 701 \\
A.6 Prolate Spheroidal Coordinates / 701 \\
A.7 Oblate Spheroidal Coordinates / 702 \\
A.8 Parabolic Coordinates / 703 \\
References / 703 \\
Appendix B: Root-Finding Methods / 704 \\
B.1 Newton's Method / 704 \\
B.2 Modified Newton's Method / 706 \\
B.3 Secant Method / 706 \\
Reference / 706 \\
Appendix C: About the Software / 707 \\
Index / 709 \\
Index of Computer Programs / 715",
xxauthor = "Shan-chieh Chang and Shanjie Zhang and Jianming Jin",
xxnote = "There is online bookstore and library catalog
confusion over the authors of this book. The
publisher's Web page at
http://catalog.wiley.com/remsrch.cgi has Shan-jie Zhang
(Nanjing Univ., China) / Jianming Jin (Univ. of
Illinois at Urbana-Champaign), and a price of
US\$125.00. It looks like Shan-chieh Chang is merely a
different English transcription of Shanjie Zhang.
http://www.fatbrain.com/ lists this book for US\$99.95.
My copy of the book lists the authors as Shanjie Zhang
and Jianming Jin in four places.",
}
@Article{Zhang:1996:NTM,
author = "J. Zhang",
title = "A note on the tau-method approximations for the
{Bessel} functions {$ Y_0 (z) $} and {$ Y_1 (z) $}",
journal = j-COMPUT-MATH-APPL,
volume = "31",
number = "9",
pages = "63--70",
month = may,
year = "1996",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(96)00043-0",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Sun Jun 12 08:43:36 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122196000430",
abstract = "This paper is to complete and improve the work
reported in [1,2], using the Lanczos $ \tau $-method
(in Coleman's version) to approximate the Bessel
functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce
symbolic representations of the scaled Faber
polynomials on any fan-shaped section of the complex
plane. These Faber polynomials are used as the
perturbation terms in the $ \tau $-method. Numerical
comparison among the power series, the Chebyshev series
and the $ \tau $-method are conducted to show the
accuracy improvement achieved by this new version of
the $ \tau $-method. Some concluding remarks and
suggestions on future research are given.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Automated $\tau$-method; Bessel functions; Chebyshev
series; Symbolic Faber polynomials",
}
@Article{Zhang:1996:SNC,
author = "Jun Zhang",
title = "Symbolic and numerical computation on {Bessel}
functions of complex argument and large magnitude",
journal = j-J-COMPUT-APPL-MATH,
volume = "75",
number = "1",
pages = "99--118",
day = "12",
month = nov,
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:35:58 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042796000635",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Abad:1997:NEC,
author = "Julio Abad and Javier Sesma",
title = "A new expansion of the confluent hypergeometric
function in terms of modified {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "78",
number = "1",
pages = "97--101",
day = "3",
month = feb,
year = "1997",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:35:59 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042796001331",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Alzer:1997:HMI,
author = "Horst Alzer",
title = "A harmonic mean inequality for the gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "87",
number = "2",
pages = "195--198",
day = "23",
month = dec,
year = "1997",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:36:06 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
note = "See corrigendum \cite{Alzer:1998:CHM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042796001811",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Alzer:1997:SIG,
author = "Horst Alzer",
title = "On some inequalities for the gamma and psi functions",
journal = j-MATH-COMPUT,
volume = "66",
number = "217",
pages = "373--389",
month = jan,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33B15 (26D07)",
MRnumber = "97e:33004",
MRreviewer = "Peter Schroth",
bibdate = "Fri Jul 16 10:38:40 MDT 1999",
bibsource = "http://www.ams.org/mcom/1997-66-217;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Alzer:1997:SII,
author = "Horst Alzer",
title = "On some inequalities for the incomplete gamma
function",
journal = j-MATH-COMPUT,
volume = "66",
number = "218",
pages = "771--778",
month = apr,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33B20 (26D07)",
MRnumber = "97h:33004",
bibdate = "Fri Jul 16 10:38:42 MDT 1999",
bibsource = "http://www.ams.org/mcom/1997-66-218;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bailey:1997:RCV,
author = "David Bailey and Peter Borwein and Simon Plouffe",
title = "On the rapid computation of various polylogarithmic
constants",
journal = j-MATH-COMPUT,
volume = "66",
number = "218",
pages = "903--913",
month = apr,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Yxx",
MRnumber = "1 415 794",
bibdate = "Fri Jul 16 10:38:42 MDT 1999",
bibsource = "http://www.ams.org/mcom/1997-66-218;
http://www.jstor.org/journals/00029890.htm;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "BBP formula",
xxnote = "See \cite{Adamchik:1997:SF}.",
}
@Article{Blinn:1997:JBC,
author = "James F. Blinn",
title = "{Jim Blinn}'s Corner: Floating-Point Tricks",
journal = j-IEEE-CGA,
volume = "17",
number = "4",
pages = "80--84",
month = jul # "\slash " # aug,
year = "1997",
CODEN = "ICGADZ",
DOI = "https://doi.org/10.1109/38.595279",
ISSN = "0272-1716 (print), 1558-1756 (electronic)",
ISSN-L = "0272-1716",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Discusses use of IEEE 754 single-precision
floating-point bit patterns as integers for
implementations of fast, but low-accuracy, functions
useful in computer graphics.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Computer Graphics and Applications",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/cga",
summary = "The author discusses IEEE floating point
representation that stores numbers in what amounts to
scientific notation. He considers the sign bit, the
logarithm function, function approximations, errors and
refinements \ldots{}",
}
@InCollection{Borwein:1997:AGMa,
author = "J. M. Borwein and P. B. Borwein",
title = "The Arithmetic--Geometric Mean and Fast Computation of
Elementary Functions",
crossref = "Berggren:1997:PSB",
pages = "537--552",
year = "1997",
DOI = "https://doi.org/10.1007/978-1-4757-2736-4_56",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Reprint of \cite{Borwein:1984:AGM}.",
URL = "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bshouty:1997:TBA,
author = "Nader H. Bshouty and Yishay Mansour and Baruch
Schieber and Prasoon Tiwari",
title = "A tight bound for approximating the square root",
journal = j-INFO-PROC-LETT,
volume = "63",
number = "4",
pages = "211--213",
day = "10",
month = sep,
year = "1997",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68Q25 (65B15 68Q40)",
MRnumber = "1 477 306",
bibdate = "Sat Nov 7 17:55:54 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{El-Gabali:1997:MTA,
author = "Magdi A. El-Gabali",
title = "Multiple-term approximations for {Appell}'s {$ F_1 $}
function",
journal = j-J-AUSTRAL-MATH-SOC-SER-B,
volume = "39",
number = "1",
pages = "135--148",
month = jul,
year = "1997",
CODEN = "JAMMDU",
DOI = "https://doi.org/10.1017/S0334270000009267",
ISSN = "0334-2700",
ISSN-L = "0334-2700",
bibdate = "Fri Apr 26 16:13:39 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.cambridge.org/core/journals/anziam-journal/article/multipleterm-approximations-for-appells-f1-function/8E218109899D68FD0DC15B6E9D61E8BD",
acknowledgement = ack-nhfb,
ajournal = "J. Austral Math. Soc. Ser. B",
fjournal = "Journal of the Australian Mathematical Society. Series
B, Applied Mathematics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
onlinedate = "17 February 2009",
}
@Article{Fdil:1997:SRC,
author = "A. Fdil",
title = "Some results of convergence acceleration for a general
{$ \Theta $}-type algorithm",
journal = j-APPL-NUM-MATH,
volume = "23",
number = "2",
pages = "219--240",
day = "21",
month = mar,
year = "1997",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65B10 (65D32)",
MRnumber = "1 437 884",
bibdate = "Wed Jul 28 14:36:42 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1997&volume=23&issue=2;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/cas/tree/store/apnum/sub/1997/23/2/738.pdf",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@Article{Forrey:1997:CHF,
author = "Robert C. Forrey",
title = "Computing the hypergeometric function",
journal = j-J-COMPUT-PHYS,
volume = "137",
number = "1",
pages = "79--100",
month = oct,
year = "1997",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1997.5794",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
MRclass = "33C05 (33-04 65D20)",
MRnumber = "MR1481885 (99g:33004)",
bibdate = "Thu Dec 01 09:06:55 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
remark = "The author gives a FORTRAN program for computing $_2
F_1$ for real variable and parameters, using
rapidly-convergent power series in six separate
intervals.",
}
@Article{Ghanem:1997:SBF,
author = "Riadh Ben Ghanem and Cl{\'e}ment Frappier",
title = "Spherical {Bessel} functions and explicit quadrature
formula",
journal = j-MATH-COMPUT,
volume = "66",
number = "217",
pages = "289--296",
month = jan,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33C10 (41A55 65D32)",
MRnumber = "97c:33005",
MRreviewer = "N. Hayek Calil",
bibdate = "Fri Jul 16 10:38:40 MDT 1999",
bibsource = "http://www.ams.org/mcom/1997-66-217;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Goano:1997:RA7,
author = "Michele Goano",
title = "Remark on {Algorithm 745}",
journal = j-TOMS,
volume = "23",
number = "2",
pages = "295--295",
month = jun,
year = "1997",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/264029.643581",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 9 10:19:38 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Goano:1995:ACC}.",
acknowledgement = ack-rfb # " and " # ack-kr # "\slash " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Hare:1997:CPB,
author = "D. E. G. Hare",
title = "Computing the Principal Branch of {log-Gamma}",
journal = j-J-ALG,
volume = "25",
number = "2",
pages = "221--236",
month = nov,
year = "1997",
CODEN = "JOALDV",
DOI = "https://doi.org/10.1006/jagm.1997.0881",
ISSN = "0196-6774 (print), 1090-2678 (electronic)",
ISSN-L = "0196-6774",
bibdate = "Tue Dec 11 09:16:52 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jalg.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0196677497908816",
abstract = "The log-Gamma function is an important special
function of mathematics, and its principal branch is
required in many applications. We develop here the
mathematics required to evaluate the principal branch
to arbitrary precision, including a new bound for the
error in Stirling's asymptotic series. We conclude with
a discussion of the implementation of the principal
branch of the log-Gamma function in the Maple symbolic
algebra system, starting with version Maple V, Release
3.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms",
journal-URL = "http://www.sciencedirect.com/science/journal/01966774",
}
@Article{Harris:1997:NAC,
author = "Frank E. Harris",
title = "New Approach to Calculation of the Leaky Aquifer
Function",
journal = j-IJQC,
volume = "63",
number = "5",
pages = "913--916",
month = "????",
year = "1997",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/(SICI)1097-461X(1997)63:5<913::AID-QUA1>3.0.CO%3B2-Z",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Tue Oct 4 06:59:09 MDT 2011",
bibsource = "Compendex database;
http://www.interscience.wiley.com/jpages/0020-7608;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ijqc.bib;
https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42641;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42641&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Quantum Chem.",
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
journalabr = "Int J Quant Chem",
onlinedate = "6 Dec 1998",
}
@Article{Ito:1997:EIA,
author = "M. Ito and N. Takagi and S. Yajima",
title = "Efficient initial approximation for multiplicative
division and square root by a multiplication with
operand modification",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "4",
pages = "495--498",
month = apr,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.588066",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "An efficient initial approximation method for
multiplicative division and square root is proposed. It
is a modification of the piecewise linear
approximation. The multiplication and the addition
required for the linear approximation are replaced by
\ldots{}",
}
@Article{Karp:1997:HPD,
author = "Alan H. Karp and Peter Markstein",
title = "High-Precision Division and Square Root",
journal = j-TOMS,
volume = "23",
number = "4",
pages = "561--589",
month = dec,
year = "1997",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/279232.279237",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Nov 8 14:50:37 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
abstract = "We present division and square root algorithms for
calculation with more bits than are handled by the
floating-point hardware. These algorithms avoid the
need to multiply two high-precision numbers, speeding
up the last iteration by as much as a factor of 10. We
also show how to produce the floating-point number
closest to the exact result with relatively few
additional operations.",
accepted = "June 1997",
acknowledgement = ack-rfb # " and " # ack-kr,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms, performance, division, quad precision,
square root.",
subject = "G.1.0 [Numerical Analysis]: General -- computer
arithmetic. G.4 [Mathematics of Computing]:
Mathematical Software.",
}
@Article{Kolbig:1997:TEH,
author = "K. S. K{\"o}lbig",
title = "Table errata: {{\booktitle{Handbook of elliptic
integrals for engineers and scientists}} [Second
edition, Springer, New York, 1971, MR {\bf 43} \#3506]
by P. F. Byrd and M. D. Friedman}",
journal = j-MATH-COMPUT,
volume = "66",
number = "220",
pages = "1767--1767",
month = oct,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "44-00 (33-00)",
MRnumber = "1 434 945",
bibdate = "Tue Dec 2 11:25:56 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lee:1997:PRF,
author = "M. Howard Lee",
title = "Polylogarithms and {Riemann}'s $ \zeta $ function",
journal = j-PHYS-REV-E,
volume = "56",
number = "4",
pages = "3909--3912",
month = oct,
year = "1997",
CODEN = "PLEEE8",
DOI = "https://doi.org/10.1103/physreve.56.3909",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
journal-URL = "http://pre.aps.org/browse",
remark = "The paper presents increasingly complicated closed
forms of $ \Li_n(x) $ for negative $n$ to $ n = - 8$,
and reports that no general form for negative $n$ is
apparent. See https://oeis.org/A131758 for related
functions and sequences. Maple and Mathematica can
produce such formulas with code like
simplify(expand(polylog(-13,x))) and PolyLog[-13, x].",
}
@Article{Lether:1997:CNM,
author = "Frank G. Lether",
title = "Constrained near-minimax rational approximations to
{Dawson}'s integral",
journal = j-APPL-MATH-COMP,
volume = "88",
number = "2--3",
pages = "267--274",
day = "30",
month = dec,
year = "1997",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(96)00330-X",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Nov 20 21:02:59 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S009630039600330X",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@InProceedings{Li:1997:ISP,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the 5th Annual {IEEE} Symposium on
{FPGAs} for Custom Computing Machines, 16--18 April
1997",
title = "Implementation of single precision floating point
square root on {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "226--232",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The square root operation is hard to implement on
FPGAs because of the complexity of the algorithms. In
this paper, we present a non-restoring square root
algorithm and two very simple single precision floating
point square root implementations \ldots{}",
}
@InProceedings{Li:1997:PAI,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the 1997 {IEEE} International
Conference on Computer Design: {VLSI} in Computers and
Processors: {ICCD '97}",
title = "Parallel-array implementations of a non-restoring
square root algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "690--695",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "In this paper we present a parallel-array
implementation of a new non-restoring square root
algorithm (PASQRT). The carry-save adder (CSA) is used
in the parallel array. The PASQRT has several features
unlike other implementations. First, it does \ldots{}",
}
@InCollection{Lozier:1997:PST,
author = "Daniel W. Lozier",
title = "A Proposed Software Test Service for Special
Functions",
crossref = "Boisvert:1997:QNS",
pages = "167--178",
year = "1997",
bibdate = "Fri Jul 09 06:00:46 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "See preprint \cite{Lozier:1996:PST}.",
}
@TechReport{Lozier:1997:TRN,
author = "Daniel W. Lozier",
title = "Toward a Revised {NBS} Handbook of Mathematical
Functions",
type = "Technical Report",
number = "NISTIR 6072",
institution = pub-NIST,
address = pub-NIST:adr,
pages = "8",
month = sep,
year = "1997",
bibdate = "Fri Jul 09 06:35:07 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6072.ps.gz",
acknowledgement = ack-nhfb,
}
@Article{MacLeod:1997:AEE,
author = "Allan J. MacLeod",
title = "Accurate and efficient evaluation of the
{Bose--Einstein} functions $ g_{3 / 2} $ and $ g_{5 /
2} $",
journal = j-COMPUT-PHYS,
volume = "11",
number = "4",
pages = "385--??",
month = jul,
year = "1997",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.168609",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:46:08 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.168609",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@InProceedings{Matsubara:1997:LPZ,
author = "G. Matsubara and N. Ide",
booktitle = "Proceedings of the Third International Symposium on
Advanced Research in Asynchronous Circuits and Systems,
7--10 April 1997",
title = "A low power zero-overhead self-timed division and
square root unit combining a single-rail static circuit
with a dual-rail dynamic circuit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "198--209",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "An asynchronous pipeline scheme that combines a low
power static circuit with a high-speed dual-rail
dynamic circuit is proposed. The scheme utilizes a
dual-rail circuit only in the critical path of an SRT
division and square root calculation unit. \ldots{}",
}
@Book{Muller:1997:EFA,
author = "Jean-Michel Muller",
title = "Elementary Functions: Algorithms and Implementation",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xv + 204",
year = "1997",
ISBN = "0-8176-3990-X",
ISBN-13 = "978-0-8176-3990-7",
LCCN = "QA331.M866 1997",
bibdate = "Fri Jul 25 12:00:55 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "US\$59.95",
URL = "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X;
http://www.ens-lyon.fr/~jmmuller/book_functions.html",
acknowledgement = ack-nhfb,
tableofcontents = "1 Introduction / 1 \\
2 Computer Arithmetic / 9 \\
2.1 Floating-Point Arithmetic / 9 \\
2.1.1 Floating-point formats / 9 \\
2.1.2 Rounding modes / 10 \\
2.1.3 Subnormal numbers and exceptions / 12 \\
2.1.4 ULPs / 13 \\
2.1.5 Testing your computational environment / 13 \\
2.2 Redundant Number Systems / 13 \\
2.2.1 Signed-digit number systems / 14 \\
2.2.2 Radix-2 redundant number systems / 15 \\
I Algorithms Based on Polynomial Approximation and/or
Table Lookup / 19 \\
3 Polynomial Approximations / 21 \\
3.1 Least Squares Polynomial Approximations / 22 \\
3.1.1 Legendre polynomials / 23 \\
3.1.2 Chebyshev polynomials / 23 \\
3.1.3 Jacobi polynomials / 23 \\
3.2 Least Maximum Approximations / 24 \\
3.3 Speed of Convergence / 31 \\
3.4 Rational Approximations / 34 \\
3.5 Actual Computation / 38 \\
3.6 Example: the Cyrix FastMath Processor / 41 \\
3.7 Algorithms and Architectures / 43 \\
3.7.1 The $E$-Method / 45 \\
3.7.2 Estrin's Method / 47 \\
3.8 Miscellaneous / 47 \\
4 Table-Based Methods / 51 \\
4.1 Introduction / 51 \\
4.2 Table-Driven Algorithms / 53 \\
4.2.1 Tang's algorithm for $\exp(x)$ in IEEE
floating-point arithmetic / 55 \\
4.2.2 $\ln(x)$ on $[1, 2]$ / 57 \\
4.2.3 $\sin(x)$ on $[0, \pi/4]$ / 58 \\
4.3 Gal's Accurate Tables Method / 58 \\
4.4 Methods Requiring Specialized Hardware / 62 \\
4.4.1 Wong and Goto, logarithm / 62 \\
4.4.2 Wong and Goto, exponential / 65 \\
II Shift-and-Add Algorithms / 69 \\
5 Shift-and-Add algorithms / 71 \\
5.1 The Restoring and Nonrestoring Algorithms / 73 \\
5.2 Simple Algorithms for Exponentials and Logarithms /
77 \\
5.2.1 The restoring algorithm for exponentials / 77 \\
5.2.2 The restoring algorithm for logarithms / 79 \\
5.3 Faster Algorithms '. / 81 \\
5.3.1 Faster computation of exponentials / 81 \\
5.3.2 Faster computation of logarithms / 87 \\
5.4 Baker's Predictive Algorithm / 90 \\
5.5 Bibliographic notes / 98 \\
6 The CORDIC Algorithm / 101 \\
6.1 Introduction / 101 \\
6.2 The Conventional Iteration / 101 \\
6.3 Scale Factor Compensation / 107 \\
6.4 CORDIC With Redundant Number Systems / 109 \\
6.4.1 Signed-digit implementation / 111 \\
6.4.2 Carry-save implementation / 111 \\
6.4.3 The variable scale factor problem / 112 \\
6.5 The Double Rotation Method / 112 \\
6.6 Branching CORDIC / 115 \\
6.7 Differential CORDIC / 118 \\
6.8 Computation of $\cos^{-1}$ and $\sin^{-1}$ / 122
\\
6.9 Variations on CORDIC / 124 \\
7 Other Shift-and-Add Algorithms / 127 \\
7.1 High-Radix Algorithms / 127 \\
7.1.1 Ercegovac's radix-16 algorithms / 127 \\
7.2 The BKM Algorithm / 131 \\
7.2.1 The BKM iteration / 133 \\
7.2.2 Computation of the exponential function (E-mode)
/ 133 \\
7.2.3 Computation of the logarithm function (L-mode) /
137 \\
7.2.4 Application to the computation of elementary
functions / 138 \\
III Range Reduction, Final Rounding and Exceptions /
141 \\
8 Range Reduction / 143 \\
8.1 Introduction / 143 \\
8.2 Cody and Waite's Method for Range Reduction / 148
\\
8.3 Worst Cases for Range Reduction / 149 \\
8.3.1 A few basic notions on continued fractions / 149
\\
8.3.2 Finding worst cases using continued fractions /
151 \\
8.4 The Payne and Hanek Algorithm / 154 \\
8.5 The Modular Algorithm / 158 \\
8.5.1 Fixed-point reduction / 158 \\
8.5.2 Floating-point reduction / 161 \\
8.5.3 Architectures for Modular Reduction / 161 \\
9 Final Rounding / 163 \\
9.1 Introduction / 163 \\
9.2 Monotonicity / 164 \\
9.3 Exact Rounding: Presentation of the Problem / 165
\\
9.4 Some Experiments / 168 \\
9.5 A ``Probabilistic'' Approach / 168 \\
9.6 Upper Bounds on $m$ / 171 \\
9.6.1 Frequency of failures / 173 \\
9.6.2 Computing with one million bits / 173 \\
10 Miscellaneous / 175 \\
10.1 Exceptions / 175 \\
10.1.1 NaNs / 176 \\
10.1.2 Exact results / 177 \\
10.2 Notes on $x^y$ / 178 \\
10.3 Multiple Precision / 180",
}
@InProceedings{Schulte:1997:AFA,
author = "M. J. Schulte and James E. Stine",
title = "Accurate Function Approximations by Symmetric Table
Lookup and Addition",
crossref = "Thiele:1997:IIC",
pages = "144--153",
year = "1997",
bibdate = "Sun Mar 04 10:55:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1997:SBT,
author = "M. Schulte and J. Stine",
title = "Symmetric Bipartite Tables for Accurate Function
Approximation",
crossref = "Lang:1997:ISC",
pages = "175--183",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
URL = "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf",
acknowledgement = ack-nhfb,
}
@Article{Segura:1997:CEM,
author = "J. Segura and P. Fern{\'a}ndez de C{\'o}rdoba and Yu.
L. Ratis",
title = "A code to evaluate modified {Bessel} functions based
on the continued fraction method",
journal = j-COMP-PHYS-COMM,
volume = "105",
number = "2--3",
pages = "263--272",
day = "1",
month = oct,
year = "1997",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(97)00069-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:19 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465597000696",
abstract = "We present an algorithm to evaluate the modified
Bessel functions $ I \_ n u $ and $ K_\nu $ of integral
and half-integral order based on the calculation of the
continued fraction for the $ I \_ n u $'s, the
Wronskian and the application of forward recurrence
relations for the $ K_\nu $'s and backward recurrence
for the $ I \_ n u $'s. The main feature of the
algorithm is that it does not require recalculations
using normalization relations nor trial values to start
the recurrences; the code evaluates in each step
(already normalized) Bessel functions. The accuracy of
the method ($ 10^{-16} $ for half-integral order and
better than $ 2 \times 10^{-7} $ for integral order in
our code) is limited only by the precision in the
initial values for the recurrence and the maximum order
available for a given value of the argument is
restricted only by the maximum real number available in
the computer.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Soderquist:1997:DSR,
author = "Peter Soderquist and Miriam Leeser",
title = "Division and Square Root: Choosing the Right
Implementation: Exploring the major design choices for
microprocessor implementations of floating-point
division and square root",
journal = j-IEEE-MICRO,
volume = "17",
number = "4",
pages = "56--66",
month = jul # "\slash " # aug,
year = "1997",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.612224",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
Science Citation Index database (1980--2000)",
URL = "http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Book{Thompson:1997:ACMa,
author = "William J. (William Jackson) Thompson",
title = "Atlas for Computing Mathematical Functions: an
Illustrated Guidebook for Practitioners: with Programs
in {C} and {Mathematica}",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 903",
year = "1997",
ISBN = "0-471-00260-7 (cloth)",
ISBN-13 = "978-0-471-00260-4 (cloth)",
LCCN = "QA331.T385 1997",
bibdate = "Fri May 21 07:11:19 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
annote = "A Wiley-Interscience publication. Includes CD-ROM.",
keywords = "C (Computer program language); Functions -- Computer
programs; Mathematica (Computer program language);
Science -- Mathematics -- Computer programs",
tableofcontents = "Preface / xiii \\
INTRODUCTION \\
The Atlas of Functions / 1 \\
What This Atlas Contains / 1 \\
How to Use the Atlas / 2 \\
About the Production of the Atlas / 2 \\
The Computer Interface / 3 \\
What the CD-ROM Contains / 3 \\
How to Locate a Function / 3 \\
Exploring Functions with Mathematica / 4 \\
The C Functions: No Assembly Required / 7 \\
Hints for Fortran and Pascal Programmers / 3 \\
File Names for PC-Based Systems / 12 \\
Reliability of Programs: Disclaimer / 12 \\
References on the Computer Interface / 12 \\
PART I. THE FUNCTIONS \\
1 Introduction to the Functions / 15 \\
How the Function Descriptions Are Organized / 16 \\
2 A Visual Tour of the Atlas / 17 \\
3 Computing Strategies / 25 \\
3.1 General Computing Strategies / 25 \\
3.2 Iteration and Recursion / 27 \\
3.3 Continued Fractions and Rational Approximations /
30 \\
3.4 Using Asymptotic Expansions / 31 \\
3.5 Euler--Maclaurin Summation Formula / 32 \\
3.6 Accuracy and Precision of the Functions / 33 \\
3.7 Mathematical Constants Used in the Atlas / 34 \\
References on Computing Strategies / 34 \\
4 Elementary Transcendental Functions / 35 \\
4.1 Exponential and Logarithmic Functions / 35 \\
4.1.1 Exponentials / 36 \\
4.1.2 Logarithms / 38 \\
4.2 Circular and Inverse Circular Functions / 40 \\
42.1 Circular Functions / 40 \\
4.2.2 Inverse Circular Functions / 44 \\
4.3 Hyperbolic and Inverse Hyperbolic Functions / 49
\\
4.3.1 Hyperbolic Functions / 49 \\
4.3.2 Inverse Hyperbolic Functions / 53 \\
References on Elementary Transcendental Functions / 58
\\
S Exponential Integrals and Related Functions / 59 \\
5.1 Exponential and Logarithmic Integrals / 59 \\
5.1.1 Exponential Integral of the First Kind / 59 \\
5.1.2 Exponential Integral of the Second Kind / 64 \\
5.1.3 Logarithmic Integral / 69 \\
5.2 Cosine and Sine Integrals / 72 \\
References on Exponential Integrals and Related
Functions / 78 \\
6 Gamma and Beta Functions / 79 \\
6.1 Gamma Function and Beta Function / 79 \\
6.1.1 Gamma Function / 79 \\
6.1.2 Beta Function / 84 \\
6.2 Psi (Digamma) and Polygamma Functions / 86 \\
6.2.1 Psi Function / 87 \\
6.2.2 Polygamma Functions / 91 \\
6.3 Incomplete Gamma and Beta Functions / 97 \\
6.3.1 Incomplete Gamma Function / 97 \\
6.3.2 Incomplete Beta Function / 102 \\
References on Gamma and Beta Functions / 106 \\
7 Combinatorial Functions / 109 \\
7.1 Factorials and Rising Factorials / 109 \\
7.1.1 Factorial Function / 110 \\
7.1.2 Rising Factorial Function / 113 \\
7.2 Binomial and Multinomial Coefficients / 115 \\
7.2.1 Binomial Coefficients / 115 \\
7.2.2 Multinomial Coefficients / 118 \\
7.3 Stirling Numbers of First and Second Kinds / 121
\\
7.3.1 Stirling Numbers of the First Kind / 121 \\
7.3.2 Stirling Numbers of the Second Kind / 124 \\
7.4 Fibonacci and Lucas Polynomials / 126 \\
7.4.1 Fibonacci Polynomials and Fibonacci Numbers / 126
\\
7.4.2 Lucas Polynomials and Lucas Numbers / 128 \\
References on Combinatorial Functions / 130 \\
8 Number Theory Functions / 133 \\
8.1 Bernoulli Numbers and Bernoulli Polynomials / 133
\\
8.1.1 Bernoulli Numbers / 133 \\
8.1.2 Bernoulli Polynomials / 137 \\
8.2 Euler Numbers and Euler Polynomials / 139 \\
8.2.1 Euler Numbers / 139 \\
8.2.2 Euler Polynomials / 142 \\
8.3 Riemann Zeta Function / 144 \\
8.4 Other Sums of Reciprocal Powers / 147 \\
8.5 Polylogarithms / 151 \\
References on Number Theory Functions / 156 \\
9 Probability Distributions / 159 \\
9.1 Overview of Probability Distribution Functions /
160 \\
9.2 Discrete Probability Distributions / 160 \\
9.2.1 Binomial Distribution / 162 \\
9.2.2 Negative Binomial (Pascal) Distribution / 164 \\
9.2.3 Geometric Distribution / 166 \\
9.2.4 Hypergeometric Distribution / 168 \\
9.2.5 Logarithmic Series Distribution / 171 \\
9.2.6 Poisson Distribution / 173 \\
9.3 Normal Probability Distributions / 175 \\
9.3.1 Gauss (Normal) Probability Function / 177 \\
9.3.2 Bivariate Normal Probability Function / 179 \\
9.3.3 Chi-Square Probability Functions / 182 \\
9.3.4 $F$-(Variance-Ratio) Distribution Functions / 188
\\
9.3.5 Student's $t$-Distribution Functions / 192 \\
9.3.6 Lognormal Distribution / 196 \\
9.4 Other Continuous Probability Distributions / 199
\\
9.4.1 Cauchy (Lorentz) Distribution / 200 \\
9.4.2 Exponential Distribution / 203 \\
9.4.3 Pareto Distribution / 205 \\
9.4.4 Weibull Distribution / 208 \\
9.4.5 Logistic Distribution / 211 \\
9.4.6 Laplace Distribution / 213 \\
9.4.7 Kolmogorov--Smirnov Distribution / 215 \\
9.4.8 Beta Distribution / 218 \\
References on Probability Distribution Functions / 221
\\
10 Error Function, Fresnel and Dawson Integrals / 223
\\
10.1 Error Function / 223 \\
10.2 Fresnel Integrals / 226 \\
10.3 Dawson Integral / 234 \\
References on Error Functions, Fresnel and Dawson
Integrals / 238 \\
11 Orthogonal Polynomials / 239 \\
11.1 Overview of Orthogonal Polynomials / 239 \\
11.2 Chebyshev Polynomials / 244 \\
11.2.1 Chebyshev Polynomials of the First Kind / 245
\\
11.2.2 Chebyshev Polynomials of the Second Kind / 247
\\
11.3 Gegenbauer (Ultraspherical) Polynomials / 251 \\
11.4 Hermite Polynomials / 254 \\
11.5 Laguerre Polynomials / 257 \\
11.6 Legendre Polynomials / 260 \\
11.7 Jacobi Polynomials / 263 \\
References on Orthogonal Polynomials / 267 \\
12 Legendre Functions / 269 \\
12.1 Overview of Legendre Functions / 269 \\
12.1.1 Visualizing Legendre Functions of the First Kind
/ 270 \\
12.1.2 Visualizing Legendre Functions of the Second
Kind / 273 \\
12.1.3 Legendre Functions and Coordinate Systems / 277
\\
12.2 Spherical Legendre Functions / 278 \\
12.2.1 Spherical Polar Coordinates / 278 \\
12.2.2 Legendre Functions of the First Kind for Integer
$m$ and $n$ / 279 \\
12.2.3 Legendre Functions of the Second Kind for
Integer $m$ and $n$ / 284 \\
12.3 Toroidal Legendre Functions / 291 \\
12.3.1 Toroidal Coordinates / 291 \\
12.3.2 Toroidal Functions of the First Kind / 293 \\
12.3.3 Toroidal Functions of the Second Kind / 296 \\
12.4 Conical Legendre Functions / 300 \\
12.4.1 Laplace Equation on a Cone / 300 \\
12.4.2 Conical Functions / 301 \\
References on Legendre Functions / 304 \\
13 Spheroidal Wave Functions / 307 \\
13.1 Overview of Spheroidal Wave Functions / 307 \\
13.1.1 Spheroidal Coordinates / 308 \\
13.1.2 Scalar Wave Equation in Spheroidal Coordinates /
309 \\
13.1.3 Eigenvalues for Spheroidal Equations / 310 \\
13.1.4 Auxiliary Functions for Eigenvalues / 320 \\
13.2 Spheroidal Angular Functions / 321 \\
13.2.1 Expansion Coefficients for Angular Functions /
321 \\
13.2.2 Spheroidal Angular Functions / 331 \\
13.3 Spheroidal Radial Functions / 336 \\
13.3.1 Expansion Coefficients for Radial Functions /
336 \\
13.3.2 Spheroidal Radial Functions / 340 \\
References on Spheroidal Wave Functions / 344 \\
14 Bessel Functions / 345 \\
14.1 Overview of Bessel Functions / 345 \\
14.2 Bessel Functions of Integer Order / 350 \\
14.2.1 Regular Cylindrical Bessel Function / 351 \\
14.2.2 Irregular Cylindrical Bessel Function / 357 \\
14.2.3 Regular Hyperbolic Bessel Function / 361 \\
14.2.4 Irregular Hyperbolic Bessel Function / 368 \\
14.3 Kelvin Functions / 375 \\
14.3.1 Regular Kelvin Functions / 375 \\
14.3.2 Irregular Kelvin Functions / 385 \\
14.4 Bessel Functions of Half-Integer Order / 394 \\
14.4.1 Regular Spherical Bessel Function / 394 \\
14.4.2 Irregular Spherical Bessel Function / 401 \\
14.4.3 Regular Modified Spherical Bessel Function / 405
\\
14.4.4 Irregular Modified Spherical Bessel Function /
412 \\
14.5 Airy Functions / 416 \\
14.5.1 Airy Functions / 416 \\
14.5.2 Derivatives of Airy Functions / 425 \\
References on Bessel Functions / 434 \\
15 Struve, Anger, and Weber Functions / 435 \\
15.1 Struve Functions / 435 \\
15.1.1 Struve Function / 435 \\
15.1.1 Modified Struve Function / 442 \\
15.2 Anger and Weber Functions / 448 \\
15.2.1 Overview of Anger and Weber Functions / 448 \\
15.2.2 Anger Function / 449 \\
15.2.3 Weber Function / 455 \\
References on Struve, Anger, and Weber Functions / 458
\\
16 Hypergeometric Functions and Coulomb Wave Functions
/ 461 \\
16.1 Hypergeometric Functions / 461 \\
16.2 Confluent Hypergeometric Functions / 465 \\
16.2.1 Regular Function / 465 \\
16.2.2 Irregular Function / 471 \\
16.3 Coulomb Wave Functions / 478 \\
16.3.1 Regular Functions and Derivatives / 478 \\
16.3.2 Irregular Functions and Derivatives / 487 \\
References on Hypergeometric Functions and Coulomb Wave
Functions / 493 \\
17 Elliptic Integrals and Elliptic Functions / 495 \\
17.1 Overview of Elliptic Integrals and Elliptic
Functions / 495 \\
17.2 Elliptic Integrals / 496 \\
17.2.1 Elliptic Integrals of the First Kind / 496 \\
17.2.2 Elliptic Integrals of the Second Kind / 502 \\
17.2.3 Jacobi Zeta Function / 506 \\
17.2.4 Heuman Lambda Function / 510 \\
17.2.5 Elliptic Integrals of the Third Kind / 513 \\
17.3 Jacobi Elliptic Functions and Theta Functions /
517 \\
17.3.1 Jacobi Elliptic Functions / 517 \\
17.3.2 Theta Functions / 525 \\
17.3.3 Logarithmic Derivatives of Theta Functions / 531
\\
References on Elliptic Integrals and Elliptic Functions
/ 536 \\
18 Parabolic Cylinder Functions / 539 \\
18.1 Parabolic Cylinder Coordinates / 539 \\
18.2 Parabolic Cylinder Functions / 540 \\
18.2.1 Parabolic Cylinder Functions U / 540 \\
18.2.2 Parabolic Cylinder Functions V / 546 \\
References on Parabolic Cylinder Functions / 550 \\
19 Miscellaneous Functions for Science and Engineering
/ 551 \\
19.1 Debye Functions / 551 \\
19.2 Sievert Integral / 554 \\
19.3 Abramowitz Function / 557 \\
19.4 Spence Integeral / 562 \\
19.5 Clausen Integral / 565 \\
19.6 Voigt (Plasma Dispersion) Function / 570 \\
19.7 Angular Momentum Coupling Coefficients 576 / 539
\\
19.7.1 3-j Coefficients / 578 \\
19.7.2 6-j Coefficients / 582 \\
19.7.3 9-j Coefficients / 586 \\
References on Miscellaneous Functions for Science and
Engineering \\
PART II. THE COMPUTER INTERFACE \\
20 The Mathematica Notebooks / 593 \\
20.1 Introduction to the Notebooks / 593 \\
20.2 Exploring with the Notebook Cells / 594 \\
20.3 The Annotated Notebooks / 594 \\
20.4 Elementary Transcendental Functions / 595 \\
20.5 Exponential Integrals and Related Functions / 602
\\
20.6 Gamma and Beta Functions / 607 \\
20.7 Combinatorial Functions / 618 \\
20.8 Number Theory Functions / 627 \\
20.9 Probability Distributions / 633 \\
20.10 Error Function, Fresnel and Dawson Integrals /
663 \\
20.11 Orthogonal Polynomials / 667 \\
20.12 Legendre Functions / 676 \\
20.14 Bessel Functions / 708 \\
20.15 Struve, Anger, and Weber Functions / 747 \\
20.16 Hypergeometric Functions and Coulomb Wave
Functions / 756 \\
20.17 Elliptic Integrals and Elliptic Functions / 765
\\
20.18 Parabolic Cylinder Functions / 782 \\
20.19 Miscellaneous Functions for Science and
Engineering / 788 \\
21 The C Driver Programs / 797 \\
21.1 Introduction to the C Driver Programs / 797 \\
21.2 How the C Drivers are Organized / 797 \\
21.3 Annotations to the C Driver Programs / 798 \\
21.4 Elementary Transcendental Functions / 798 \\
21.4.1 Exponential and Logarithmic Functions / 798 \\
21.4.2 Circular and Inverse Circular Functions / 799
\\
21.4.3 Hyperbolic and Inverse Hyperbolic Functions /
800 \\
21.5 Exponential Integrals and Related Functions / 802
\\
21.5.1 Exponential and Logarithmic Integrals / 802 \\
21.5.2 Cosine and Sine Integrals / 803 \\
21.6 Gamma and Beta Functions / 804 \\
21.6.1 Gamma Function and Beta Function / 804 \\
21.6.2 Psi (Digamma) and Polygamma Functions / 805 \\
21.6.3 Incomplete Gamma and Beta Functions / 807 \\
21.7 Combinatorial Functions / 808 \\
21.7.1 Factorials and Rising Factorials / 808 \\
21.7.2 Binomial and Multinomial Coefficients / 809 \\
21.7.3 Stirling Numbers of the First and Second Kinds /
811 \\
21.7.4 Fibonacci and Lucas Polynomials / 811 \\
21.8 Number Theory Functions / 813 \\
21.8.1 Bernoulli Numbers and Bernoulli Polynomials /
813 \\
21.8.2 Euler Numbers and Euler Polynomials / 814 \\
21.8.3 Riemann Zeta Function / 814 \\
21.8.4 Other Sums of Reciprocal Powers / 815 \\
21.8.5 Polylogarithms / 816 \\
21.9 Probability Distributions / 816 \\
21.9.1 Organization of the PDFs / 816 \\
21.9.2 Discrete Probability Distributions / 816 \\
21.9.3 Normal Probability Distributions / 820 \\
21.9.4 Other Continuous Probability Distributions / 825
\\
21.10 Error Function, Fresnel and Dawson Integrals /
830 \\
21.10.1 Error Function / 830 \\
21.10.2 Fresnel Integrals / 831 \\
21.10.3 Dawson Integral / 832 \\
21.11 Orthogonal Polynomials / 833 \\
21.11.1 Orthogonal Polynomial Functions / 833 \\
21.11.2 Chebyshev Polynomials / 833 \\
21.11.3 Gegenbauer (Ultraspherical) Polynomials / 834
\\
21.11.4 Hermite Polynomials / 835 \\
21.11.5 Laguerre Polynomials / 835 \\
21.11.6 Legendre Polynomials / 836 \\
21.11.7 Jacobi Polynomials / 837 \\
21.12 Legendre Functions / 837 \\
21.12.1 Overview of Legendre Functions / 838 \\
21.12.2 Spherical Legendre Functions / 838 \\
21.12.3 Toroidal Legendre Functions / 840 \\
21.12.4 Conical Legendre Functions / 841 \\
21.13 Spheroidal Wave Functions / 842 \\
21.13.1 Overview of Spheroidal Wave Functions / 842 \\
21.13.2 Spheroidal Angular Functions / 843 \\
21.13.3 Spheroidal Radial Functions / 844 \\
21.14 Bessel Functions / 846 \\
21.14.1 Overview of Bessel Functions / 846 \\
21.14.2 Bessel Functions of Integer Order / 846 \\
21.14.3 Kelvin Functions / 850 \\
21.14.4 Bessel Functions of Half-Integer Order / 852
\\
21.14.5 Airy Functions / 856 \\
21.15 Struve, Anger, and Weber Functions / 857 \\
21.15.1 Struve Functions / 857 \\
21.15.2 Anger and Weber Functions / 859 \\
21.16 Hypergeometric Functions and Coulomb Wave
Functions / 861 \\
21.16.1 Hypergeometric Functions / 861 \\
21.16.2 Confluent Hypergeometric Functions / 862 \\
21.16.3 Coulomb Wave Functions / 863 \\
21.17 Elliptic Integrals and Elliptic Functions / 864
\\
21.17.1 Overview of Elliptic Integrals and Elliptic
Functions / 864 \\
21.17.2 Elliptic Integrals / 864 \\
21.17.3 Jacobi Elliptic Functions and Theta Functions /
867 \\
21.18 Parabolic Cylinder Functions / 870 \\
21.18.1 Parabolic Cylinder Functions / 870 \\
21.19 Miscellaneous Functions for Science and
Engineering / 872 \\
21.19.1 Debye Functions / 872 \\
21.19.2 Sievert Integral / 873 \\
21.19.3 Abramowitz Function / 873 \\
21.19.4 Spence Integral / 874 \\
21.19.5 Clausen Integral / 875 \\
21.19.6 Voigt (Plasma Dispersion) Function / 876 \\
21.19.7 Angular Momentum Coupling Coefficients / 876
\\
APPENDIX: File Names for PC-Based Systems / 879 \\
INDEXES \\
Index of Function Notations / 883 \\
Index of Programs and Dependencies / 886 \\
Index of Subjects and Authors / 889",
}
@Book{Thompson:1997:ACMb,
author = "William J. (William Jackson) Thompson",
title = "Atlas for Computing Mathematical Functions: an
Illustrated Guide for Practitioners with Programs in
{Fortran 90} and {Mathematica}",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 888",
year = "1997",
ISBN = "0-471-18171-4 (cloth)",
ISBN-13 = "978-0-471-18171-2 (cloth)",
LCCN = "QA331.T386 1997",
bibdate = "Fri May 21 07:11:19 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Includes CD-ROM.",
acknowledgement = ack-nhfb,
annote = "A Wiley-Interscience publication. System requirements
for accompanying computer disc: Windows; Macintosh
compatible.",
keywords = "FORTRAN (Computer program language); Functions --
Computer programs; Mathematica (Computer program
language); Science -- Mathematics -- Computer
programs",
}
@Book{Yoshida:1997:HFM,
author = "Masaaki Yoshida",
title = "Hypergeometric Functions, My Love: Modular
Interpretations of Configuration Spaces",
volume = "E 32",
publisher = pub-VIEWEG,
address = pub-VIEWEG:adr,
pages = "xvi + 292",
year = "1997",
ISBN = "3-528-06925-2",
ISBN-13 = "978-3-528-06925-4",
ISSN = "0179-2156",
LCCN = "QA353.H9 Y67 1997",
bibdate = "Sat Oct 30 21:12:24 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Aspects of mathematics",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions; Configuration space",
tableofcontents = "Part 1: The Story of the Configuration Space
$X(2,4)$ of Four Points on the Projective Line \\
I. Configuration Spaces --- The Simplest Case \\
II. Elliptic Curves \\
III. Modular Interpretations of X(2,4) \\
IV. Hypergeometric Integrals and Loaded Cycles \\
2 The Story of the Configuration Space X(2,n) of n
Points on the Projective Line \\
V. The Configuration Space X(2,5) \\
VI. Modular Interpretation of the Configuration Space
X(2,n) \\
3 The Story of the Configuration Space X(3,6) of Six
Lines on the Projective Plane \\
VII The Configuration Space X(3,6) \\
VIII. Hypergeometric Functions of Type (3,6) \\
IX. Modular Interpretation of the Configuration Space
X(3,6)",
}
@Article{Yousif:1997:BFF,
author = "Hashim A. Yousif and Richard Melka",
title = "{Bessel} function of the first kind with complex
argument",
journal = j-COMP-PHYS-COMM,
volume = "106",
number = "3",
pages = "199--206",
month = nov,
year = "1997",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(97)00087-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:21 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465597000878",
abstract = "A new method of computing integral order Bessel
functions of the first kind $ J_n(z) $ when either the
absolute value of the real part or the imaginary part
of the argument $ z = x + i y $ is small, is described.
This method is based on computing the Bessel functions
from asymptotic expressions when $ x \sim 0 $ (or $ y
\sim 0 $ ). These expansions are derived from the
integral definition of Bessel functions. This method is
necessary because some existing algorithms and methods
fail to give correct results for small $x$ or small
$y$. In addition, our overall method of computing
Bessel functions of any order and argument is discussed
and the logarithmic derivative is used in computing
these functions. The starting point of the backward
recurrence relations needed to evaluate the Bessel
function and their logarithmic derivatives are
investigated in order to obtain accurate numerical
results. Our numerical method, together with
established techniques of computing the Bessel
functions, is easy to implement, efficient, and
produces reliable results for all $z$.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Zhang:1997:CSA,
author = "Jun Zhang and John A. Belward",
title = "{Chebyshev} series approximations for the {Bessel}
function {$ Y_n(z) $} of complex argument",
journal = j-APPL-MATH-COMP,
volume = "88",
number = "2--3",
pages = "275--286",
day = "30",
month = dec,
year = "1997",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(96)00335-9",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Nov 20 21:02:59 MST 2012",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300396003359",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Aberbour:1998:PMF,
author = "M. Aberbour and A. Houelle and H. Mehrez and N.
Vaucher and A. Guyot",
title = "On portable macrocell {FPU} generators for division
and square root operators complying to the full
{IEEE-754} standard",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "6",
number = "1",
pages = "114--121",
month = mar,
year = "1998",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/92.661253",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
summary = "In this paper, we investigate the design of macrocell
generators of division and square root floating-point
operators. The number representation used in our
operators is the IEEE-754-1985 standard for binary
floating-point numbers. The design and \ldots{}",
}
@Article{Adamchik:1998:PFN,
author = "Victor S. Adamchik",
title = "{Polygamma} functions of negative order",
journal = j-J-COMPUT-APPL-MATH,
volume = "100",
number = "2",
pages = "191--199",
day = "21",
month = dec,
year = "1998",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:39:42 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042798001927",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Alzer:1998:CHM,
author = "Horst Alzer",
title = "Corrigendum: {A harmonic mean inequality for the gamma
function [J. Comput. Appl. Math. {\bf 87} (1997)
195--198]}",
journal = j-J-COMPUT-APPL-MATH,
volume = "90",
number = "2",
pages = "265--265",
day = "17",
month = apr,
year = "1998",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(98)00040-5",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:36:08 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
note = "See \cite{Alzer:1997:HMI}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042798000405",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Book{Andrews:1998:SFM,
author = "Larry C. Andrews",
title = "Special functions of mathematics for engineers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
edition = "Second",
pages = "xvii + 479",
year = "1998",
ISBN = "0-19-856558-5 (Oxford hardcover), 0-8194-2616-4 (SPIE
Press hardcover)",
ISBN-13 = "978-0-19-856558-1 (Oxford hardcover),
978-0-8194-2616-1 (SPIE Press)",
LCCN = "QA351 .A75 1998",
bibdate = "Sat Oct 30 16:44:00 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
library.ox.ac.uk:210/ADVANCE;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Originally published: New York : McGraw-Hill, c1992.",
subject = "Functions, Special",
tableofcontents = "Preface to the Second Edition \\
Preface to the First Edition \\
Notation for Special Functions \\
Infinite Series, Improper Integrals, and Infinite
Products \\
The Gamma Function and Related Functions \\
Other Functions Defined by Integrals \\
Legendre Polynomials and Related Functions \\
Other Orthogonal Polynomials \\
Bessel Functions \\
Bessel Functions of Other Kinds \\
Applications Involving Bessel Functions \\
The Hypergeometric Function \\
The Confluent Hypergeometric Functions \\
Generalized Hypergeometric Functions \\
Applications Involving Hypergeometric-Type Functions
\\
Bibliography \\
Appendix: A List of Special Function Formulas \\
Selected Answers to Exercises \\
Index",
}
@Book{Anonymous:1998:AMS,
editor = "Anonymous",
title = "Analytical methods and special functions",
publisher = "Gordon and Breach Science Publishers",
address = "Amsterdam, The Netherlands",
pages = "????",
year = "1998",
ISSN = "1027-0264",
LCCN = "A299.6 A533 v. 1 1998",
bibdate = "Sat Oct 30 19:02:18 2010",
bibsource = "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Antelo:1998:CVH,
author = "E. Antelo and T. Lang and J. D. Bruguera",
title = "Computation of $ \sqrt {(x / d)} $ in a very high
radix combined division\slash square-root unit with
scaling and selection by rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "2",
pages = "152--161",
month = feb,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.663761",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A very-high radix digit-recurrence algorithm for the
operation {\surd}(x/d) is developed, with residual
scaling and digit selection by rounding. This is an
extension of the division and square-root algorithms
presented previously, and for which a \ldots{}",
}
@Article{BenGhanem:1998:QFU,
author = "Riadh {Ben Ghanem}",
title = "Quadrature formulae using zeros of {Bessel} functions
as nodes",
journal = j-MATH-COMPUT,
volume = "67",
number = "221",
pages = "323--336",
month = jan,
year = "1998",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D32",
MRnumber = "98c:65031",
MRreviewer = "Kai Diethelm",
bibdate = "Fri Jul 16 10:38:50 MDT 1999",
bibsource = "http://www.ams.org/mcom/1998-67-221;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Borwein:1998:CSR,
author = "Jonathan M. Borwein and David M. Bradley and Richard
E. Crandall",
title = "Computational Strategies for the {Riemann} Zeta
Function",
type = "Report",
number = "CECM-98-118",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "68",
day = "30",
month = oct,
year = "1998",
bibdate = "Mon Oct 24 11:29:15 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Borwein:2000:CSR}.",
URL = "http://docserver.carma.newcastle.edu.au/211;
http://people.reed.edu/~crandall/papers/attach01.pdf",
abstract = "We provide a compendium of evaluation methods for the
Riemann zeta function, presenting formulae ranging from
historical attempts to recently found convergent series
to curious oddities old and new. We concentrate
primarily on practical computational issues, such
issues depending on the domain of the argument, the
desired speed of computation, and the incidence of what
we call ``value recycling.''",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
Richard Eugene Crandall (29 December 1947--20 December
2012)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Buhring:1998:ACG,
author = "Wolfgang B{\"u}hring and H. M. Srivastava",
editor = "Themistocles M. Rassias",
booktitle = "Approximation theory and applications",
title = "Analytic Continuation of the Generalized
Hypergeometric Series Near Unit Argument with Emphasis
on the Zero-Balanced Series",
publisher = "Hadronic Press",
address = "Palm Harbor, FL, USA",
bookpages = "v + 193",
pages = "17--35",
year = "1998",
ISBN = "1-57485-041-5",
ISBN-13 = "978-1-57485-041-3",
LCCN = "QA297.5 .A685 1998",
MRclass = "33C20; 41-06 (00B15)",
MRnumber = "MR1924838 (2003i:33006); MR1924835 (2003c:41003)",
bibdate = "Thu Dec 01 10:08:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/42786578.html",
acknowledgement = ack-nhfb,
remark = "The paper treats $_{p + 1F}_p(z)$ for $ z \approx 1 $.
Available as arxiv:math/0102032.",
}
@Article{Carsky:1998:IGF,
author = "Petr C{\'a}rsky and Martin Pol{\'a}sek",
title = "Incomplete Gamma {$ F_m(x) $} Functions for Real
Negative and Complex Arguments",
journal = j-J-COMPUT-PHYS,
volume = "143",
number = "1",
pages = "259--265",
day = "10",
month = jun,
year = "1998",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1998.5975",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999198959757",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Cornea-Hasegan:1998:PIC,
author = "Marius Cornea-Hasegan",
title = "Proving the {IEEE} Correctness of Iterative
Floating-Point Square Root, Divide, and Remainder
Algorithms",
journal = j-INTEL-TECH-J,
volume = "Q2",
number = "Q2",
pages = "11",
year = "1998",
ISSN = "1535-766X",
bibdate = "Fri Jun 01 06:02:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://developer.intel.com/technology/itj/q21998/articles/art_3.htm;
http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf",
acknowledgement = ack-nhfb,
}
@Article{Crenshaw:1998:ISR,
author = "Jack W. Crenshaw",
title = "Integer Square Roots",
journal = j-EMBED-SYS-PROG,
volume = "11",
number = "2",
pages = "15--32",
month = feb,
year = "1998",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Fri Nov 28 16:31:58 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.embedded.com/98/9802fe2.htm",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Embedded Systems Programming",
}
@Article{Dattoli:1998:GBF,
author = "G. Dattoli and A. Torre and S. Lorenzutta and G.
Maino",
title = "Generalized {Bessel} functions and {Kapteyn} series",
journal = j-COMPUT-MATH-APPL,
volume = "35",
number = "8",
pages = "117--125",
month = apr,
year = "1998",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:48 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122198000509",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Deleglise:1998:C,
author = "Marc Del{\'e}glise and Jo{\"e}l Rivat",
title = "Computing $ \psi (x) $",
journal = j-MATH-COMPUT,
volume = "67",
number = "224",
pages = "1691--1696",
month = oct,
year = "1998",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y35 (11N56)",
MRnumber = "1 474 649",
bibdate = "Fri Jul 16 10:38:58 MDT 1999",
bibsource = "http://www.ams.org/mcom/1998-67-224;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fowler:1998:SRA,
author = "David Fowler and Eleanor Robson",
title = "Square Root Approximations in Old {Babylonian}
Mathematics: {YBC 7289} in Context",
journal = j-HIST-MATH,
volume = "25",
number = "4",
pages = "366--378",
month = nov,
year = "1998",
CODEN = "HIMADS",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Jun 26 06:19:31 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086098922091",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860",
}
@InProceedings{Gautschi:1998:IGF,
author = "Walter Gautschi",
title = "The incomplete gamma functions since {Tricomi}",
crossref = "Anonymous:1998:TIC",
pages = "203--237",
year = "1998",
bibdate = "Fri May 31 16:38:24 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://web.archive.org/web/20070503103643/http://citeseer.ist.psu.edu/gautschi98incomplete.html",
acknowledgement = ack-nhfb,
}
@Article{Giordano:1998:UTG,
author = "C. Giordano and A. Laforgia and J. Pecari{\'c}",
title = "Unified treatment of {Gautschi--Kershaw} type
inequalities for the gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "99",
number = "1--2",
pages = "167--175",
day = "16",
month = nov,
year = "1998",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:36:13 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704279800154X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Harris:1998:MAL,
author = "Frank E. Harris",
title = "More About the Leaky Aquifer Function",
journal = j-IJQC,
volume = "70",
number = "4--5",
pages = "623--626",
month = "????",
year = "1998",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/(SICI)1097-461X(1998)70:4/5<623::AID-QUA8>3.0.CO%3B2-X",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Tue Oct 4 06:59:18 MDT 2011",
bibsource = "http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ijqc.bib;
https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=75040;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=75040&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Quantum Chem.",
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
onlinedate = "7 Dec 1998",
}
@Article{Homeier:1998:AHC,
author = "Herbert H. H. Homeier",
title = "An asymptotically hierarchy-consistent, iterative
sequence transformation for convergence acceleration of
{Fourier} series",
journal = j-NUMER-ALGORITHMS,
volume = "18",
number = "1",
pages = "1--30",
month = sep,
year = "1998",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Sep 29 08:36:54 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/fulltext.pdf;
http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA972",
ZMnumber = "914.65140",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "convergence acceleration",
tech = "Technical Report TC-NA-97-2, Institut f{\"u}r
{Physikalische} und {Theoretische Chemie,
Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}
@Article{Homeier:1998:CAM,
author = "H. H. H. Homeier",
title = "On Convergence Acceleration of Multipolar and
Orthogonal Expansions",
journal = j-INTERNET-J-CHEM,
volume = "1",
number = "Article 28",
pages = "????",
year = "1998",
CODEN = "IJCHFJ",
ISSN = "1099-8292",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the {4$^{th}$ Electronic Computational
Chemistry Conference}.",
URL = "http://www.ijc.com/articles/1998v1/28/",
fjournal = "Internet Journal of Chemistry",
keywords = "convergence acceleration",
tech = "Technical Report TC-QM-97-5, Institut f{\"u}r
{Physikalische} und {Theoretische Chemie,
Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}
@Article{Jukic:1998:DTN,
author = "D. Juki{\'c} and T. Maros{\v{s}}evi{\'c} and R.
Scitovski",
title = "Discrete total $ l_p $-norm approximation problem for
the exponential function",
journal = j-APPL-MATH-COMP,
volume = "94",
number = "2--3",
pages = "137--143",
day = "15",
month = aug,
year = "1998",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(97)10068-6",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Nov 20 21:03:11 MST 2012",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300397100686",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Kiranon:1998:SRV,
author = "W. Kiranon and N. Kumprasert",
title = "Square-rooting and vector summation circuits using
current conveyors",
journal = "IEE Proceedings on Circuits, Devices and Systems [see
also IEE Proceedings G - Circuits, Devices and
Systems]",
volume = "145",
number = "2",
pages = "139",
month = apr,
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Recently, Lui [1995] presented a square-rooting
circuit using CCII, MOS transistors and a buffered
unity-gain inverting amplifier. It is interesting since
it finds various applications as described in his
paper. However, an error occurred in the \ldots{}",
}
@InBook{Knuth:1998:EP,
author = "Donald E. Knuth",
title = "Evaluation of polynomials",
crossref = "Knuth:1998:SA",
chapter = "4",
pages = "485--524",
year = "1998",
bibdate = "Fri Oct 20 11:29:58 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "number of multiplications to evaluate a polynomial",
remark = "This is the definitive treatment of the rearrangement
of polynomial coefficients to reduce the multiplication
count. See \cite{Todd:1955:MWN} and references therein
to early papers on the subject.",
}
@Article{Kramer:1998:PWC,
author = "W. Kramer",
title = "A priori worst case error bounds for floating-point
computations",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "7",
pages = "750--756",
month = jul,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.709374",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See \cite{Tang:1992:TDI}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
abstract = "A new technique for the a priori calculation of
rigorous error bounds for floating-point computations
is introduced. The theorems given in the paper combined
with interval arithmetic lead to the implementation of
reliable software routines, which enable the user to
compute the desired error bounds automatically by a
suitable computer program. As a prominent example, a
table-lookup algorithm for calculating the function $ e
x p(x) - 1 $ that has been published by P. T. P. Tang
(1992) is analyzed using these new tools. The result
shows the high quality of the new approach",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
author-dates = "1952--2014 (WK)",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kravanja:1998:ZMS,
author = "P. Kravanja and O. Ragos and M. N. Vrahatis and F. A.
Zafiropoulos",
title = "{ZEBEC}: a mathematical software package for computing
simple zeros of {Bessel} functions of real order and
complex argument",
journal = j-COMP-PHYS-COMM,
volume = "113",
number = "2--3",
pages = "220--238",
month = oct,
year = "1998",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(98)00064-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:30 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465598000642",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Kuhlmann:1998:FLP,
author = "M. Kuhlmann and K. K. Parhi",
booktitle = "{Proceedings of the 1998 International Conference on
Computer Design: VLSI in Computers and Processors. ICCD
'98}",
title = "Fast low-power shared division and square-root
architecture",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "128--135",
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This paper addresses a fast low-power implementation
of a shared division and square-root architecture. Two
approaches are considered in this paper; these include
the SRT (Sweeney, Robertson and Tocher) approach which
does not require prescaling and \ldots{}",
}
@Article{Lefevre:1998:TCR,
author = "V. Lef{\`e}vre and J.-M. Muller and A. Tisserand",
title = "Toward correctly rounded transcendentals",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "11",
pages = "1235--1243",
month = nov,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.736435",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "The Table Maker's Dilemma is the problem of always
getting correctly rounded results when computing the
elementary functions. After a brief presentation of
this problem, we present new developments that have
helped us to solve this problem for the \ldots{}",
}
@Article{Lopez:1998:SSC,
author = "Jos{\'e}L. L{\'o}pez",
title = "Several series containing gamma and polygamma
functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "90",
number = "1",
pages = "15--23",
day = "6",
month = apr,
year = "1998",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:36:07 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042798000077",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Miller:1998:CGI,
author = "Allen R. Miller and Ira S. Moskowitz",
title = "On certain generalized incomplete gamma functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "91",
number = "2",
pages = "179--190",
day = "4",
month = may,
year = "1998",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:36:08 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042798000314",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Morozov:1998:NWR,
author = "D. Kh. Morozov and V. V. Voitsekhovich",
title = "A new wide-range approximation of modified {Bessel}
functions in terms of elementary functions",
journal = "Rev. Mexicana F\'\i s.",
volume = "44",
number = "3",
pages = "231--234",
year = "1998",
CODEN = "RMXFAT",
ISSN = "0035-001X",
MRclass = "65D20",
MRnumber = "MR1629601",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Revista Mexicana de F\'\i sica",
}
@Article{Nguyen:1998:MLS,
author = "Phong Nguyen",
title = "A {Montgomery}-Like Square Root for the Number Field
Sieve",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1423",
pages = "151--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:52:18 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Palumbo:1998:GSI,
author = "Biagio Palumbo",
title = "A generalization of some inequalities for the gamma
function",
journal = j-J-COMPUT-APPL-MATH,
volume = "88",
number = "2",
pages = "255--268",
day = "2",
month = mar,
year = "1998",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:36:06 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042797001878",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Qiu:1998:SIG,
author = "S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen",
title = "Some Inequalities for the Growth of Elliptic
Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "29",
number = "5",
pages = "1224--1237",
month = sep,
year = "1998",
CODEN = "SJMAAH",
DOI = "https://doi.org/10.1137/S0036141096310491",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sat Dec 5 14:39:16 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/29/5;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31049",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Rivolo:1998:CDR,
author = "M. T. Rivolo and A. Simi",
title = "Il Calcolo delle Radici Quadrate e Cubiche in {Italia}
da {Fibonacci} a {Bombelli}. ({Italian}) [{The}
calculation of square and cube roots in {Italy} from
{Fibonacci} to {Bombelli}]",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "52",
number = "2",
pages = "161--193",
month = feb,
year = "1998",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/s004070050015",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A35 (01A40)",
MRnumber = "1610136 (99d:01015)",
MRreviewer = "Massimo Galuzzi",
bibdate = "Fri Feb 4 21:50:33 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2;
https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
language = "Italian",
MRtitle = "The computation of square and cube roots in {Italy}
from {Fibonacci} to {Bombelli}",
}
@Article{Russinoff:1998:MCP,
author = "David M. Russinoff",
title = "A Mechanically Checked Proof of {IEEE} Compliance of
the Floating Point Multiplication, Division and Square
Root Algorithms of the {AMD-K7} Processor",
journal = j-LMS-J-COMPUT-MATH,
volume = "1",
pages = "148--200",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1112/S1461157000000176",
ISSN = "1461-1570",
ISSN-L = "1461-1570",
MRclass = "68M07 (65Y99 68T15)",
MRnumber = "99m:68015",
MRreviewer = "J. Michel Muller",
bibdate = "Fri Nov 29 08:13:48 2002",
bibsource = "http://journals.cambridge.org/action/displayJournal?jid=JCM;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
note = "Appendices A and B available to subscribers
electronically
(http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and
http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)",
URL = "http://www.lms.ac.uk/jcm/1/lms1998-001/",
acknowledgement = ack-nhfb,
ajournal = "LMS J. Comput. Math.",
fjournal = "LMS Journal of Computation and Mathematics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=JCM",
onlinedate = "01 February 2010",
}
@Article{Segura:1998:PCF,
author = "J. Segura and A. Gil",
title = "Parabolic cylinder functions of integer and
half-integer orders for nonnegative arguments",
journal = j-COMP-PHYS-COMM,
volume = "115",
number = "1",
pages = "69--86",
day = "1",
month = dec,
year = "1998",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(98)00097-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:32 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465598000976",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Sidi:1998:UBC,
author = "Avram Sidi and Yair Shapira",
title = "Upper bounds for convergence rates of acceleration
methods with initial iterations",
journal = j-NUMER-ALGORITHMS,
volume = "18",
number = "2",
pages = "113--132",
month = sep,
year = "1998",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Sep 29 08:36:55 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "convergence acceleration",
}
@Article{Wei:1998:NFS,
author = "Liqiang Wei",
title = "New formula for $9$--$j$ symbols and their direct
calculation",
journal = j-COMPUT-PHYS,
volume = "12",
number = "6",
pages = "632--??",
month = nov,
year = "1998",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.168745",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:46:17 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.168745",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@InProceedings{Agarwal:1999:SAM,
author = "R. C. Agarwal and F. G. Gustavson and M. S.
Schmookler",
title = "Series approximation methods for divide and square
root in the {Power3{\TM}} processor",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "116--123",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-144.pdf;
http://euler.ecs.umass.edu/paper/final/paper-144.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
summary = "The Power3 processor is a 64-bit implementation of the
PowerPC TM architecture and is the successor to the
Power2 TM processor for workstations and servers which
REQUIRE high performance floating point capability. The
previous \ldots{}",
}
@Article{Alzer:1999:SPP,
author = "Horst Alzer and O. G. Ruehr",
title = "A submultiplicative property of the psi function",
journal = j-J-COMPUT-APPL-MATH,
volume = "101",
number = "1--2",
pages = "53--60",
day = "15",
month = jan,
year = "1999",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:39:42 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042798001903",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Book{Andrews:1999:SF,
author = "George E. Andrews and Richard Askey and Ranjan Roy",
title = "Special Functions",
volume = "71",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvi + 664",
year = "1999",
DOI = "https://doi.org/10.1017/CBO9781107325937",
ISBN = "0-521-62321-9 (hardcover), 0-521-78988-5 (paperback),
1-107-32593-5 (e-book)",
ISBN-13 = "978-0-521-62321-6 (hardcover), 978-0-521-78988-2
(paperback), 978-1-107-32593-7 (e-book)",
LCCN = "QA351 .A74 1999",
bibdate = "Mon Sep 17 18:52:30 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$90.00 (hardcover), US\$34.95 (paperback)",
series = "Encyclopedia of mathematics and its applications",
acknowledgement = ack-nhfb,
subject = "Functions, Special",
tableofcontents = "Frontmatter / i--vi \\
Contents / vii--xii \\
Preface / xiii--xvi \\
1: The Gamma and Beta Functions / 1--60 \\
2: The Hypergeometric Functions / 61--123 \\
3: Hypergeometric Transformations and Identities /
124--186 \\
4: Bessel Functions and Confluent Hypergeometric
Functions / 187--239 \\
5: Orthogonal Polynomials / 240--276 \\
6: Special Orthogonal Polynomials / 277--354 \\
7: Topics in Orthogonal Polynomials / 355--400 \\
8: The Selberg Integral and Its Applications / 401--444
\\
9: Spherical Harmonics / 445--480 \\
10: Introduction to $q$-Series / 481--552 \\
11: Partitions / 553--576 \\
12: Bailey Chains / 577--594 \\
A: Infinite Products / 595--598 \\
B: Summability and Fractional Integration / 599--610
\\
C: Asymptotic Expansions / 611--616 \\
D: Euler--Maclaurin Summation Formula / 617--628 \\
E: Lagrange Inversion Formula / 629--636 \\
F: Series Solutions of Differential Equations /
637--640 \\
Bibliography / 641--654 \\
Index / 655--658 \\
Subject Index / 659--662 \\
Symbol Index / 663--664",
xxURL = "http://www.loc.gov/catdir/toc/cam024/98025757.html;
http://www.loc.gov/catdir/description/cam029/98025757.html",
}
@Article{Bach:1999:NTS,
author = "E. Bach and K. Huber",
title = "Note on taking square-roots modulo {$N$}",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "45",
number = "2",
pages = "807--809",
month = mar,
year = "1999",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/18.749034",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
summary = "In this article it is shown how Gauss' (1981) famous
cyclotomic sum formula can be used for extracting
square-roots modulo \ldots{}",
}
@InProceedings{Batten:1999:IBO,
author = "D. Batten and S. Jinturkar and J. Glossner and M.
Schulte and R. Peri and P. D'arcy",
editor = "????",
booktitle = "Proceedings of the International Conference on Signal
Processing Applications and Technologies, Orlando,
Florida, November, 1999",
title = "Interactions Between Optimizations and a New Type of
{DSP} Intrinsic Function",
publisher = "????",
address = "????",
year = "1999",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 04 11:05:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Shortened version in \cite{Batten:1999:IFB}.",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf",
acknowledgement = ack-nhfb,
}
@Article{Batten:1999:IFB,
author = "D. Batten and P. D'arcy",
title = "Intrinsic Functions Boost Compilers",
journal = "Electrical Engineering Times",
volume = "1085",
pages = "104--104",
month = nov,
year = "1999",
bibdate = "Sun Mar 04 11:06:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Beebe:1999:FAE,
author = "Nelson H. F. Beebe",
title = "Fast Approximate Exponential Functions",
type = "Report",
institution = inst-CSC,
address = inst-CSC:adr,
day = "7",
month = dec,
year = "1999",
bibdate = "Sat Feb 02 15:08:59 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This package contains software conforming to 1989
ANSI/ISO Standard C (ANSI X3.159-1989, ISO/IEC
9899-1990) and 1998 ISO Standard C++ (ISO/IEC
14882:1998) for testing an interesting algorithm for
fast approximate exp() functions, published in
\cite{Schraudolph:1999:FCA}. There is a font error in
figure 2 of that paper: all carets should be replaced
by underscore.",
acknowledgement = ack-nhfb,
remark = "From the report: ``Schraudolph's formula for the
approximate exponential function computes $ a \times x
+ b - c $ in floating-point arithmetic, then converts
it to a 32-bit integer which is stored in the
appropriate integer word overlaying the floating-point
representation. The entire cost is thus a
floating-point multiply and add (one instruction on
some RISC architectures), a conversion to an integer,
and a storage to memory.''",
}
@InCollection{Brezinski:1999:EEC,
author = "C. Brezinski",
booktitle = "Error control and adaptivity in scientific computing
({Antalya}, 1998)",
title = "Error estimates and convergence acceleration",
volume = "536",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "87--94",
year = "1999",
MRclass = "65B05 (65D15)",
MRnumber = "1735125",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "NATO Sci. Ser. C Math. Phys. Sci.",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@InProceedings{Bui:1999:DSI,
author = "H. Bui and S. Tahar",
booktitle = "1999 {IEEE} Canadian Conference on Electrical and
Computer Engineering, 9--12 May 1999",
title = "Design and synthesis of an {IEEE-754} exponential
function",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "450--455",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 17:14:11 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We have designed a floating-point exponential function
using the table-driven method. The algorithm was first
implemented using sequential VHDL and later translated
to Concurrent Verilog. The main part of the work
consisted of creating modules that \ldots{}",
}
@Article{Cappuccino:1999:HSS,
author = "G. Cappuccino and G. Cocorullo and P. Corsonello and
S. Perri",
title = "High speed self-timed pipelined datapath for square
rooting",
journal = "IEE Proceedings on Circuits, Devices and Systems [see
also IEE Proceedings G --- Circuits, Devices and
Systems]",
volume = "146",
number = "1",
pages = "16--22",
month = feb,
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The authors describe a new high-performance self-timed
circuit for asynchronous square rooting. The new
architecture is based on a modified nonrestoring
algorithm. An asynchronous pipelined cellular array
without auxiliary system for the \ldots{}",
}
@Article{Carlson:1999:TSI,
author = "B. C. Carlson",
title = "Toward Symbolic Integration of Elliptic Integrals",
journal = j-J-SYMBOLIC-COMP,
volume = "28",
number = "6",
pages = "739--753",
month = dec,
year = "1999",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1006/jsco.1999.0336",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Tue Mar 7 11:48:04 MST 2000",
bibsource = "http://www.idealibrary.com/cgi-bin/links/toc/sy;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production;
http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/pdf;
http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/ref",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
}
@InProceedings{Cornea-Hasegan:1999:CPO,
author = "M. A. Cornea-Hasegan and R. A. Golliver and P.
Markstein",
title = "Correctness proofs outline for {Newton--Raphson} based
floating-point divide and square root algorithms",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "96--105",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-121.pdf;
http://euler.ecs.umass.edu/paper/final/paper-121.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
summary = "This paper describes a study of a class of algorithms
for the floating-point divide and square root
operations, based on the Newton--Raphson iterative
method. The two main goals were. (1) Proving the IEEE
correctness of these iterative floating-point
\ldots{}",
}
@Article{Corsonello:1999:HPS,
author = "P. Corsonello and S. Perri",
title = "High performance square rooting circuit using hybrid
radix-$2$ adders",
journal = j-ELECT-LETTERS,
volume = "35",
number = "3",
pages = "185--186",
day = "4",
month = feb,
year = "1999",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "A new high performance bit parallel architecture for
computing square roots is proposed. The architecture
implements a non-restoring algorithm and is structured
as a pipelined cellular array. To improve the
performance, hybrid radix-$2$ adders are \ldots{}",
}
@TechReport{DiDonato:1999:TFC,
author = "Armido R. DiDonato and Russ Gnoffo",
title = "Testing a {Fortran 90} Compiler Using the {NSWC
Fortran 77 Mathematics Library}",
type = "Technical Report",
number = "NSWCDD/TR-98/75",
institution = "Naval Surface Warfare Center",
address = "Dahlgren, VA 22448-5100, USA",
pages = "v + 64",
month = feb,
year = "1999",
bibdate = "Tue Jun 13 11:49:57 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
URL = "https://apps.dtic.mil/sti/pdfs/ADA360604.pdf",
abstract = "This report describes the analysis and associated
Fortran program (TEST90) that were developed to aid in
establishing the validity of a new Fortran 90 mainframe
compiler. The FORTRAN 77 Naval Surface Warfare Center
(NSWC) Mathematics library (MLJB) is used as a source
of routines for checking the Fortran 90 compiler. At
the same time, this study can be considered as an aid
to determine whether MLIB can operate in a Fortran 90
environment. The inputs for the routines were chosen so
that many of the different possible paths of the
routines were executed. Seventy-four directly callable
routines, with 293 supporting routines, were chosen for
testing. All but 17, and their supporting routines,
were taken from MLIB. The ones not belonging to MLIB,
are double-precision versions of routines in MLIB.
Thirteen hundred and twenty five numerical cases were
submitted for testing. A true value for each test was
obtained independently and given correctly to 35 digits
by using MAPLE software. If the difference in the test
output and the corresponding true value exceeds a
prespecified error tolerance, an error message is
printed identifying the routine and the input
Additional test cases were also prepared to check the
bit and string instructions, since these do not appear
in MLIB.\par
TEST90 has been used to test the latest Fortran 90
compilers of the CRAY EL98 and IBM PC machines. No
errors were found; however, TEST90 did reveal a complex
arithmetic error in an earlier version of the Cray EL98
compiler. MLIB routines ran under TEST90 without any
problems on both machines.\par
The transportability of MLIB allows TEST90 to be used
as an aid in testing Fortran 90 compilers on a variety
of computers, with a single-precision word length no
larger than 64 bits.",
acknowledgement = ack-nhfb,
}
@Article{Elbert:1999:SFZ,
author = "{\'A}rp{\'a}d Elbert and Panayiotis D. Siafarikas",
title = "On the Square of the First Zero of the {Bessel}
Function {$ J_\nu (z) $}",
journal = j-CAN-MATH-BULL,
volume = "42",
number = "1",
pages = "56--77",
month = mar,
year = "1999",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1999-007-4",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "33A40",
bibdate = "Thu Sep 8 10:22:25 MDT 2011",
bibsource = "http://cms.math.ca/cmb/v42/;
https://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Let $ j_{\nu, 1} $ be the smallest (first) positive
zero of the Bessel function $ J_{\nu }(z) $, $ \nu > -
1 $, which becomes zero when $ \nu $ approaches $ - 1
$. Then $ j_{\nu, 1}^2 $ can be continued analytically
to $ - 2 < \nu < - 1 $, where it takes on negative
values. We show that $ j_{\nu, 1}^2 $ is a convex
function of $ \nu $ in the interval $ - 2 < \nu \leq 0
$, as an addition to an old result [{\'A}. Elbert and
A. Laforgia, SIAM J. Math. Anal. {\bf 15}(1984),
206--212], stating this convexity for $ \nu > 0 $. Also
the monotonicity properties of the functions $ \frac
{j_{\nu, 1}^24 (\nu + 1)} $, $ \frac {j_{\nu, 1}^24(\nu
+ 1) \sqrt {\nu + 2}} $ are determined. Our approach is
based on the series expansion of Bessel function $
J_{\nu }(z) $ and it turned out to be effective,
especially when $ - 2 < \nu < - 1 $.",
acknowledgement = ack-nhfb,
ams-subject-primary = "33A40",
fjournal = "Canadian mathematical bulletin = Bulletin canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
journalabbrev = "CMB",
refnum = "7139",
xxpages = "56--67",
}
@TechReport{Ercegovac:1999:IGD,
author = "Milo{\v{s}} D. Ercegovac and Laurent Imbert and David
W. Matula and Jean-Michel Muller and Guoheng Wei",
title = "Improving {Goldschmidt} Division, Square Root, and
Square Root Reciprocal",
type = "Research Report",
number = "99-41",
institution = "Laboratoire de l'Informatique du Parall{\'e}lisme",
address = "Lyon, France",
pages = "ii + 17",
month = sep,
year = "1999",
bibdate = "Mon Dec 11 07:53:15 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/inria-00072909/file/RR1999-41.pdf",
abstract = "The aim of this paper is to accelerate division,
square root and square root reciprocal computations,
when Goldschmidt method is used on a pipelined
multiplier. This is done by replacing the last
iteration by the addition of a correcting term that can
be looked up during the early iterations. We describe
several variants of the Goldschmidt algorithm assuming
4-cycle pipelined multiplier and discuss obtained
number of cycles and error achieved. Extensions to
other than 4-cycle multipliers are given",
acknowledgement = ack-nhfb,
keywords = "Computer Arithmetic; Convergence division; Division;
Goldschmidt iteration; Square root; Square root
reciprocal",
}
@Article{Fabijonas:1999:RAE,
author = "Bruce R. Fabijonas and F. W. J. Olver",
title = "On the Reversion of an Asymptotic Expansion and the
Zeros of the {Airy} Functions",
journal = j-SIAM-REVIEW,
volume = "41",
number = "4",
pages = "762--773",
month = dec,
year = "1999",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144598349538",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "http://epubs.siam.org/toc/siread/41/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/34953",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "Dec-1999",
}
@Article{Fuller:1999:HVH,
author = "A. Thomas Fuller",
title = "{Horner} versus {Holdred}: an Episode in the History
of Root Computation",
journal = j-HIST-MATH,
volume = "26",
number = "1",
pages = "29--51",
day = "1",
month = feb,
year = "1999",
CODEN = "HIMADS",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Jun 26 06:19:37 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086098922145",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860",
}
@Article{Gautschi:1999:NRC,
author = "Walter Gautschi",
title = "A Note on the Recursive Calculation of Incomplete
Gamma Functions",
journal = j-TOMS,
volume = "25",
number = "1",
pages = "101--107",
month = mar,
year = "1999",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Jul 15 19:01:02 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://doi.acm.org/10.1145/305658.305717;
http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gautschi:1999:NRC;
http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/",
abstract = "It is known that the recurrence relation for
incomplete gamma functions $ \Gamma (a + n, x), 0 \le a
< 1 $, $ n = 0, 1, 2 \ldots $, when $x$ is positive, is
unstable---more so the larger $x$. Nevertheless, the
recursion can be used in the range $ 0 \le n \le x $
practically without error growth, and in larger ranges
$ 0 \le n \le N $ with a loss of accuracy that can be
controlled by suitably limiting $N$.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; reliability",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Stability (and instability). {\bf
G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation.",
}
@TechReport{Gourdon:1999:NCC,
author = "Xavier Gourdon and Pascal Sebah",
title = "Numbers, constants, and computation",
institution = "????",
address = "Paris, France",
year = "1999",
bibdate = "Sat Mar 15 16:28:07 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "World-Wide Web site.",
URL = "http://numbers.computation.free.fr/Constants/home.html",
acknowledgement = ack-nhfb,
annote = "Although this site concentrates mainly on computation
of particular mathematical constants, it also treats
high-precision computation of inverse and square
root.",
}
@Article{Harrison:1999:CTF,
author = "John Harrison and Ted Kubaska and Shane Story and Ping
Tak Peter Tang",
title = "The Computation of Transcendental Functions on the
{IA-64} Architecture",
journal = j-INTEL-TECH-J,
number = "Q4",
pages = "7",
day = "22",
month = nov,
year = "1999",
bibdate = "Fri Jun 01 06:02:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://developer.intel.com/technology/itj/q41999/articles/art_5.htm;
http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf",
acknowledgement = ack-nhfb,
}
@Article{Hayashi:1999:SRR,
author = "Takao Hayashi",
title = "A set of rules for the root-extraction prescribed by
the sixteenth-century {Indian} mathematicians,
{N{\=\i}laka{\d{n}}{\d{t}}ha Somastuvan} and
{{\'S}a{\.n}kara V{\=a}riyar}",
journal = j-HIST-SCI-2,
volume = "9",
number = "2",
pages = "135--153",
month = nov,
year = "1999",
CODEN = "HISCDU",
ISSN = "0285-4821",
ISSN-L = "0285-4821",
MRclass = "01A32",
MRnumber = "1762168",
MRreviewer = "A. I. Volodarski{\u\i}",
bibdate = "Sat Oct 6 17:22:25 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/histscijpn.bib",
acknowledgement = ack-nhfb,
fjournal = "Historia Scientiarum. Second Series. International
Journal of the History of Science Society of Japan",
journal-URL = "http://hssj.info/",
}
@Article{Homeier:1999:CAL,
author = "H. H. H. Homeier",
title = "Convergence acceleration of logarithmically convergent
series avoiding summation",
journal = j-APPL-MATH-LETT,
volume = "12",
number = "3",
pages = "29--32",
year = "1999",
CODEN = "AMLEEL",
DOI = "https://doi.org/10.1016/S0893-9659(98)00167-0",
ISSN = "0893-9659 (print), 1873-5452 (electronic)",
ISSN-L = "0893-9659",
MRclass = "65B05",
MRnumber = "1749733",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/08939659",
keywords = "convergence acceleration",
}
@InProceedings{Hyogo:1999:LVF,
author = "A. Hyogo and Y. Fukutomi and K. Sekine",
booktitle = "Proceedings of the 1999 {IEEE} International Symposium
on Circuits and Systems: {ISCAS '99}, 2 June 1999",
title = "Low voltage four-quadrant analog multiplier using
square-root circuit based on {CMOS} pair",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "274--277",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We proposed a square-root circuit based on CMOS pairs.
In this paper, we propose a low voltage four-quadrant
analog multiplier using the square-root circuit. Also
we confirmed this operation by PSpice \ldots{}",
}
@Article{Iordache:1999:ARS,
author = "Cristina Iordache and David W. Matula",
title = "Analysis of Reciprocal and Square Root Reciprocal
Instructions in the {AMD K6-2} Implementation of
{3DNow!}",
journal = j-ELECT-NOTES-THEOR-COMP-SCI,
volume = "24",
pages = "34--62",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1016/S1571-0661(05)80621-8",
ISSN = "1571-0661",
bibdate = "Fri Jun 24 20:23:13 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Reciprocal and root reciprocal functions at ``half''
and IEEE single precision formats are specified in the
AMD 3DNow! instruction set. Implementations in the
recently released AMD K6-2 microprocessor are analyzed
herein by exhaustive computation and timing loops to
ascertain the accuracy and monotonicity properties of
the output and throughput\slash latency cycle counts.
Periodicities in stepwise function output were observed
and employed to construct an underlying bipartite table
that can serve as the core of the respective reciprocal
function outputs. The recommended RISC instruction
macros generated single precision reciprocals and root
reciprocals accurate to a unit in the last place.
However, the root reciprocal functions failed to
satisfy the desirable monotonicity property typically
implemented as an industry standard for elementary
functions on x86 floating point units. Reasons for the
failure are provided and an adjusted table is shown to
satisfy the monotonicity standard. Results are
summarized in Table 1 and described in the body of this
report.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Notes in Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/15710661",
}
@InProceedings{Iordache:1999:IPR,
author = "Cristina Iordache and David W. Matula",
title = "On Infinitely Precise Rounding for Division, Square
Root, Reciprocal and Square Root Reciprocal",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "233--240",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-164.pdf;
http://euler.ecs.umass.edu/paper/final/paper-164.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Iordache.pdf",
abstract = "Quotients, reciprocals, square roots and square root
reciprocals all have the property that infinitely
precise p-bit rounded results for p-bit input operands
can be obtained from approximate results of bounded
accuracy. We investigate lower bounds on the number of
bits of an approximation accurate to a unit in the last
place sufficient to guarantee that correct round and
sticky bits can be determined. Known lower bounds for
quotients and square roots are given and/or sharpened,
and a new lower bound for root reciprocals is proved.
Specifically for reciprocals, quotients and square
roots, tight bounds of order $ 2 p + O(1) $ are
presented. For infinitely precise rounding of the root
reciprocal a lower bound can be found at $ 3 p + O(1)
$, but exhaustive testing for small sizes of the
operand suggests that in practice $ (2 + \epsilon)p $
for small $ \epsilon $ is usually sufficient.
Algorithms can be designed for obtaining the round and
sticky bits based on the bit pattern of an
approximation computed to the required accuracy. We
show that some improvement of the known lower bound for
reciprocals and division is achievable at the cost of
somewhat more complex hardware for rounding. Tests for
the exactness of the quotient and square root are also
provided.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic; IEEE",
summary = "Quotients, reciprocals, square roots and square root
reciprocals all have the property that infinitely
precise p-bit rounded results for p-bit input operands
can be obtained from approximate results of bounded
accuracy. We investigate lower bounds \ldots{}",
}
@Article{Jamieson:1999:NRF,
author = "M. J. Jamieson",
title = "Notes: On rational function approximations to square
roots",
journal = j-AMER-MATH-MONTHLY,
volume = "106",
number = "1",
pages = "50--52",
month = jan,
year = "1999",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11Yxx",
MRnumber = "1 674 202",
bibdate = "Tue Jun 22 10:29:34 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{Jeffreys:1999:MMP,
author = "Harold Jeffreys and Bertha {Swirles Jeffreys}",
title = "Methods of Mathematical Physics",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Third",
pages = "viii + 718",
year = "1999",
ISBN = "0-521-66402-0 (paperback)",
ISBN-13 = "978-0-521-66402-8 (paperback)",
LCCN = "QA401 .J4 1999",
bibdate = "Thu Aug 17 10:48:45 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
note = "Reprint of \cite{Jeffreys:1956:MMP}.",
URL = "https://en.wikipedia.org/wiki/Bertha_Swirles;
https://en.wikipedia.org/wiki/Harold_Jeffreys",
acknowledgement = ack-nhfb,
author-dates = "Sir Harold Jeffreys (22 April 1891--18 March 1989);
Lady Bertha Swirles Jeffreys (22 May 1903--18 December
1999)",
remark = "First edition 1946, second edition 1950, third edition
1956, first paperback edition 1972, reprinted 1978,
1980, 1988, 1992, 1999, 2001. Third edition preface is
dated April 1953. Second edition preface is dated 15
November 1948. First edition preface is dated 1946.",
subject-dates = "Douglas Rayner Hartree (27 March 1897--12 February
1958)",
tableofcontents = "Preface \\
Authors' Notes \\
1: The Real Variable \\
2: Scalars and Vectors \\
3: Tensors \\
4: Matrices \\
5: Multiple Integrals \\
6: Potential Theory \\
7: Operational Methods \\
8: Physical Applications of the Operational Method \\
9: Numerical Methods \\
10: Calculus of Variations \\
11: Functions of a Complex Variable \\
12: Contour Integration and Bromwich's Integral \\
13: Conformal Representation \\
14: Fourier's Theorem \\
15: The Factorial and Related Functions \\
16: Solution of Linear Differential Equation \\
17: Asymptotic Expansions \\
18: The Equations of Potential, Waves, and Heat
Conduction \\
19: Waves in One Dimension and Waves With Spherical
Symmetry \\
20: Conduction of Heat in One and Three Dimensions \\
21: Bessel Functions \\
22: Applications of Bessel Functions \\
23: The Confluent Hypergeometric Function \\
24: Legendre Functions and Associated Functions \\
25: Elliptic Functions \\
Notes \\
Appendix on Notation \\
Index",
}
@Misc{Kahan:1999:SRD,
author = "W. Kahan",
title = "Square Root Without Division",
howpublished = "World-Wide Web document",
pages = "3",
day = "23",
month = feb,
year = "1999",
bibdate = "Mon Apr 25 18:01:49 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf",
acknowledgement = ack-nhfb,
}
@Article{Krukier:1999:CAT,
author = "L. A. Krukier",
title = "Convergence acceleration of triangular iterative
methods based on the skew-symmetric part of the
matrix",
journal = j-APPL-NUM-MATH,
volume = "30",
number = "2--3",
pages = "281--290",
day = "10",
month = jun,
year = "1999",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Wed Jul 28 14:37:31 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=30&issue=2-3;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1999&volume=30&issue=2-3&aid=981",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@Article{Kzaz:1999:CAG,
author = "M. Kzaz",
title = "Convergence acceleration of the {Gauss--Laguerre}
quadrature formula",
journal = j-APPL-NUM-MATH,
volume = "29",
number = "2",
pages = "201--220",
day = "1",
month = feb,
year = "1999",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Wed Jul 28 14:37:22 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=29&issue=2;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/cas/tree/store/apnum/sub/1999/29/2/940.pdf",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@Article{Lang:1999:VHR,
author = "T. Lang and P. Montuschi",
title = "Very high radix square root with prescaling and
rounding and a combined division\slash square root
unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "8",
pages = "827--841",
month = aug,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.795124",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "An algorithm for square root with prescaling and
selection by rounding is developed and combined with a
similar scheme for division. Since division is usually
more frequent than square root, the main concern of the
combined implementation is to \ldots{}",
}
@InProceedings{Lee:1999:STS,
author = "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and
Seung-Ho Hwang",
booktitle = "6th International Conference on {VLSI} and {CAD}:
{ICVC '99}",
title = "Self-timed shared division and square-root
implementation using full redundant signed digit
numbers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "541--544",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A radix-$2$ square root implementation for self-timed
dividers using redundant signed-digit (RSD) adders is
presented. In this method, two self-timed RSD adder
stages are used for each result bit selection. A very
efficient and simple result bit \ldots{}",
}
@InProceedings{Lozier:1999:DDM,
author = "Daniel W. Lozier and B. R. Miller and B. V. Saunders",
title = "Design of a Digital Mathematical Library for Science,
Technology and Education",
crossref = "IEEE:1999:PIF",
pages = "118--128",
year = "1999",
bibdate = "Fri Jul 09 06:33:35 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://dlmf.nist.gov/about/publications/nistir6297.ps.gz",
acknowledgement = ack-nhfb,
remark = "Preprint: NISTIR 6297, Feb. 1999, 13 pages",
}
@Article{Morita:1999:CEI,
author = "T. Morita",
title = "Calculation of the elliptic integrals of the first and
second kinds with complex modulus",
journal = j-NUM-MATH,
volume = "82",
number = "4",
pages = "677--688",
month = jun,
year = "1999",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 10:45:11 MDT 1999",
bibsource = "http://link.springer-ny.com/link/service/journals/00211/tocs/t9082004.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer-ny.com/link/service/journals/00211/bibs/9082004/90820677.htm;
http://link.springer-ny.com/link/service/journals/00211/papers/9082004/90820677.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Muller:1999:CAT,
author = "J. M{\"u}ller",
title = "Convergence acceleration of {Taylor} sections by
convolution",
journal = j-CONST-APPROX,
volume = "15",
number = "4",
pages = "523--536",
year = "1999",
DOI = "https://doi.org/10.1007/s003659900120",
ISSN = "0176-4276 (print), 1432-0940 (electronic)",
ISSN-L = "0176-4276",
MRclass = "41A58 (30E10)",
MRnumber = "1702803 (2000i:41040)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Constructive Approximation",
journal-URL = "http://link.springer.com/journal/365",
keywords = "convergence acceleration",
}
@Article{Muroi:1999:ESR,
author = "Kazuo Muroi",
title = "Extraction of square roots in {Babylonian}
mathematics",
journal = j-HIST-SCI-2,
volume = "9",
number = "2",
pages = "127--133",
month = nov,
year = "1999",
CODEN = "HISCDU",
ISSN = "0285-4821",
ISSN-L = "0285-4821",
MRclass = "01A17",
MRnumber = "1762167",
MRreviewer = "Bruno Poizat",
bibdate = "Sat Oct 6 17:22:25 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/histscijpn.bib",
acknowledgement = ack-nhfb,
fjournal = "Historia Scientiarum. Second Series. International
Journal of the History of Science Society of Japan",
journal-URL = "http://hssj.info/",
}
@InProceedings{Nannarelli:1999:LPR,
author = "A. Nannarelli and T. Lang",
booktitle = "{(ICCD '99)} International Conference on Computer
Design",
title = "Low-power radix-$4$ combined division and square
root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "236--242",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Because of the similarities in the algorithm it is
quite common to implement division and square root in
the same unit. The purpose of this work is to implement
a low-power combined radix-$4$ division and square root
floating-point double precision \ldots{}",
}
@InProceedings{Oberman:1999:FPD,
author = "S. F. Oberman",
title = "Floating point division and square root algorithms and
implementation in the {AMD-K7{\TM}} microprocessor",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "106--115",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-139.pdf;
http://euler.ecs.umass.edu/paper/final/paper-139.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
summary = "This paper presents the AMD-K7 IEEE 754 and $\times$87
compliant floating point division and square root
algorithms and implementation. The AMD-K7 processor
employs an iterative implementation of a series
expansion to converge quadratically to the \ldots{}",
}
@InProceedings{Parhami:1999:ALT,
author = "B. Parhami",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "Analysis of the lookup table size for square-rooting",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1327--1330",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Convergence methods are widely used for division,
reciprocation, and square-rooting. With such methods,
it is common to use an initial table lookup step for
obtaining an approximate result that leads to faster
convergence. In the case of division \ldots{}",
}
@Article{Russinoff:1999:MCP,
author = "David M. Russinoff",
title = "A mechanically checked proof of correctness of the
{AMD K5} floating point square root microcode",
journal = j-FORM-METHODS-SYST-DES,
volume = "14",
number = "1",
pages = "75--125",
month = jan,
year = "1999",
CODEN = "FMSDE6",
ISSN = "0925-9856 (print), 1572-8102 (electronic)",
ISSN-L = "0925-9856",
bibdate = "Sat Jun 02 07:51:51 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Special issue on arithmetic circuits.",
URL = "http://www.wkap.nl/jrnltoc.htm/0925-9856;
http://www.wkap.nl/oasis.htm/194808",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
}
@Article{Schraudolph:1999:FCA,
author = "N. N. Schraudolph",
title = "A Fast, Compact Approximation of the Exponential
Function",
journal = j-NEURAL-COMP,
volume = "11",
number = "4",
pages = "853--862",
day = "1",
month = may,
year = "1999",
CODEN = "NEUCEB",
DOI = "https://doi.org/10.1162/089976699300016467",
ISSN = "0899-7667 (print), 1530-888x (electronic)",
ISSN-L = "0899-7667",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
URL = "https://www.mitpressjournals.org/doi/abs/10.1162/089976699300016467",
acknowledgement = ack-nhfb,
fjournal = "Neural Computation",
journal-URL = "http://www.mitpressjournals.org/loi/neco",
pagecount = "10",
}
@Article{Schulte:1999:AEF,
author = "M. Schulte and J. Stine",
title = "Approximating Elementary Functions with Symmetric
Bipartite Tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "8",
pages = "842--847",
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.795125",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 20:20:58 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Schulte:1999:ESO,
author = "M. J. Schulte and K. E. Wires",
title = "Efficient Second Order Approximations for Reciprocals
and Square Roots",
crossref = "Luk:1999:PSA",
volume = "3807",
pages = "10--18",
year = "1999",
bibdate = "Sun Mar 04 11:10:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1999:HSI,
author = "Michael J. Schulte and Kent E. Wires",
title = "High-Speed Inverse Square Roots",
crossref = "Koren:1999:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "124--131",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-109.pdf;
http://euler.ecs.umass.edu/paper/final/paper-109.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
summary = "Inverse square roots are used in several digital
signal processing, multimedia, and scientific computing
applications. This paper presents a high-speed method
for computing inverse square roots. This method uses a
table lookup, operand modification, \ldots{}",
}
@Article{Segura:1999:EGT,
author = "J. Segura and A. Gil",
title = "{ELF} and {GNOME}: Two tiny codes to evaluate the real
zeros of the {Bessel} functions of the first kind for
real orders",
journal = j-COMP-PHYS-COMM,
volume = "117",
number = "3",
pages = "250--262",
day = "11",
month = mar,
year = "1999",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(98)00193-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:36 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465598001933",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Seidel:1999:HSR,
author = "P.-M. Seidel",
title = "High-speed redundant reciprocal approximation",
journal = j-INTEGRATION-VLSI-J,
volume = "28",
number = "1",
pages = "1--12",
month = sep,
year = "1999",
CODEN = "IVJODL",
ISSN = "0167-9260 (print), 1872-7522 (electronic)",
ISSN-L = "0167-9260",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Integration, the VLSI journal",
pagecount = "12",
}
@Article{Stine:1999:STA,
author = "E. Stine and M. J. Schulte",
title = "The Symmetric Table Addition Method for Accurate
Function Approximation",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "21",
number = "2",
pages = "167--177",
month = jun,
year = "1999",
CODEN = "JVSPED",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sun Mar 04 11:02:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Story:1999:NAI,
author = "S. Story and P. T. P. Tang",
title = "New Algorithms for Improved Transcendental Functions
on {IA-64}",
crossref = "Koren:1999:ISC",
pages = "4--11",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-118.pdf;
http://euler.ecs.umass.edu/paper/final/paper-118.ps",
acknowledgement = ack-nhfb,
keywords = "ARITH; computer arithmetic; IEEE",
}
@Book{Suetin:1999:OPT,
author = "P. K. (Pavel Kondratevich) Suetin",
title = "Orthogonal Polynomials in Two Variables",
volume = "3",
publisher = "Gordon and Breach Science Publishers",
address = "Amsterdam, The Netherlands",
pages = "xx + 348",
year = "1999",
ISBN = "90-5699-167-1",
ISBN-13 = "978-90-5699-167-8",
LCCN = "QA404.5 .S8813 1999",
bibdate = "Sat Oct 30 17:21:54 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Translated from the Russian by E. V. Pankratiev.",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
remark = "Originally published in Russian in 1988 by Nauka,
Moscow.",
subject = "Orthogonal polynomials",
tableofcontents = "Preface / ix \\
Preface to the English Edition / xv \\
Notation / xix \\
I. General properties of polynomials orthogonal over a
domain / 1 \\
1. Polynomials in two variables orthogonal over a
domain / 1 \\
2. The existence theorem and criteria of orthogonality
/ 6 \\
3. Algebraic properties / 10 \\
4. Monic orthogonal polynomials / 18 \\
5. Normal biorthogonal Systems / 24 \\
6. Fourier series of orthogonal polynomials in two
variables / 28 \\
7. Fourier series for differentiable functions / 31 \\
II. Some typical examples and special cases of
orthogonality over a domain / 37 \\
1. Different products of classical orthogonal
polynomials / 37 \\
2. Various cases of connection between orthogonality
over a domain and orthogonality on an interval / 42 \\
3. Some theorems in the case of a weight function with
separating variables / 48 \\
4. Conditions of interconnection between the weight
function and the domain of orthogonality / 52 \\
5. Examples of computations of weight function moments
/ 57 \\
III. Classical Appell's orthogonal polynomials / 63 \\
1. Rodrigues formula for Appell's polynomials / 63 \\
2. Representation of the Appell polynomials via the
hypergeometric function of two variables / 69 \\
3. Differential equation for the Appell polynomials /
72 \\
4. Orthogonality of eigenfunctions of the Appell
equation / 75 \\
5. Normal biorthogonal Appell System / 79 \\
6. Series in the Appell polynomials / 83 \\
IV. Admissible differential equation for polynomials
orthogonal over a domain / 87 \\
1. The main differential Operator and a theorem on
orthogonality / 87 \\
2. Admissibility conditions for the main differential
equation / 92 \\
3. Some examples and properties of admissible
differential equations / 97 \\
4. Affine transformations of the arguments of the main
differential equation / 101 \\
5. Transformation of the coefficients of the
characteristic polynomial / 105 \\
6. Normal forms of the admissible differential equation
/ 115 \\
7. Normal forms when reducing the degree of the
characteristic polynomial / 123 \\
V. Potentially self-adjoint equation and Rodrigues
formula / 131 \\
1. Potentially self-adjoint Operators / 131 \\
2. Admissible and potentially self-adjoint equations /
135 \\
3. Rodrigues formula for polynomials orthogonal over a
domain / 146 \\
4. Weight functions and the Rodrigues formula in the
most typical cases / 153 \\
VI. Harmonic polynomials orthogonal over a domain / 163
\\
1. Homogeneous harmonic polynomials / 163 \\
2. An analogue of the Christoffel--Darboux formula /
169 \\
3. Harmonic polynomials orthogonal in the unit disk /
173 \\
4. Harmonic polynomials orthogonal over a domain in the
general case / 176 \\
5. Harmonic polynomials superorthogonal over a domain /
179 \\
VII. Polynomials in two variables orthogonal on a
contour / 187 \\
1. Main definitions and the simplest properties / 187
\\
2. Polynomials in two variables orthogonal on an
algebraic curve / 191 \\
3. Harmonic polynomials orthogonal on a contour / 196
\\
4. Fourier series in harmonic polynomials orthogonal on
a contour / 200 \\
5. Harmonic polynomials superorthogonal on a contour /
206 \\
6. Examples of superorthogonal Systems of harmonic
polynomials / 213 \\
VIII. Generalized orthogonal polynomials in two
variables / 223 \\
1. Main definitions and the simplest properties / 223
\\
2. The existence theorem in the most general form / 228
\\
3. Fourier series in generalized orthogonal polynomials
in two variables / 233 \\
4. Monic orthogonal polynomials under minimal
conditions / 241 \\
5. Generalized generating functions for monic
orthogonal polynomials / 247 \\
IX. Other results concerning the connection between
orthogonal polynomials and differential equations / 253
\\
1. Canonical admissible differential equation and monic
orthogonal polynomials / 253 \\
2. Necessary consistency conditions of the canonical
Operator and the functional / 258 \\
3. Sufficient conditions of consistency of the
canonical Operator and the functional / 262 \\
4. The deduction of the differential equation from the
Pearson equation System / 268 \\
5. An admissible partial differential equation of an
arbitrary order / 276 \\
X. Original results of T. Koornwinder / 285 \\
1. Examples of the representation of polynomials
orthogonal over a domain via the Jacobi polynomials /
285 \\
2. Orthogonal polynomials in two conjugate complex
variables / 291 \\
3. The Chebyshev polynomials in two conjugate complex
variables for the Steiner domain / 296 \\
4. Another generalization of the Jacobi polynomials
onto the case of two variables / 308 \\
XI. Some recent results / 313 \\
1. A new generalization of the Appell polynomials / 313
\\
2. Some properties of the Koornwinder--Steiner
polynomials / 318 \\
3. A two-dimensional analogue of the
Chebyshev--Laguerre polynomials / 319 \\
Comments and Supplements / 323 \\
References / 329 \\
Author Index / 343 \\
Subject Index / 345",
}
@Article{Vrahatis:1999:ESP,
author = "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
Zafiropoulos and T. N. Grapsa",
title = "Erratum to: {{\booktitle{RFSFNS: a portable package
for the numerical determination of the number and the
calculation of roots of Bessel functions}} [Comput.
Phys. Commun. {\bf 92} (1995) 252--266]}",
journal = j-COMP-PHYS-COMM,
volume = "117",
number = "3",
pages = "290--290",
day = "11",
month = mar,
year = "1999",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(98)00109-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:30:36 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Vrahatis:1995:RPP}.",
URL = "http://www.sciencedirect.com/science/article/pii/S001046559800109X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Vyridis:1999:ICA,
author = "D. G. Vyridis and S. D. Panteliou and I. N. Katz",
title = "An inverse convergence approach for arguments of
{Jacobian} elliptic functions",
journal = j-COMPUT-MATH-APPL,
volume = "37",
number = "2",
pages = "21--26",
month = jan,
year = "1999",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:56 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122198002508",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Wieder:1999:ANH,
author = "Thomas Wieder",
title = "{Algorithm 794}: Numerical {Hankel} transform by the
{Fortran} program {HANKEL}",
journal = j-TOMS,
volume = "25",
number = "2",
pages = "240--250",
month = jun,
year = "1999",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/317275.317284",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Oct 20 18:21:35 MDT 1999",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "ftp://netlib.bell-labs.com/netlib/toms/794.gz;
http://phase.etl.go.jp/netlib/toms/794;
http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/;
http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH;
http://www.hensa.ac.uk/netlib/toms/794.gz;
http://www.netlib.no/netlib/toms/794;
http://www.netlib.org/toms/794",
abstract = "The numerical evaluation of the Hankel transform poses
the problems of both infinite integration and Bessel
function calculation. Using the corresponding numerical
program routines from the literature, a Fortran program
has been written to perform the Hankel transform for
real functions, given either in analytical form as
subroutines or in discrete form as tabulated data.",
accepted = "February 1999",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Hankel transform; numerical analysis",
subject = "Software --- Programming Languages --- Language
Classifications (D.3.2): FORTRAN 77; Theory of
Computation --- Analysis of Algorithms and Problem
Complexity --- Numerical Algorithms and Problems
(F.2.1): Computation of transforms",
}
@TechReport{Zimmermann:1999:KSR,
author = "Paul Zimmermann",
title = "{Karatsuba} Square Root",
type = "Research Report",
number = "3805",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "8",
year = "1999",
bibdate = "Sun Sep 10 08:56:48 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz;
http://www.inria.fr/rrrt/rr-3805.html",
abstract = "We exhibit an algorithm to compute the square-root
with remainder of a $n$-word number in $ 3 / 2 $ word
operations, where $ K(n) $ is the number of words
operations to multiply two $n$-word numbers using
Karatsuba's algorithm. If the remainder is not needed,
the cost can be reduced to $ K(n) $ on average. This
algorithm can be used for floating-point or polynomial
computations too; although not optimal asymptotically,
its simplicity gives a wide range of use, from about 50
to 1,000,000 digits, as shown by computer
experiments.",
acknowledgement = ack-nhfb,
}
@Article{Ziv:1999:SUR,
author = "Abraham Ziv",
title = "Sharp {ULP} rounding error bound for the hypotenuse
function",
journal = j-MATH-COMPUT,
volume = "68",
number = "227",
pages = "1143--1148",
month = jul,
year = "1999",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri Jul 16 10:39:05 MDT 1999",
bibsource = "http://www.ams.org/mcom/1999-68-227;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-01103-5&u=/mcom/1999-68-227/",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Alhargan:2000:ACA,
author = "Fayez A. Alhargan",
title = "Algorithms for the Computation of all {Mathieu}
Functions of Integer Orders",
journal = j-TOMS,
volume = "26",
number = "3",
pages = "390--407",
month = sep,
year = "2000",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/358407.358420",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "The paper presents methods for the computation of all
Mathieu functions of integer order, which cover a large
range of $n$ and $h$; previous algorithms were limited
to small values of $n$. The algorithms are given in
sufficient details to enable straightforward
implementation. The algorithms can handle a large range
of the order $n$ (0-200) and the parameter $h$ (0-4$n$
).",
accepted = "19 May 2000",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Alhargan:2000:ASC,
author = "Fayez A. Alhargan",
title = "{Algorithm 804}: subroutines for the computation of
{Mathieu} functions of integer orders",
journal = j-TOMS,
volume = "26",
number = "3",
pages = "408--414",
month = sep,
year = "2000",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/358407.358422",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Computer subroutines in C++ for computing Mathieu
functions of integer orders are described. The core
routines for computing Mathieu characteristic numbers
and Mathieu coefficients are described in details, the
rest of the subroutines are standard implementation of
the series summations for each function. The routines
can handle a large range of the order $n$ and the
parameter $h$.",
accepted = "19 May 2000",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Anderson:2000:RAF,
author = "Stuart Anderson",
title = "Remark on {Algorithm 723}: {Fresnel} integrals",
journal = j-TOMS,
volume = "26",
number = "4",
pages = "617--617",
month = dec,
year = "2000",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/365723.365737",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
accepted = "16 October 2000",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Ball:2000:ACZ,
author = "James S. Ball",
title = "Automatic Computation of Zeros of {Bessel} Functions
and Other Special Functions",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "4",
pages = "1458--1464",
month = jul,
year = "2000",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827598339074",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Oct 27 13:32:22 MDT 2000",
bibsource = "http://epubs.siam.org/toc/sjoce3/21/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/33907",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{Batten:2000:NAD,
author = "D. Batten and S. Jinturkar and J. Glossner and M.
Schulte and P. D'arcy",
title = "A New Approach to {DSP} Intrinsic Functions",
crossref = "Sprague:2000:PAH",
pages = "2892--2901",
year = "2000",
bibdate = "Sun Mar 04 11:18:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf",
acknowledgement = ack-nhfb,
}
@Article{Becken:2000:ACG,
author = "W. Becken and P. Schmelcher",
title = "The analytic continuation of the {Gaussian}
hypergeometric function {$_2 F_1 (a, b; c; z)$} for
arbitrary parameters",
journal = j-J-COMPUT-APPL-MATH,
volume = "126",
number = "1--2",
pages = "449--478",
day = "30",
month = dec,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00267-3",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "33C05 (33F05)",
MRnumber = "MR1806771 (2002e:33003)",
bibdate = "Sat Feb 25 12:43:38 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700002673",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InCollection{Borwein:2000:AGM,
author = "J. M. Borwein and P. B. Borwein",
title = "The Arithmetic--Geometric Mean and Fast Computation of
Elementary Functions",
crossref = "Berggren:2000:PSB",
pages = "537--552",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-3240-5_56",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Reprint of \cite{Borwein:1984:AGM}.",
URL = "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2000:CSR,
author = "Jonathan M. Borwein and David M. Bradley and Richard
E. Crandall",
title = "Computational Strategies for the {Riemann} Zeta
Function",
journal = j-J-COMPUT-APPL-MATH,
volume = "121",
number = "1--2",
pages = "247--296",
month = sep,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00336-8",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "11M06 (11Y35 33F05)",
MRnumber = "1780051",
MRreviewer = "Cem Y. Y{\i}ld{\i}r{\i}m",
bibdate = "Mon Oct 24 11:41:28 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://people.reed.edu/~crandall/papers/attach01.pdf",
abstract = "We provide a compendium of evaluation methods for the
Riemann zeta function, presenting formulae ranging from
historical attempts to recently found convergent series
to curious oddities old and new. We concentrate
primarily on practical computational issues, such
issues depending on the domain of the argument, the
desired speed of computation, and the incidence of what
we call ``value recycling''.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:118.",
}
@Book{Bressoud:2000:CCN,
author = "David M. Bressoud and S. Wagon",
title = "A Course in Computational Number Theory",
publisher = "Key College Publishers in cooperation with Springer",
address = "New York, NY, USA",
pages = "xii + 367",
year = "2000",
ISBN = "1-930190-10-7",
ISBN-13 = "978-1-930190-10-8",
LCCN = "QA241 .B788 2000",
bibdate = "Fri Sep 26 14:29:31 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html;
http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html",
acknowledgement = ack-nhfb,
shorttableofcontents = "Fundamentals \\
Congruences, equations, and powers \\
Euler's function \\
Prime numbers \\
Some applications \\
Quadratic residues \\
Continued fractions \\
Prime testing with Lucas sequences \\
Prime imaginaries and imaginary primes \\
Appendix A. Mathematica basics \\
Appendix B. Lucas certificates exist",
subject = "Number theory; Algorithms",
tableofcontents = "Preface Vv \\
Notation Xi \\
Chapter 1. Fundamentals / 1 \\
1.0 Introduction / 1 \\
1.1 A Famous Sequence of Numbers / 2 \\
1.2 The Euclidean Algorithm / 6 \\
The Oldest Algorithm \\
Reversing the Euclidean Algorithm \\
The Extended GCD Algorithm \\
The Fundamental Theorem of Arithmetic \\
Two Applications \\
1.3 Modular Arithmetic / 25 \\
1.4 Fast Powers / 30 \\
A Fast Algorithm for Exponentiation \\
Powers of Matrices, Big-O Notation \\
Chapter 2. Congruences, Equations, and Powers / 41 \\
2.0 Introduction / / 41 \\
2.1 Solving Linear Congruences / 41 \\
Linear Diophantine Equations in Two Variables \\
Linear Equations in Several Variables \\
Linear Congruences \\
The Conductor \\
An Important Quadratic Congruence \\
2.2 The Chinese Remainder Theorem / 49 \\
2.3 PowerMod Patterns / 55 \\
Fermat's Little Theorem \\
More Patterns in Powers \\
2.4 Pseudoprimes / 59 \\
Using the Pseudoprime Test \\
Chapter 3. Euler's $\phi$ Function / 65 \\
3.0 Introduction / 65 \\
3.1 Euler's $\phi$ Function / 656 \\
3.2 Perfect Numbers and Their Relatives / 12 \\
The Sum of Divisors Function \\
Perfect Numbers \\
Amicable, Abundant, and Deficient Numbers \\
3.3 Euler's Theorem / 81 \\
3.4 Primitive Roots for Primes / 84 \\
The Order of an Integer \\
Primes Have Primitive Roots \\
Repeating Decimals \\
3.5 Primitive Roots for Composites / 70 \\
3.6 The Universal Exponent / 73 \\
Universal Exponents \\
Power Towers \\
The Form of Carmichael Numbers \\
Chapter 4. Prime Numbers / 99 \\
4.0 Introduction / 99 \\
4.1 The number of Primes / 100 \\
We'll Never Run Out of Primes \\
The Sieve of Eratosthenes \\
Chebyshev's Theorem and Bertrand's Postulate \\
4.2 Prime Testing and Certification / 114 \\
Strong Pseudoprimes \\
Industrial-Grade Primes \\
Prime Certification Via Primitive Roots \\
An Improvement \\
Pratt Certificates \\
4.3 Refinements and Other Directions / 131 \\
Other Primality Tests \\
Strong Liars Are Scarce \\
Finding the $n$th Prime \\
4.4 A Dozen Prime Mysteries / 141 \\
5.0 Introduction / 145 \\
5.1 Coding Secrets / 145 \\
Tossing a Coin into a Well \\
The RSA Cryptosystem \\
Digital Signatures \\
5.2 The Yao Millionaire Problem / 155 \\
5.3 Check Digits .158 \\
Basic Check Digit Schemes \\
A Perfect Check Digit Method \\
Beyond Perfection: Correcting Errors \\
5.4 Factoring Algorithms / 167 \\
Trial Division \\
Fermat's Algorithm \\
Pollard Rho \\
Pollard $p - 1$ \\
The Current Scene \\
Chapter 6. Quadratic Residues / 179 \\
6.0 Introduction / 179 \\
6.1 P{\'e}pin's Test / 119 \\
Quadratic Residues \\
P{\'e}pin's Test \\
Primes Congruent to 1 (Mod 4) \\
6.2 Proof of Quadratic Reciprocity / 185 \\
Gauss's Lemma \\
Proof of Quadratic Reciprocity \\
Jacobi's Extension \\
An Application to Factoring \\
6.3 Quadratic Equations / 194 \\
Chapter 7. Continued Fractions / 201 \\
7.0 Introduction / 201 \\
7.1 Finite Continued Fractions / 202 \\
7.2 Infinite Continued Fractions / 207 \\
7.3 Periodic Continued Fractions / 213 \\
7.4 Pell's Equation / 227 \\
7.5 Archimedes and the Sun God's Cattle / 232 \\
Wurm's Version: Using Rectangular Bulls \\
The Real Cattle Problem \\
7.6 Factoring via Continued Fractions / 238 \\
Chapter 8. Prime Testing with Lucas Sequences / 247 \\
8.0 Introduction / 247 \\
8.1 Divisibility Properties of Lucas Sequences / 248
\\
8.2 Prime Tests Using Lucas Sequences / 259 \\
Lucas Certification \\
The Lucas--Lehmer Algorithm Explained \\
Lucas Pseudoprimes \\
Strong Quadratic Pseudoprimes \\
Primality Testing's Holy Grail \\
Chapter 9. Prime Imaginaries and Imaginary Primes / 279
\\
9.0 Introduction / 279 \\
9.1 Sums of Two Squares / 279 \\
Primes \\
The General Problem \\
How Many Ways \\
Number Theory and Salt \\
9.2 The Gaussian Integers / 302 \\
Complex Number Theory \\
Gaussian Primes \\
The Moat Problem \\
The Gaussian Zoo \\
9.3 Higher Reciprocity / 325 \\
Appendix A. Mathematica Basics / 333 \\
A.0 Introduction / 333 \\
A.1 Plotting / 336 \\
A.2 Typesetting / 338 \\
Sending Files By E-Mail \\
A.3 Types of Functions / 341 \\
A.4 Programs / 345 \\
A.6 Solving Equations / 347 \\
A.7 Symbolic Algebra / 349 \\
Appendix B. Lucas Certificates Exist / 351 \\
References / 355 \\
Index of Mathematica Objects / 359 \\
Subject Index / 363",
}
@Article{Brezinski:2000:CAD,
author = "C. Brezinski",
title = "Convergence acceleration during the 20th century",
journal = j-J-COMPUT-APPL-MATH,
volume = "122",
number = "1--2",
pages = "1--21",
month = oct,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00360-5",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65-03 (01A60)",
MRnumber = "1794649",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Numerical analysis 2000, Vol. II: Interpolation and
extrapolation",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "convergence acceleration",
}
@Article{Carlson:2000:RTE,
author = "B. C. Carlson and James FitzSimons",
title = "Reduction theorems for elliptic integrands with the
square root of two quadratic factors",
journal = j-J-COMPUT-APPL-MATH,
volume = "118",
number = "1--2",
pages = "71--85",
day = "1",
month = jun,
year = "2000",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:43:35 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270000282X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Cawley:2000:FCA,
author = "G. C. Cawley",
title = "On a Fast, Compact Approximation of the Exponential
Function",
journal = j-NEURAL-COMP,
volume = "12",
number = "9",
pages = "2009--2012",
day = "1",
month = sep,
year = "2000",
CODEN = "NEUCEB",
ISSN = "0899-7667 (print), 1530-888x (electronic)",
ISSN-L = "0899-7667",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Neural Computation",
journal-URL = "http://www.mitpressjournals.org/loi/neco",
pagecount = "4",
}
@Article{Cherri:2000:PCC,
author = "A. K. Cherri and M. S. Alam",
title = "Parallel computation of complex elementary functions
using quaternary signed-digit arithmetic",
journal = "Optics and Laser Technology",
volume = "32",
number = "6",
pages = "391--399",
year = "2000",
CODEN = "????",
ISSN = "0030-3992",
bibdate = "Sat Dec 7 09:21:28 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
pagecount = "9",
}
@InProceedings{Chu:2000:CPT,
author = "Wanming Chu and Yamin Li",
booktitle = "{ACAC 2000}: 5th Australasian Computer Architecture
Conference",
title = "Cost\slash performance tradeoff of $n$-select square
root implementations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "9--16",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Hardware square-root units require large numbers of
gates even for iterative implementations. In this paper
we present four low-cost high-performance
fully-pipelined n-select implementations (nS-Root)
based on a non-restoring-remainder square root
\ldots{}",
}
@Article{Cohen:2000:CAA,
author = "Henri Cohen and Fernando {Rodriguez Villegas} and Don
Zagier",
title = "Convergence Acceleration of Alternating Series",
journal = j-EXP-MATH,
volume = "9",
number = "1",
pages = "3--12",
year = "2000",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11Y55 (65B05)",
MRnumber = "1758796 (2001m:11222)",
bibdate = "Thu Dec 1 17:36:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://projecteuclid.org/euclid.em/1046889587;
http://www.math.u-bordeaux.fr/~cohen/sumalt2new.ps",
ZMnumber = "0972.11115",
abstract = "We discuss some linear acceleration methods for
alternating series which are in theory and in practice
much better than that of Euler--Van Wijngaarden. One of
the algorithms, for instance, allows one to calculate $
\sum ( - 1)^k a_k $ with an error of about $ 17.93^{-n}
$ from the first $n$ terms for a wide class of
sequences $ \{ a_k \} $. Such methods are useful for
high precision calculations frequently appearing in
number theory.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
keywords = "convergence acceleration",
}
@Article{Ercegovac:2000:IGD,
author = "Milos D. Ercegovac and Laurent Imbert and David W.
Matula and Jean-Michel Muller and Guoheng Wei",
title = "Improving {Goldschmidt} Division, Square Root, and
Square Root Reciprocal",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "759--763",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863046",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
summary = "The aim of this paper is to accelerate division,
square root, and square root reciprocal computations
when the Goldschmidt method is used on a pipelined
multiplier. This is done by replacing the last
iteration by the addition of a correcting term
\ldots{}",
}
@Article{Ercegovac:2000:RSR,
author = "Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel
Muller and Arnaud Tisserand",
title = "Reciprocation, Square Root, Inverse Square Root, and
Some Elementary Functions Using Small Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "628--637",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863031",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68M07 (65B15)",
MRnumber = "MR1783602 (2001e:68016)",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Institute of Electrical and Electronics Engineers.
Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
summary = "This paper deals with the computation of reciprocals,
square roots, inverse square roots, and some elementary
functions using small tables, small multipliers, and,
for some functions, a final ``large'' (almost
full-length) multiplication. \ldots{}",
}
@Article{Favati:2000:SAC,
author = "P. Favati and G. Lotti and O. Menchi and F. Romani",
title = "Separable asymptotic cost of evaluating elementary
functions",
journal = j-NUMER-ALGORITHMS,
volume = "24",
number = "3",
pages = "255--274",
year = "2000",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65Y20",
MRnumber = "MR1780414 (2001d:65174)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
pagecount = "20",
}
@Article{Galue:2000:MTG,
author = "L. Galu{\'e} and H. G. Khajah and Shyam L. Kalla",
title = "Multiplication theorems for generalized and
double-index {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "118",
number = "1--2",
pages = "143--150",
day = "1",
month = jun,
year = "2000",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:43:35 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700002855",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Harris:2000:SBE,
author = "Frank E. Harris",
title = "Spherical {Bessel} expansions of sine, cosine, and
exponential integrals",
journal = j-APPL-NUM-MATH,
volume = "34",
number = "1",
pages = "95--98",
month = jun,
year = "2000",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/S0168-9274(99)00031-8",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "33B10; 65D30 (33F05 65D20)",
MRnumber = "1755696 (2001a:65027)",
bibdate = "Sat Oct 21 13:09:35 MDT 2000",
bibsource = "http://www.elsevier.com/locate/issn/01689274;
https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/abstract.html;
http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/article.pdf;
http://www.sciencedirect.com/science/article/pii/S0168927499000318",
ZMnumber = "Zbl 0951.33002",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
}
@InProceedings{Hasan:2000:FPI,
author = "M. A. Hasan and A. A. Hasan and S. Rahman",
booktitle = "Proceedings of the 39th {IEEE} Conference on Decision
and Control",
title = "Fixed point iterations for computing square roots and
the matrix sign function of complex matrices",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "4253--4258",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The purpose of this work has been the development of
new set of rational iterations for computing square
roots and the matrix sign function of complex matrices.
Given any positive integer r{\&}ges;2, we presented a
systematic way of deriving rth order \ldots{}",
}
@InProceedings{Hassibi:2000:ESR,
author = "B. Hassibi",
booktitle = "Proceedings. 2000 {IEEE} International Conference on
Acoustics, Speech, and Signal Processing: {ICASSP '00},
5--9 June 2000",
title = "An efficient square-root algorithm for {BLAST}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II737--II740",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Bell Labs Layered Space-Time (BLAST) is a scheme for
transmitting information over a rich-scattering
wireless environment using multiple receive and
transmit antennas. The main computational bottleneck in
the BLAST algorithm is a ``nulling and \ldots{}",
}
@InProceedings{Hassibi:2000:FSR,
author = "B. Hassibi",
booktitle = "{Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000}",
title = "A fast square-root implementation for {BLAST}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1255--1259",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Bell Labs Layered Space-Time (BLAST) is a scheme for
transmitting information over a rich-scattering
wireless environment using multiple receive and
transmit antennas. The main computational bottleneck in
the BLAST algorithm is a ``nulling and \ldots{}",
}
@Article{Holmgren:2000:CAL,
author = "Sverker Holmgren and Henrik Brand{\'e}n and Erik
Sterner",
title = "Convergence Acceleration for the Linearized
{Navier--Stokes} Equations using Semicirculant
Approximations",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "4",
pages = "1524--1550",
month = jul,
year = "2000",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827597317983",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Oct 27 13:32:22 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31798",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "convergence acceleration",
}
@Misc{Intel:2000:DSR,
author = "{Intel}",
title = "Divide, Square Root, and Remainder Algorithms for the
{Itanium} Architecture",
howpublished = "Intel Software Development Products",
month = jul,
year = "2000",
bibdate = "Fri Sep 22 17:06:23 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://studylib.net/doc/7921762/divide--square-root-and-remainder-algorithms-for-the-ia-64",
acknowledgement = ack-nhfb,
}
@Book{Jeffrey:2000:HMF,
author = "Alan Jeffrey",
title = "Handbook of Mathematical Formulas and Integrals",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
edition = "Second",
pages = "xxvi + 433",
year = "2000",
ISBN = "0-12-382251-3",
ISBN-13 = "978-0-12-382251-2",
LCCN = "QA47 .J38 2000",
bibdate = "Wed Jun 12 14:47:49 MDT 2024",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
shorttableofcontents = "0: Quick Reference List of Frequently Used
Data \\
1: Numerical, Algebraic, and Analytical Results for
Series and Calculus \\
2: Functions and Identities \\
3: Derivatives of Elementary Functions \\
4: Indefinite Integrals of Algebraic Functions \\
5: Indefinite Integrals of Exponential Functions \\
6: Indefinite Integrals of Logarithmic Functions \\
7: Indefinite Integrals of Hyperbolic Functions \\
8: Indefinite Integrals Involving Inverse Hyperbolic
Functions \\
9: Indefinite Integrals of Trigonometric Functions \\
10: Indefinite Integrals of Inverse Trigonometric
Functions \\
11: The Gamma, Beta, Pi, and Psi Functions \\
12: Elliptic Integrals and Functions \\
13: Probability Integrals and the Error Function \\
14: Fresnel Integrals \\
15: Definite Integrals \\
16: Different Forms of Fourier Series \\
17: Bessel Functions \\
18: Orthogonal Polynomials \\
19: Laplace Transformation \\
20: Fourier Transforms \\
21: Numerical Integration \\
22: Solutions of Standard Ordinary Differential
Equations \\
23: Vector Analysis \\
24: Systems of Orthogonal Coordinates \\
25: Partial Differential Equations and Special
Functions",
subject = "Mathematics; Tables; Formulae; Mathematics.",
tableofcontents = "0: Quick Reference List of Frequently Used Data \\
0.1: Useful Identities / 1 \\
0.2: Complex Relationships / 2 \\
0.3: Constants / 2 \\
0.4: Derivatives of Elementary Functions / 3 \\
0.5: Rules of Differentiation and Integration / 3 \\
0.6: Standard Integrals / 4 \\
0.7: Standard Series / 11 \\
0.8: Geometry / 13 \\
1: Numerical, Algebraic, and Analytical Results for
Series and Calculus \\
1.1: Algebraic Results Involving Real and Complex
Numbers / 25 \\
1.2: Finite Sums / 29 \\
1.3: Bernoulli and Euler Numbers and Polynomials / 37
\\
1.4: Determinants / 47 \\
1.5: Matrices / 55 \\
1.6: Permutations and Combinations / 62 \\
1.7: Partial Fraction Decomposition / 63 \\
1.8: Convergence of Series / 66 \\
1.9: Infinite Products / 71 \\
1.10: Functional Series / 73 \\
1.11: Power Series / 74 \\
1.12: Taylor Series / 79 \\
4.13: Fourier Series / 81 \\
4.14: Asymptotic Expansions / 85 \\
1.15: Basic Results from the Calculus / 86 \\
2: Functions and Identities \\
2.1: Complex Numbers and Trigonometric and Hyperbolic
Functions / 101 \\
2.2: Logarithms and Exponentials / 112 \\
2.3: Exponential Function / 114 \\
2.4: Trigonometric Identities / 115 \\
2.5: Hyperbolic Identities / 121 \\
2.6: Logarithm / 126 \\
2.7: Inverse Trigonometric and Hyperbolic Functions 128
\\
2.8: Series Representations of Trigonometric and
Hyperbolic Functions / 133 \\
2.9: Useful Limiting Values and Inequalities Involving
Elementary Functions / 136 \\
3: Derivatives of Elementary Functions \\
3.1: Derivatives of Algebraic, Logarithmic, and
Exponential Functions / 139 \\
3.2: Derivatives of Trigonometric Functions / 140 \\
3.3: Derivatives of Inverse Trigonometric Functions 140
\\
3.4: Derivatives of Hyperbolic Functions / 141 \\
3.5: Derivatives of Inverse Hyperbolic Functions 142
\\
4: Indefinite Integrals of Algebraic Functions \\
4.1: Algebraic and Transcendental Functions / 145 \\
4.2: Indefinite Integrals of Rational Functions / 146
\\
4.3: Nonrational Algebraic Functions / 158 \\
5: Indefinite Integrals of Exponential Functions \\
5.1: Basic Results / 167 \\
6: Indefinite Integrals of Logarithmic Functions \\
6.1: Combinations of Logarithms and Polynomials / 173
\\
7: Indefinite Integrals of Hyperbolic Functions \\
7.1: Basic Results / 179 \\
7.2: Integrands Involving Powers of sinh(bx) or
cosh(bx) / 180 \\
7.3: Integrands Involving (a [plus or minus]
bx)[superscript m] sinh(cx) or (a + bx)[superscript m]
cosh(cx) / 181 \\
7.4: Integrands Involving x[superscript m]
sinh[superscript n] x or x[superscript m]
cosh[superscript n] x / 183 \\
7.5: Integrands Involving x[superscript m]
sinh[superscript -n] x or x[superscript m]
cosh[superscript -n] x / 183 \\
7.6: Integrands Involving (1 [plus or minus] cosh
x)[superscript -m] / 185 \\
7.7: Integrands Involving sinh(ax)cosh[superscript -n]
x or cosh(ax)sinh[superscript -n] x / 185 \\
7.8: Integrands Involving sinh(ax + b) and cosh(cx + d)
/ 186 \\
7.9: Integrands Involving tanh kx and coth kx / 188 \\
7.10: Integrands Involving (a + bx)[superscript m] sinh
kx or (a + bx)[superscript m] cosh kx / 189 \\
8: Indefinite Integrals Involving Inverse Hyperbolic
Functions \\
8.1: Basic Results / 191 \\
8.2: Integrands Involving x[superscript -n]
arcsinh(x/a) or x[superscript -n] arccosh(x/a) / 193
\\
8.3: Integrands Involving x[superscript n] arctanh(x/a)
or x[superscript n] arccoth(x/a) / 194 \\
8.4: Integrands Involving x[superscript -n]
arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195
\\
9: Indefinite Integrals of Trigonometric Functions \\
9.1: Basic Results / 197 \\
9.2: Integrands Involving Powers of x and Powers of sin
x or cos x / 197 \\
9.3: Integrands Involving tan x and/or cot x / 205 \\
9.4: Integrands Involving sin x and cos x / 207 \\
9.5: Integrands Involving Sines and Cosines with Linear
Arguments and Powers of x / 211 \\
10: Indefinite Integrals of Inverse Trigonometric
Functions \\
10.1: Integrands Involving Powers of x and Powers of
Inverse Trigonometric Functions 215 --. 11: Gamma,
Beta, Pi, and Psi Functions \\
11.1: Euler Integral and Limit and Infinite Product
Representations for [Gamma] (x) / 221 \\
12: Elliptic Integrals and Functions \\
12.1: Elliptic Integrals / 229 \\
12.2: Jacobian Elliptic Functions / 235 \\
12.3: Derivatives and Integrals / 237 \\
12.4: Inverse Jacobian Elliptic Functions / 237 \\
13: Probability Integrals and the Error Function \\
13.1: Normal Distribution / 239 \\
13.2: Error Function / 242 \\
14: Fresnel Integrals, Sine and Cosine Integrals \\
14.1: Definitions, Series Representations, and Values
at Infinity / 245 \\
14.2: Definitions, Series Representations, and Values
at Infinity / 247 \\
15: Definite Integrals \\
15.1: Integrands Involving Powers of x / 249 \\
15.2: Integrands Involving Trigonometric Functions 251
\\
15.3: Integrands Involving the Exponential Function 254
\\
15.4: Integrands Involving the Hyperbolic Function 256
\\
15.5: Integrands Involving the Logarithmic Function 256
\\
16: Different Forms of Fourier Series \\
16.1: Fourier Series for f(x) on -[pi] [less than or
equal] x [less than or equal] [pi] / 257 \\
16.2: Fourier Series for f(x) on -L [less than or
equal] x [less than or equal] L / 258 \\
16.3: Fourier Series for f(x) on a [less than or equal]
x [less than or equal] b / 258 \\
16.4: Half-Range Fourier Cosine Series for f(x) on 0
[less than or equal] x [less than or equal] [pi] 259
\\
16.5: Half-Range Fourier Cosine Series for f(x) on 0
[less than or equal] x [less than or equal] L / 259 \\
16.6: Half-Range Fourier Sine Series for f(x) on 0
[less than or equal] x [less than or equal] [pi] 260
\\
16.7: Half-Range Fourier Sine Series for f(x) on 0
[less than or equal] x [less than or equal] L / 260 \\
16.8: Complex (Exponential) Fourier Series for f(x) on
-[pi] [less than or equal] x [less than or equal] [pi]
/ 260 \\
16.9: Complex (Exponential) Fourier Series for f(x) on
-L [less than or equal] x [less than or equal] L 261
\\
16.10: Representative Examples of Fourier Series 261
\\
16.11: Fourier Series and Discontinuous Functions 265
\\
17: Bessel Functions \\
17.1: Bessel's Differential Equation / 269 \\
17.2: Series Expansions for J[subscript v](x) and
Y[subscript v](x) / 270 \\
17.3: Bessel Functions of Fractional Order / 272 \\
17.4: Asymptotic Representations for Bessel Functions /
273 \\
17.5: Zeros of Bessel Functions / 273 \\
17.6: Bessel's Modified Equation / 274 \\
17.7: Series Expansions for I[subscript v](x) and
K[subscript v](x) / 276 \\
17.8: Modified Bessel Functions of Fractional Order 277
\\
17.9: Asymptotic Representations of Modified Bessel
Functions / 278 \\
17.10: Relationships between Bessel Functions / 278 \\
17.11: Integral Representations of J[subscript n](x),
I[subscript n](x), and K[subscript n](x) / 281 \\
17.12: Indefinite Integrals of Bessel Functions / 281
\\
17.13: Definite Integrals Involving Bessel Functions /
282 \\
17.14: Spherical Bessel Functions / 283 \\
18: Orthogonal Polynomials \\
18.2: Legendre Polynomials P[subscript n](x) / 286 \\
18.3: Chebyshev Polynomials T[subscript n](x) and
U[subscript n](x) / 290 \\
18.4: Laguerre Polynomials L[subscript n](x) / 294 \\
18.5: Hermite Polynomials H[subscript n](x) / 296 \\
19: Laplace Transformation \\
20: Fourier Transforms \\
21: Numerical Integration \\
21.1: Classical Methods / 315 \\
22: Solutions of Standard Ordinary Differential
Equations \\
22.2: Separation of Variables / 323 \\
22.3: Linear First-Order Equations / 323 \\
22.4: Bernoulli's Equation / 324 \\
22.5: Exact Equations / 325 \\
22.6: Homogeneous Equations / 325 \\
22.7: Linear Differential Equations / 326 \\
22.8: Constant Coefficient Linear Differential
Equations--Homogeneous Case / 327 \\
22.9: Linear Homogeneous Second-Order Equation / 330
\\
22.10: Constant Coefficient Linear Differential
Equations--Inhomogeneous Case / 331 \\
22.11: Linear Inhomogeneous Second-Order Equation 333
\\
22.12: Determination of Particular Integrals by the
Method of- Undetermined Coefficients / 334 \\
22.13: Cauchy-Euler Equation / 336 \\
22.14: Legendre's Equation / 337 \\
22.15: Bessel's Equations / 337 \\
22.16: Power Series and Frobenius Methods / 339 \\
22.17: Hypergeometric Equation / 344 \\
22.18: Numerical Methods / 345 \\
23: Vector Analysis \\
23.1: Scalars and Vectors / 353 \\
23.2: Scalar Products / 358 \\
23.3: Vector Products / 359 \\
23.4: Triple Products / 360 \\
23.5: Products of Four Vectors / 361 \\
23.6: Derivatives of Vector Functions of a Scalar t 361
\\
23.7: Derivatives of Vector Functions of Several Scalar
Variables / 362 \\
23.8: Integrals of Vector Functions of a Scalar
Variable t / 363 \\
23.9: Line Integrals / 364 \\
23.10: Vector Integral Theorems / 366 \\
23.11: A Vector Rate of Change Theorem / 368 \\
23.12: Useful Vector Identities and Results / 368 \\
24: Systems of Orthogonal Coordinates \\
24.1: Curvilinear Coordinates / 369 \\
24.2: Vector Operators in Orthogonal Coordinates 371
\\
24.3: Systems of Orthogonal Coordinates / 371 \\
25: Partial Differential Equations and Special
Functions \\
25.1: Fundamental Ideas / 381 \\
25.2: Method of Separation of Variables / 385 \\
25.3: Sturm--Liouville Problem and Special Functions
387 \\
25.4: A First-Order System and the Wave Equation 390
\\
25.5: Conservation Equations (Laws) / 391 \\
25.6: Method of Characteristics / 392 \\
25.7: Discontinuous Solutions (Shocks) / 396 \\
25.8: Similarity Solutions / 398 \\
25.9: Burgers's Equation, the KdV Equation, and the
KdVB Equation / 400 \\
26: Z-Transform \\
26.1: Z-Transform and Transform Pairs / 403 \\
27: Numerical Approximation \\
27.2: Economization of Series / 411 \\
27.3: Pade Approximation / 413 \\
27.4: Finite Difference Approximations to Ordinary and
Partial Derivatives / 415",
}
@Article{Kilbas:2000:CFI,
author = "A. A. Kilbas and J. J. Trujillo",
title = "Computation of fractional integrals via functions of
hypergeometric and {Bessel} type",
journal = j-J-COMPUT-APPL-MATH,
volume = "118",
number = "1--2",
pages = "223--239",
day = "1",
month = jun,
year = "2000",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:43:35 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700002910",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Lefevre:2000:CRF,
author = "V. D. Lefevre and J.-M. Muller",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "Correctly rounded functions for better arithmetic",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "875--878",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The IEEE 754 standard for floating-point arithmetic
requires that the four arithmetic operations and the
square root should be correctly rounded. This has
improved the accuracy, reliability and portability of
numerical software. Unfortunately, such \ldots{}",
}
@Article{Lopez:2000:AES,
author = "Jos{\'e} L. L{\'o}pez",
title = "Asymptotic Expansions of Symmetric Standard Elliptic
Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "31",
number = "4",
pages = "754--775",
year = "2000",
CODEN = "SJMAAH",
DOI = "https://doi.org/10.1137/S0036141099351176",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Fri Oct 27 08:17:04 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/31/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35117",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@InProceedings{Lozier:2000:DPN,
author = "Daniel W. Lozier",
title = "The {DLMF Project}: a New Initiative in Classical
Special Functions",
crossref = "Dunkl:2000:PIW",
pages = "207--220",
year = "2000",
bibdate = "Fri Jul 09 06:31:32 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Markstein:2000:IEF,
author = "Peter Markstein",
title = "{IA-64} and elementary functions: speed and
precision",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xix + 298",
year = "2000",
ISBN = "0-13-018348-2",
ISBN-13 = "978-0-13-018348-4",
LCCN = "QA76.9.A73 M365 2000",
bibdate = "Fri Jan 5 08:00:52 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib;
University of California MELVYL catalog.",
series = "Hewlett--Packard professional books",
URL = "http://www.markstein.org/",
acknowledgement = ack-nhfb,
keywords = "IA-64 (computer architecture)",
remark = "Besides recipes for accurate computation of elementary
functions, this book also contains algorithms for the
correctly-rounded computation of floating-point
division and square-root, and of integer division,
starting from low-precision reciprocal approximations.
There is also a wealth of information on the tradeoffs
between integer and floating-point instruction use in a
pipelined parallel architecture.",
tableofcontents = "IA-64 Architecture \\
New Architecture Objectives \\
VLIW \\
Memory Enhancements \\
Software Pipelining \\
Floating Point Enhancements \\
Summary \\
IA-64 Instructions And Registers \\
Instructions \\
Register Sets \\
Accessing Memory \\
Assembly Language \\
Problems \\
Increasing Instruction Level Parallelism \\
Branching \\
Speculation \\
Problems \\
Floating Point Architecture \\
Floating Point Status Register \\
Precision \\
Fused Multiply-Add \\
Division and Square Root Assists \\
Floating Comparisons \\
Communication between Floating Point and General
Purpose Registers \\
Fixed Point Multiplication \\
SIMD Arithmetic \\
Problems \\
Programming For IA-64 \\
Compiler Options \\
Pragmas \\
Floating Point Data Types \\
In-Line Assembly \\
The fenv.h Header \\
Extended Examples \\
Quad Precision \\
Problems \\
Computation of Elementary Functions \\
Mathematical Preliminaries \\
Floating Point \\
Approximation and Error Analysis \\
The Exclusion Theorem \\
Ulps \\
Problems \\
Approximation Of Functions \\
Taylor Series \\
Lagrangian Interpolation \\
Chebychev Approximation \\
Remez Approximation \\
Practical Considerations \\
Function Evaluation \\
Table Construction \\
Problems \\
Division \\
Approximations for the Reciprocal \\
Computing the Quotient \\
Division Using Only Final Precision Results \\
Fast Variants of Division \\
Remainder \\
Integer Division \\
An Implementation of Division \\
Problems \\
Square Root \\
Approximations \\
Rounding the Square Root \\
Computing the Square Root \\
Calculating the Reciprocal Square Root \\
An Implementation of Square Root \\
Problems \\
Exponential Functions \\
Definitions and Formulas \\
Argument Reduction \\
Error Containment \\
Computing the Exponential \\
The Function expm \\
Problems \\
Logarithmic Functions \\
General Relations \\
Argument Reductions \\
Error Analysis \\
The Function log1p \\
Computing the Logarithm \\
Problems \\
The Power Function \\
Definition \\
Single Precision \\
Double Precision \\
Double-Extended Precision \\
Quad Precision \\
Computing the Power Function \\
Problems \\
Trigonometric Functions \\
Formulas and Identities \\
Argument Reduction \\
Error Analysis \\
Computing the Trigonometric Functions \\
Problems \\
Inverse Sine And Cosine \\
Definitions and Formulas \\
Argument Reduction \\
Error Analysis \\
Computing the arcsin \\
Problems \\
Inverse Tangent Functions \\
Definitions and Formulas \\
Argument Reduction \\
Error Analysis \\
Computing the arctan \\
Problems \\
Hyperbolic Functions \\
Definitions and Formulas \\
Argument Reduction \\
Error Analysis \\
Computing the Hyperbolic Functions \\
Problems \\
Inverse Hyperbolic Functions \\
Definitions and Formulas. arcsinh. arccosh. arctanh \\
Problems \\
Odds And Ends \\
Correctly Rounded Functions \\
Monotonicity \\
Alternative Algorithms \\
Testing \\
New Architectural Directions \\
Problems \\
In-Line Assembly \\
Solutions To Problems \\
Bibliography \\
Subject Index",
}
@Article{Paliouras:2000:FPP,
author = "V. Paliouras and K. Karagianni and T. Stouraitis",
title = "A floating-point processor for fast and accurate
sine\slash cosine evaluation",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "47",
number = "5",
pages = "441--451",
month = may,
year = "2000",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.842112",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "A VLSI architecture for fast and accurate
floating-point sine/cosine evaluation is presented,
combining floating-point and simple fixed-point
arithmetic. The algorithm implemented by the
architecture is based on second order polynomial
interpolation \ldots{}",
}
@Book{Simon:2000:DCF,
author = "Marvin Kenneth Simon and Mohamed-Slim Alouini",
title = "Digital Communication over Fading Channels: a Unified
Approach to Performance Analysis",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 544",
year = "2000",
ISBN = "0-471-31779-9",
ISBN-13 = "978-0-471-31779-1",
LCCN = "TK5103.7 .S523 2000",
bibdate = "Sat Dec 16 17:34:06 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley series in telecommunications and signal
processing",
URL = "http://www.loc.gov/catdir/bios/wiley043/99056352.html;
http://www.loc.gov/catdir/description/wiley035/99056352.html;
http://www.loc.gov/catdir/toc/onix06/99056352.html",
acknowledgement = ack-nhfb,
author-dates = "1939--",
subject = "Digital communications; Reliability; Mathematics;
Radio; Transmitters and transmission; Fading",
tableofcontents = "1.1: System Performance Measures 4 \\
1.1.1: Average Signal-to-Noise Ratio 4 \\
1.1.2: Outage Probability 5 \\
1.1.3: Average Bit Error Probability 6 \\
Chapter 2: Fading Channel Characterization and Modeling
15 \\
2.1: Main Characteristics of Fading Channels 15 \\
2.1.1: Envelope and Phase Fluctuations 15 \\
2.1.2: Slow and Fast Fading 16 \\
2.1.3: Frequency-Flat and Frequency-Selective Fading 16
\\
2.2: Modeling of Flat Fading Channels 17 \\
2.2.1: Multipath Fading 18 \\
2.2.2: Log-Normal Shadowing 23 \\
2.2.3: Composite Multipath/Shadowing 24 \\
2.2.4: Combined (Time-Shared) Shadowed/Unshadowed
Fading 25 \\
2.3: Modeling of Frequency-Selective Fading Channels 26
\\
Chapter 3: Types of Communication 31 \\
3.1: Ideal Coherent Detection 31 \\
3.1.1: Multiple Amplitude-Shift-Keying or Multiple
Amplitude Modulation 33 \\
3.1.2: Quadrature Amplitude-Shift-Keying or Quadrature
Amplitude Modulation 34 \\
3.1.3: M-ary Phase-Shift-Keying 35 \\
3.1.4: Differentially Encoded M-ary Phase-Shift-Keying
39 \\
3.1.5: Offset QPSK or Staggered QPSK 41 \\
3.1.6: M-ary Frequency-Shift-Keying 43 \\
3.1.7: Minimum-Shift-Keying 45 \\
3.2: Nonideal Coherent Detection 47 \\
3.3: Noncoherent Detection 53 \\
3.4: Partially Coherent Detection 55 \\
3.4.1: Conventional Detection: One-Symbol Observation
55 \\
3.4.2: Multiple Symbol Detection 57 \\
3.5: Differentially Coherent Detection 59 \\
3.5.1: M-ary Differential Phase Shift Keying 59 \\
3.5.2: [pi]/4-Differential QPSK 65 \\
Part 2: Mathematical Tools \\
Chapter 4: Alternative Representations of Classical
Functions 69 \\
4.1: Gaussian $Q$-Function 70 \\
4.1.1: One-Dimensional Case 70 \\
4.1.2: Two-Dimensional Case 72 \\
4.2: Marcum $Q$-Function 74 \\
4.2.1: First-Order Marcum $Q$-Function 74 \\
4.2.2: Generalized ($m$th-Order) Marcum $Q$-Function 81
\\
4.3: Other Functions 90 \\
Appendix 4A: Derivation of Eq. (4.2) 95 \\
Chapter 5: Useful Expressions for Evaluating Average
Error Probability Performance 99 \\
5.1: Integrals Involving the Gaussian $Q$-Function 99
\\
5.1.1: Rayleigh Fading Channel 101 \\
5.1.2: Nakagami-q (Hoyt) Fading Channel 101 \\
5.1.3: Nakagami-n (Rice) Fading Channel 102 \\
5.1.4: Nakagami-m Fading Channel 102 \\
5.1.5: Log-Normal Shadowing Channel 104 \\
5.1.6: Composite Log-Normal Shadowing/Nakagami-m Fading
Channel 104 \\
5.2: Integrals Involving the Marcum $Q$-Function 107
\\
5.2.1: Rayleigh Fading Channel 108 \\
5.2.2: Nakagami-q (Hoyt) Fading Channel 109 \\
5.2.3: Nakagami-n (Rice) Fading Channel 109 \\
5.2.4: Nakagami-m Fading Channel 109 \\
5.2.5: Log-Normal Shadowing Channel 109 \\
5.2.6: Composite Log-Normal Shadowing/Nakagami-m Fading
Channel 110 \\
5.3: Integrals Involving the Incomplete Gamma Function
111 \\
5.3.1: Rayleigh Fading Channel 112 \\
5.3.2: Nakagami-q (Hoyt) Fading Channel 112 \\
5.3.3: Nakagami-n (Rice) Fading Channel 112 \\
5.3.4: Nakagami-m Fading Channel 113 \\
5.3.5: Log-Normal Shadowing Channel 114 \\
5.3.6: Composite Log-Normal Shadowing/Nakagami-m Fading
Channel 114 \\
5.4: Integrals Involving Other Functions 114 \\
5.4.1: M-PSK Error Probability Integral 114 \\
5.4.2: Arbitrary Two-Dimensional Signal Constellation
Error Probability Integral 116 \\
5.4.3: Integer Powers of the Gaussian $Q$-Function 117
\\
5.4.4: Integer Powers of M-PSK Error Probability
Integrals 121 \\
Appendix 5A: Evaluation of Definite Integrals
Associated with Rayleigh and Nakagami-$m$ Fading 124
\\
Chapter 6: New Representations of Some PDF's and CDF's
for Correlative Fading Applications 141 \\
6.1: Bivariate Rayleigh PDF and CDF 142 \\
6.2: PDF and CDF for Maximum of Two Rayleigh Random
Variables 146 \\
6.3: PDF and CDF for Maximum of Two Nakagami-m Random
Variables 149 \\
Part 3: Optimum Reception and Performance Evaluation
\\
Chapter 7: Optimum Receivers for Fading Channels 157
\\
7.1: Case of Known Amplitudes, Phases, and Delays:
Coherent, Detection 159 \\
7.2: Case of Known Phases and Delays, Unknown
Amplitudes 163 \\
7.2.1: Rayleigh Fading 163 \\
7.2.2: Nakagami-m Fading 164 \\
7.3: Case of Known Amplitudes and Delays, Unknown
Phases 166 \\
7.4: Case of Known Delays and Unknown Amplitudes and
Phases 168 \\
7.4.1: One-Symbol Observation: Noncoherent Detection
168 \\
7.4.2: Two-Symbol Observation: Conventional
Differentially Coherent Detection 181 \\
7.4.3: N-Symbol Observation: Multiple Symbol
Differentially Coherent Detection 186 \\
7.5: Case of Unknown Amplitudes, Phases, and Delays 188
\\
7.5.1: One-Symbol Observation: Noncoherent Detection
188 \\
7.5.2: Two-Symbol Observation: Conventional
Differentially Coherent Detection 190 \\
Chapter 8: Performance of Single Channel Receives 193
\\
8.1: Performance Over the AWGN Channel 193 \\
8.1.1: Ideal Coherent Detection 194 \\
8.1.2: Nonideal Coherent Detection 206 \\
8.1.3: Noncoherent Detection 209 \\
8.1.4: Partially Coherent Detection 210 \\
8.1.5: Differentially Coherent Detection 213 \\
8.1.6: Generic Results for Binary Signaling 218 \\
8.2: Performance Over Fading Channels 219 \\
8.2.1: Ideal Coherent Detection 220 \\
8.2.2: Nonideal Coherent Detection 234 \\
8.2.3: Noncoherent Detection 239 \\
8.2.4: Partially Coherent Detection 242 \\
8.2.5: Differentially Coherent Detection 243 \\
Appendix 8A: Stein's Unified Analysis of the Error
Probability Performance of Certain Communication
Systems 253 \\
Chapter 9: Performance of Multichannel Receivers 259
\\
9.1: Diversity Combining 260 \\
9.1.1: Diversity Concept 260 \\
9.1.2: Mathematical Modeling 260 \\
9.1.3: Brief Survey of Diversity Combining Techniques
261 \\
9.1.4: Complexity-Performance Trade-offs 264 \\
9.2: Maximal-Ratio Combining 265 \\
9.2.1: Receiver Structure 265 \\
9.2.2: PDF-Based Approach 267 \\
9.2.3: MGF-Based Approach 268 \\
9.2.4: Bounds and Asymptotic SER Expressions 275 \\
9.3: Coherent Equal Gain Combining 278 \\
9.3.1: Receiver Structure 279 \\
9.3.2: Average Output SNR 279 \\
9.3.3: Exact Error Rate Analysis 281 \\
9.3.4: Approximate Error Rate Analysis 288 \\
9.3.5: Asymptotic Error Rate Analysis 289 \\
9.4: Noncoherent Equal-Gain Combining 290 \\
9.4.1: DPSK, DQPSK, and BFSK: Exact and Bounds 290 \\
9.4.2: M-ary Orthogonal FSK 304 \\
9.5: Outage Probability Performance 311 \\
9.5.1: MRC and Noncoherent EGC 312 \\
9.5.2: Coherent EGC 313 \\
9.5.3: Numerical Examples 314 \\
9.6: Impact of Fading Correlation 316 \\
9.6.1: Model A: Two Correlated Branches with
Nonidentical Fading 320 \\
9.6.2: Model B: D Identically Distributed Branches with
Constant Correlation 323 \\
9.6.3: Model C: D Identically Distributed Branches with
Exponential Correlation 324 \\
9.6.4: Model D: D Nonidentically Distributed Branches
with Arbitrary Correlation 325 \\
9.6.5: Numerical Examples 329 \\
9.7: Selection Combining 333 \\
9.7.1: MGF of Output SNR 335 \\
9.7.2: Average Output SNR 336 \\
9.7.3: Outage Probability 338 \\
9.7.4: Average Probability of Error 340 \\
9.8: Switched Diversity 348 \\
9.8.1: Performance of SSC over Independent Identically
Distributed Branches 348 \\
9.8.2: Effect of Branch Unbalance 362 \\
9.8.3: Effect of Branch Correlation 366 \\
9.9: Performance in the Presence of Outdated or
Imperfect Channel Estimates 370 \\
9.9.1: Maximal-Ratio Combining 370 \\
9.9.2: Noncoherent EGC over Rician Fast Fading 371 \\
9.9.3: Selection Combining 373 \\
9.9.4: Switched Diversity 374 \\
9.9.5: Numerical Results 377 \\
9.10: Hybrid Diversity Schemes 378 \\
9.10.1: Generalized Selection Combining 378 \\
9.10.2: Generalized Switched Diversity 403 \\
9.10.3: Two-Dimensional Diversity Schemes 408 \\
Appendix 9A: Alternative Forms of the Bit Error
Probability for a Decision Statistic that is a
Quadratic Form of Complex Gaussian Random Variables 421
\\
Appendix 9B: Simple Numerical Techniques for thee
Inversion of the Laplace Transform of Cumulative
Distribution Functions 427 \\
9B.1: Euler Summation-Based Technique 427 \\
9B.2: Gauss-Chebyshev Quadrature-Based Technique 428
\\
Appendix 9C: Proof of Theorem 1 430 \\
Appendix 9D: Direct Proof of Eq. (9.331) 431 \\
Appendix 9E: Special Definite Integrals 432 \\
Part 4: Application in Practical Communication Systems
\\
Chapter 10: Optimum Combining: A Diversity Technique
for Communication Over Fading Channels in the Presence
of Interference 437 \\
10.1: Performance of Optimum Combining Receivers 438
\\
10.1.1: Single Interferer, Independent Identically
Distributed Fading 438 \\
10.1.2: Multiple Interferers, Independent Identically
Distributed Fading 454 \\
10.1.3: Comparison with Results for MRC in the Presence
of Interference 466 \\
Chapter 11: Direct-Sequence Code-Division Multiple
Access 473 \\
11.1: Single-Carrier DS-CDMA Systems 474 \\
11.1.1: System and Channel Models 474 \\
11.1.2: Performance Analysis 477 \\
11.2: Multicarrier DS-CDMA Systems 479 \\
11.2.1: System and Channel Models 480 \\
11.2.2: Performance Analysis 483 \\
11.2.3: Numerical Examples 489 \\
Part 5: Further Extensions \\
Chapter 12: Coded Communication Over Fading Channels
497 \\
12.1: Coherent Detection 499 \\
12.1.1: System Model 499 \\
12.1.2: Evaluation of Pairwise Error Probability 502
\\
12.1.3: Transfer Function Bound on Average Bit Error
Probability 510 \\
12.1.4: Alternative Formulation of the Transfer
Function Bound 513 \\
12.2: Differentially Coherent Detection 520 \\
12.2.1: System Model 520 \\
12.2.2: Performance Evaluation 522 \\
12.3: Numerical Results: Comparison of the True Upper
Bounds and Union-Chernoff Bounds 526 \\
Appendix 12A: Evaluation of a Moment Generating
Function Associated with Differential Detection of
M-PSK Sequences 532",
}
@InProceedings{Takahashi:2000:IMP,
author = "D. Takahashi",
booktitle = "Proceedings of the 2000 International Workshops on
Parallel Processing",
title = "Implementation of multiple-precision parallel division
and square root on distributed-memory parallel
computers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "229--235",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We present efficient parallel algorithms for
multiple-precision division and square root operation
of more than several million decimal digits on
distributed-memory parallel computers. It is well known
that multiple-precision division and square \ldots{}",
}
@InProceedings{Tchoumatchenko:2000:FBS,
author = "V. Tchoumatchenko and T. Vassileva and P. Gurov",
booktitle = "{Proceedings of the 22nd EUROMICRO Conference
EUROMICRO 96. 'Beyond 2000: Hardware and Software
Design Strategies'}",
title = "A {FPGA} based square-root coprocessor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "520--525",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We present an FPGA implementation of a non-restoring
integer square-root algorithm, that uses estimates for
result-digit selection and radix-$2$ redundant addition
in recurrence. On-the-fly conversion of the
result-digit and signed-digit adder/ \ldots{}",
}
@Article{Temme:2000:NAA,
author = "Nico M. Temme",
title = "Numerical and asymptotic aspects of parabolic cylinder
functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "121",
number = "1--2",
pages = "221--246",
day = "1",
month = sep,
year = "2000",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:43:36 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700003472",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Tommiska:2000:AEI,
author = "M. T. Tommiska",
booktitle = "Proceedings of the 2000 Third {IEEE} International
Caracas Conference on Devices, Circuits and Systems,
15--17 March 2000",
title = "Area-efficient implementation of a fast square root
algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "S18/1--S18/4",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "An area-efficient implementation of a fast-converging
square-root algorithm is presented. The design of
special arithmetic operations differs in many ways from
the traditional tasks that digital designers are used
to, and the role of \ldots{}",
}
@Article{Wachspress:2000:EEF,
author = "E. L. Wachspress",
title = "Evaluating elliptic functions and their inverses",
journal = j-COMPUT-MATH-APPL,
volume = "39",
number = "3--4",
pages = "131--136",
month = feb,
year = "2000",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/S0898-1221(99)00339-9",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:06 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122199003399",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "arithmetic-geometric mean (AGM)",
}
@Book{Wall:2000:ATC,
author = "H. S. Wall",
title = "Analytic Theory of Continued Fractions",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xiii + 433",
year = "2000",
ISBN = "0-8218-2106-7",
ISBN-13 = "978-0-8218-2106-0",
LCCN = "QA295 .W28 2000",
bibdate = "Thu Apr 3 20:24:06 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
note = "This is a reprint of the definitive, and widely cited,
treatise first published in 1948.",
acknowledgement = ack-nhfb,
remark = "Originally published: New York: D. Van Nostrand Co.,
1948.",
shorttableofcontents = "Preface \\
Introduction \\
Part I: Convergence Theory \\
I: The Continued fraction as a Product of Linear
Fractional Transformations \\
II: Convergence Theorems \\
III: Convergence of Continued Fractions Whose Partial
Denominators Are Equal to Unity \\
IV: Introduction to the Theory of Positive Definite
Continued Fractions \\
V: Some General Convergence Theorems \\
VI: Stieltjes Type Continued Fractions \\
VII: Extensions of the Parabola Theorem \\
VIII: The Value Region Problem \\
Part II: Function Theory \\
IX: J-Fraction Expansions for Rational Functions \\
X: Theory of Equations \\
XI: J-Fraction Expansions for Power Series \\
XII: Matrix Theory of Continued Fractions \\
XIII: Continued Fractions and Definite Integrals \\
XIV: The Moment Problem for a Finite Interval \\
XV: Bounded Analytic Functions \\
XVI: Hausdorff Summability \\
XVII: The Moment Problem for an Infinite Interval \\
XVIII: The Continued Fraction of Gauss \\
XIX: Stieltjes Summability \\
XX: The Pad{\'e} Table \\
Bibliography \\
Index",
subject = "Continued fractions",
tableofcontents = "Preface / vi \\
Introduction / 1 \\
Part I: Convergence Theory \\
\\
I: The Continued fraction as a Product of Linear
Fractional Transformations \\
1. Definitions and Formulas / 13 \\
2. Continued Fractions and Series / 17 \\
3. Equivalence Transformations / 19 \\
4. Even and Odd Parts of a Continued Fraction / 20 \\
\\
II: Convergence Theorems \\
5. Some General Remarks on the Convergence Problem / 25
\\
6. Necessary Conditions for Convergence / 27 \\
7. A Sufficient Condition for Convergence / 33 \\
8. Convergence of Periodic Continued Fractions / 35 \\
\\
III: Convergence of Continued Fractions Whose Partial
Denominators Are Equal to Unity \\
9. The First Interpretation of the Fundamental
Inequalities / 40 \\
10. Worpitzky's Theorem / 42 \\
11. Convergence of Continued Fractions Whose Partial
Quotients Are of the Form $(1 - g_{p - 1}) g_p x_p / 1$
/ 45 \\
12. A Convergence Theorem of von Koch / 50 \\
13. Second Interpretation of the Fundamental
Inequalities / 52 \\
14. The Parabola Theorem / 56 \\
15. ``Convergence Neighborhoods'' of a Point (1) / 62
\\
\\
IV: Introduction to the Theory of Positive Definite
Continued Fractions \\
16. Definition of a Positive Definite Continued
Fraction / 64 \\
17. The Nest of Circles / 170 \\
18. Positive Definite Continued Fractions and the
Parabola Theorem / 175 \\
19. Chain Sequences / 19 \\
20. Quadratic Forms and Chain Sequences / 86 \\
\\
V: Some General Convergence Theorems \\
21. Schwarz's Inequality / 95 \\
22. The Theorem of Invariability / 96 \\
23. The Indeterminate Case / 99 \\
24. Convergence Continuation Theorem / 104 \\
25. The Determinate Case / 109 \\
26. Bounded J-fractions / 110 \\
27. Real J-fractions / 114 \\
\\
VI: Stieltjes Type Continued Fractions \\
28. Convergence and Divergence of the Continued
Fraction of Stieltjes / 118 \\
29. The Condition (H) / 122 \\
30. Three Convergence Theorems / 131 \\
\\
VII: Extensions of the Parabola Theorem \\
31. A Family of Parabolic Domains / 135 \\
32. ``Convergence Neighborhoods'' of a Point (2) / 137
\\
33. A Theorem of Van Vleck / 138 \\
34. The Cardioid Theorem / 140 \\
35. An Extension of a Theorem of Sz{\'a}sz / 143 \\
\\
VIII: The Value Region Problem \\
36. A Sufficient Condition / 147 \\
37. The Two-Circle Theorem / 148 \\
38. Circular Element Regions with Centers at the Origin
/ 150 \\
39. A Family of Parabolic Element Regions / 152 \\
\\
Part II: Function Theory \\
\\
IX: J-Fraction Expansions for Rational Functions \\
40. The Expansion Algorithm / 161 \\
41. Conditions Involving Determinants / 164 \\
42. Relationship Between the J-fraction and the Power
Series for $f_1 / f_0$ / 166 \\
43. Rational Fractions with Simple Poles and Positive
Residues / 167 \\
44, Expansion of Rational Functions into Stieltjes Type
Continued Fractions / 170 \\
\\
X: Theory of Equations \\
45. The Test-Fraction / 174 \\
46. Polygonal Bounds for the Roots of a Polynomial /
176 \\
47. Polynomials Whose Roots Are in a Given Half-Plane /
178 \\
48. Determination of the Number of Roots of P(z) in
Each of the Half Planes R(z) 20 / 182 \\
49. Computation of the Roots of Polynomials / 185 \\
\\
XI: J-Fraction Expansions for Power Series \\
50. Polynomials Orthogonal Relative to a Sequence / 192
\\
51. Algorithm for Expanding a Power Series into a
J-fraction / 196 \\
52. Stieltjes Type Continued Fraction Expansions for
Power Series / 200 \\
53. Stieltjes' Expansion Theorem / 202 \\
54. Convergence Questions 208 \\
\\
XII: Matrix Theory of Continued Fractions \\
55. Linear Forms / 214 \\
56. Bilinear Forms / 216 \\
57. Bounded Matrices / 218 \\
58. Bounded Reciprocals of Bounded Matrices / 223 \\
59. The Bounded Reciprocal of a Bounded J-matrix / 226
\\
60. Reciprocals of an Arbitrary J-matrix / 228 \\
61. Reciprocals of the J-matrix Associated with a
Positive Definite J-fraction / 230 \\
62. Estimates for the Equivalent Functions / 235 \\
XIII: Continued Fractions and Definite Integrals \\
63. The Stieltjes Integral / 239 \\
64. Sequences of Stieltjes Integrals / 245 \\
65. The Stieltjes Inversion Formula / 247 \\
66. Representation of an Equivalent Function of a
Positive Definite J-fraction as a Stieltjes Transform /
250 \\
67. Proper Equivalent Functions / 254 \\
\\
XIV: The Moment Problem for a Finite Interval \\
68. Formulation of the Problem / 258 \\
69. Solution of the Moment Problem by Means of
S-fractions / 260 \\
70. Some Geometry / 263 \\
71. Totally Monotone Sequences / 267 \\
72. Composition of Moment Sequences / 269 \\
\\
XV: Bounded Analytic Functions \\
73. Integral Formulas for Bounded Analytic Functions /
275 \\
74. Continued Fraction Expansions for Real Analytic
Functions / 278 \\
75. Continued Fraction Expansions for $1/G(z)$ and for
$G[-z / (1 + z)]$ in Terms of the Expansions for $G(z)$
/ 280 \\
76. Condition for $G(z)/\sqrt{1 + z}$ to Be Bounded in
the Unit Circle / 283 \\
77. Analytic Functions Bounded in the Unit Circle / 285
\\
78. Continued Fraction Expansions for Arbitrary
Functions Which Are Analytic and Have Positive Real
Parts in $\Ext(-1, -\infty)$ / 288 \\
\\
XVI: Hausdorff Summability \\
79. Hausdorff Matrices / 302 \\
80. A Theorem on $(A, d_n)$-Transformations / 304 \\
81. Hausdorff Means / 306 \\
82. Examples of Hausdorff Means / 309 \\
83. The Hausdorff Inclusion Problem / 310 \\
\\
XVII: The Moment Problem for an Infinite Interval \\
84. Asymptotic Expressions for J-fractions / 316 \\
85. A Theorem of Hamburger / 321 \\
86. The Moment Problem for the Interval $(-\infty,
+\infty)$ / 325 \\
87. The Stieltjes Moment Problem / 327 \\
88. A Theorem of Carleman / 330 \\
\\
XVIII: The Continued Fraction of Gauss \\
89. General Properties / 335 \\
90. Elementary Functions / 342 \\
91. Certain Meromorphic Functions / 347 \\
92. A Class of Divergent Series / 349 \\
\\
XIX: Stieltjes Summability \\
93. Definition and Illustrative Examples / 362 \\
94. List of Expansion Formulas / 369 \\
\\
XX: The Pad{\'e} Table \\
95. Definitions / 37 \\
96. The Normal Pad{\'e} Table / 379 \\
97. The Pad{\'e} Table for the Series of Stieltjes /
389 \\
98. General Theorems on the Pad{\'e} Table / 393 \\
99. C-fractions / 399 \\
100. Regular C-fractions and Power Series / 405 \\
101. $\alpha$-regular C-fractions / 409 \\
102. Concluding Remarks on the Pad{\'e} Table / 410 \\
\\
Bibliography / 417 \\
Index / 427",
xxauthor = "H. S. (Hubert Stanley) Wall",
}
@TechReport{Zimmermann:2000:PGF,
author = "Paul Zimmermann",
title = "A proof of {GMP} fast division and square root
implementations",
type = "Technical report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "14",
month = sep,
year = "2000",
bibdate = "Sun Sep 10 08:48:46 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz",
abstract = "This short note gives a detailed correctness proof of
fast (i.e., subquadratic) versions of the GNU MP {\tt
mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions,
together with complete GMP code. The {\tt
mpn\_bz\_divrem\_n} function divides (with remainder) a
number of $ 2 n $ limbs by a divisor of $n$ limbs in $
2 K(n) $, where $ K(n) $ is the time spent in a $ (n
\times n) $ multiplication, using the
Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm.
The {\tt mpn\_sqrtrem} computes the square root and the
remainder of a number of $ 2 n $ limbs (square root and
remainder have about $n$ limbs each) in time $ 3 K(n) /
2 $; it uses Karatsuba Square Root.",
acknowledgement = ack-nhfb,
}
@Book{Arfken:2001:MMP,
author = "George B. (George Brown) Arfken and Hans-Jurgen
Weber",
title = "Mathematical methods for physicists",
publisher = "Harcourt/Academic Press",
address = "San Diego, CA, USA",
edition = "Fifth",
pages = "xiv + 1112",
year = "2001",
ISBN = "0-12-059825-6, 0-12-059826-4",
ISBN-13 = "978-0-12-059825-0, 978-0-12-059826-7",
LCCN = "QA37.3 .A74 2001",
MRclass = "00A06, 15-01, 26-01, 30-01, 34-01, 35-01, 65-01",
bibdate = "Wed Mar 15 06:50:49 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/45705658.html",
acknowledgement = ack-nhfb,
author-dates = "1922--",
subject = "Mathematics; Mathematical physics; Matem{\'a}ticas;
F{\'i}sica matem{\'a}tica; Mathematical physics;
Mathematics; Wiskundige methoden; Natuurkunde;
Matem{\'a}tica; F{\'i}sica; Math{\'e}matiques; Physique
math{\'e}matique",
tableofcontents = "1: Vector Analysis / 1 \\
1.2: Rotation of the Coordinate Axes / 8 \\
1.3: Scalar or Dot Product / 13 \\
1.4: Vector or Cross Product / 19 \\
1.5: Triple Scalar Product, Triple Vector Product / 27
\\
1.6: Gradient, [down triangle, open] / 35 \\
1.7: Divergence, [down triangle, open] / 40 \\
1.8: Curl, [down triangle, open] x / 44 \\
1.9: Successive Applications of [down triangle, open] /
51 \\
1.10: Vector Integration / 55 \\
1.11: Gauss's Theorem / 61 \\
1.12: Stokes's Theorem / 65 \\
1.13: Potential Theory / 69 \\
1.14: Gauss's Law, Poisson's Equation / 80 \\
1.15: Dirac Delta Function / 84 \\
1.16: Helmholtz's Theorem / 96 \\
2: Curved Coordinates, Tensors / 103 \\
2.1: Orthogonal Coordinates / 103 \\
2.2: Differential Vector Operators / 108 \\
2.3: Special Coordinate Systems: Introduction / 113 \\
2.4: Circular Cylindrical Coordinates / 114 \\
2.5: Spherical Polar Coordinates / 121 \\
2.6: Tensor Analysis / 131 \\
2.7: Contraction, Direct Product / 137 \\
2.8: Quotient Rule / 139 \\
2.9: Pseudotensors, Dual Tensors / 141 \\
2.10: Non-Cartesian Tensors / 150 \\
2.11: Tensor Derivative Operators / 160 \\
3: Determinants and Matrices / 165 \\
3.1: Determinants / 165 \\
3.2: Matrices / 174 \\
3.3: Orthogonal Matrices / 192 \\
3.4: Hermitian Matrices, Unitary Matrices / 206 \\
3.5: Diagonalization of Matrices / 213 \\
3.6: Normal Matrices / 227 \\
4: Group Theory / 237 \\
4.1: Introduction to Group Theory / 237 \\
4.2: Generators of Continuous Groups / 242 \\
4.3: Orbital Angular Momentum / 258 \\
4.4: Angular Momentum Coupling / 263 \\
4.5: Homogeneous Lorentz Group / 275 \\
4.6: Lorentz Covariance of Maxwell's Equations / 278
\\
4.7: Discrete Groups / 286 \\
5: Infinite Series / 303 \\
5.2: Convergence Tests / 306 \\
5.3: Alternating Series / 322 \\
5.4: Algebra of Series / 325 \\
5.5: Series of Functions / 329 \\
5.6: Taylor's Expansion / 334 \\
5.7: Power Series / 346 \\
5.8: Elliptic Integrals / 354 \\
5.9: Bernoulli Numbers, Euler--Maclaurin Formula / 360
\\
5.10: Asymptotic Series / 373 \\
5.11: Infinite Products / 381 \\
6: Functions of a Complex Variable I / 389 \\
6.1: Complex Algebra / 390 \\
6.2: Cauchy--Riemann Conditions / 399 \\
6.3: Cauchy's Integral Theorem / 404 \\
6.4: Cauchy's Integral Formula / 411 \\
6.5: Laurent Expansion / 416 \\
6.6: Mapping / 425 \\
6.7: Conformal Mapping / 434 \\
7: Functions of a Complex Variable II / 439 \\
7.1: Singularities / 439 \\
7.2: Calculus of Residues / 444 \\
7.3: Dispersion Relations / 469 \\
7.4: Method of Steepest Descents / 477 \\
8: Differential Equations / 487 \\
8.1: Partial Differential Equations / 487 \\
8.2: First-Order Differential Equations / 496 \\
8.3: Separation of Variables / 506 \\
8.4: Singular Points / 516 \\
8.5: Series Solutions--Frobenius's Method / 518 \\
8.6: A Second Solution / 533 \\
8.7: Nonhomogeneous Equation--Green's Function / 548
\\
8.8: Numerical Solutions / 567 \\
9: Sturm--Liouville Theory / 575 \\
9.1: Self-Adjoint ODEs / 575 \\
9.2: Hermitian Operators / 588 \\
9.3: Gram--Schmidt Orthogonalization / 596 \\
9.4: Completeness of Eigenfunctions / 604 \\
9.5: Green's Function--Eigenfunction Expansion / 616
\\
10: Gamma-Factorial Function / 631 \\
10.1: Definitions, Simple Properties / 631 \\
10.2: Digamma and Polygamma Functions / 643 \\
10.3: Stirling's Series / 649 \\
10.4: Beta Function / 654 \\
10.5: Incomplete Gamma Function / 660 \\
11: Bessel Functions / 669 \\
11.1: Bessel Functions of the First Kind J[subscript
v](x) / 669 \\
11.2: Orthogonality / 688 \\
11.3: Neumann Functions, Bessel Functions of the Second
Kind / 694 \\
11.4: Hankel Functions / 702 \\
11.5: Modified Bessel Functions I[subscript v](x) and
K[subscript v](x) / 709 \\
11.6: Asymptotic Expansions / 716 \\
11.7: Spherical Bessel Functions / 722 \\
12: Legendre Functions / 739 \\
12.1: Generating Function / 739 \\
12.2: Recurrence Relations / 748 \\
12.3: Orthogonality / 755 \\
12.4: Alternate Definitions / 767 \\
12.5: Associated Legendre Functions / 771 \\
12.6G: Spherical Harmonics / 786 \\
12.7: Orbital Angular Momentum Operators / 792 \\
12.8: Addition Theorem for Spherical Harmonics / 796
\\
12.9: Integrals of Three Ys / 802 \\
12.10: Legendre Functions of the Second Kind / 806 \\
12.11: Vector Spherical Harmonics / 813 \\
13: Special Functions / 817 \\
13.1: Hermite Functions / 817 \\
13.2: Laguerre Functions / 828 \\
13.3: Chebyshev Polynomials / 839 \\
13.4: Hypergeometric Functions / 850 \\
13.5: Confluent Hypergeometric Functions / 855 \\
14: Fourier Series / 863 \\
14.1: General Properties / 863 \\
14.2: Advantages, Uses of Fouries Series / 870 \\
14.3: Applications of Fourier Series / 874 \\
14.4: Properties of Fourier Series / 886 \\
14.5: Gibbs Phenomenon / 893 \\
14.6: Discrete Fourier Transform / 898 \\
15: Integral Transforms / 905 \\
15.1: Integral Transforms / 905 \\
15.2: Development of the Fourier Integral / 909 \\
15.3: Fourier Transforms--Inversion Theorem / 911 \\
15.4: Fourier Transform of Derivatives / 920 \\
15.5: Convolution Theorem / 924 \\
15.6: Momentum Representation / 928 \\
15.7: Transfer Functions / 935 \\
15.8: Laplace Transforms / 938 \\
15.9: Laplace Transform of Derivatives / 946 \\
15.10: Other Properties / 953 \\
15.11: Convolution or Faltungs Theorem / 965 \\
15.12: Inverse Laplace Transform / 969 \\
16: Integral Equations / 983 \\
16.2: Integral Transforms, Generating Functions / 991
\\
16.3: Neumann Series, Separable Kernels / 997 \\
16.4: Hilbert--Schmidt Theory / 1009 \\
17: Calculus of Variations / 1017 \\
17.1: A Dependent and an Independent Variable / 1018
\\
17.2: Applications of the Euler Equation / 1023 \\
17.3: Several Dependent Variables / 1031 \\
17.4: Several Independent Variables / 1036 \\
17.5: Several Dependent and Independent Variables /
1038 \\
17.6: Lagrangian Multipliers / 1039 \\
17.7: Variation With Constraints / 1045 \\
17.8: Rayleigh--Ritz Variational Technique / 1052 \\
18: Nonlinear Methods and Chaos / 1059 \\
18.2: Logistic Map / 1060 \\
18.3: Sensitivity to Initial Conditions / 1064 \\
18.4: Nonlinear Differential Equations / 1068 \\
Appendix 1: Real Zeros of a Function / 1085 \\
Appendix 2: Gaussian Quadrature / 1089",
}
@Book{Askey:2001:SFG,
editor = "R. A. Askey and Tom H. Koornwinder and Walter J.
Schempp",
title = "Special Functions: Group Theoretical Aspects and
Applications",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxiv + 311",
year = "2001",
ISBN = "90-277-1822-9",
ISBN-13 = "978-90-277-1822-8",
LCCN = "QA1 M428 v. 18 c.2",
bibdate = "Sat Oct 30 17:58:21 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics and Its Applications",
acknowledgement = ack-nhfb,
tableofcontents = "Editor's Preface / M. Hazewinkel / vii \\
Preface / R. Askey / xi \\
Jacobi functions and analysis on noncompact semisimple
Lie groups / Tom H. Koornwinder / 1 \\
Orthogonal polynomials and Chevalley groups / Dennis
Stanton /87 \\
Special functions and group theory in theoretical
physics / L. C. Biedenharn, R. A. Gustafson, M. A.
Lohe, J. D. Louck, S. C. Milne / 129 \\
Lattice gauge theory, orthogonal polynomials and
q-Hypergeometric functions / George E. Andrews, Enrico
Onofri / 163 \\
The Laguerre calculus on the Heisenberg group / R. W.
Beals, P. C. Greiner, J. Vauthier / 189 \\
Radar ambiguity functions, nilpotent harmonic analysis,
and holomorphic theta series / Walter Schempp / 217 \\
A factorization theorem for the Fourier transform of a
separable locally compact Abelian group / Louis
Auslander / 261 \\
Band and time limiting, recursion relations and some
nonlinear evolution equations / F. Alberto Gr{\"u}nbaum
/ 271 \\
Harmonics and combinatorics / J. J. Seidel / 287 \\
Subject Index / / 305",
}
@Article{Bashagha:2001:NRS,
author = "A. E. Bashagha",
title = "Novel radix-$2$ $k$ square root module",
journal = "Circuits, Devices and Systems, IEE Proceedings [see
also IEE Proceedings G-Circuits, Devices and Systems]",
volume = "148",
number = "4",
pages = "190--196",
month = aug,
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The conventional two's complement radix-$2$ $k$ square
root algorithm requires a set of $2^k$ full precision
comparisons to generate all the $2^k$ possible values
of the partial remainder. The correct remainder is the
minimum \ldots{}",
}
@Article{Berg:2001:CMF,
author = "Christian Berg and Henrik L. Pedersen",
title = "A completely monotone function related to the Gamma
function",
journal = j-J-COMPUT-APPL-MATH,
volume = "133",
number = "1--2",
pages = "219--230",
day = "1",
month = aug,
year = "2001",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700006440",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Berry:2001:WSF,
author = "Michael Berry",
title = "Why are special functions special?",
journal = j-PHYS-TODAY,
volume = "54",
number = "4",
pages = "11--12",
month = apr,
year = "2001",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.1372098",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Sat Feb 19 13:23:33 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.physicstoday.org/resource/1/phtoad/v54/i4/p11_s1",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
}
@Article{Boisvert:2001:MM,
author = "Ronald F. Boisvert and M. J. Donahue and Daniel W.
Lozier and R. McMichael and B. W. Rust",
title = "Mathematics and Measurement",
journal = "NIST Journal of Research",
volume = "106",
number = "1",
pages = "293--313",
month = jan # "\slash " # feb,
year = "2001",
bibdate = "Fri Jul 09 06:26:11 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Boyd:2001:CFS,
author = "John Philip Boyd",
title = "{Chebyshev} and {Fourier} spectral methods",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "Second (revised).",
pages = "1375",
year = "2001",
ISBN = "0-486-41183-4 (paperback), 0-486-14192-6 (e-book)",
ISBN-13 = "978-0-486-41183-5 (paperback), 978-0-486-14192-3
(e-book)",
LCCN = "QA404.5 .B69 2001",
bibdate = "Sat Feb 17 14:05:46 MST 2024",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Dover Books on Mathematics",
URL = "http://www.freading.com/ebooks/details/r:download/ZnJlYWQ6OTc4MDQ4NjE0MTkyMzpl",
abstract = "Completely revised text focuses on use of spectral
methods to solve boundary value, eigenvalue, and
time-dependent problems, but also covers Hermite,
Laguerre, rational Chebyshev, sinc, and spherical
harmonic functions, as well as cardinal functions,
linear eigenvalue problems, matrix-solving methods,
coordinate transformations, spherical and cylindrical
geometry, and more. Includes 7 appendices and over 160
text figures.",
acknowledgement = ack-nhfb,
author-dates = "1951--",
subject = "Chebyshev polynomials; Fourier analysis; Spectral
theory (Mathematics); Polyn{\'y}omes de Tchebychev;
Analyse de Fourier; Spectre (Math{\'y}ematiques);
MATHEMATICS; General.; Chebyshev polynomials; Fourier
analysis; Spectral theory (Mathematics)",
tableofcontents = "1. Introduction \\
2. Chebyshev and Fourier Series \\
3. Galerkin and Weighted Residual Methods \\
4. Interpolation, Collocation and All That \\
5. Cardinal Functions \\
6. Pseudospectral Methods for BVPs \\
7. Linear Eigenvalue Problems \\
8. Symmetry and Parity \\
9. Explicit Time-Integration Methods \\
10. Partial Summation, the FFT and MMT \\
11. Aliasing, Spectral Blocking, and Blow-Up \\
12. Implicit Schemes and the Slow Manifold \\
13. Splitting and its Cousins \\
14. Semi-Lagrangian Advection \\
15. Matrix-Solving Methods \\
16. Coordinate Transformations \\
17. Methods for Unbounded Intervals \\
18. Spherical and Cylindrical Geometry \\
19. Special Tricks \\
20. Symbolic Calculations \\
21. The Tau Method \\
22. Domain Decomposition Methods \\
23. Books and Reviews",
}
@InProceedings{Burgess:2001:DIR,
author = "N. Burgess and C. Hinds",
booktitle = "Conference Record of the Thirty-Fifth Asilomar
Conference on Signals, Systems and Computers, 2001",
title = "Design issues in radix-$4$ {SRT} square root {\&}
divide unit",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1646--1650",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This paper introduces a number of design issues not
covered in the open literature that arose during the
design of a radix-$4$ SRT divide/square root unit for a
vector processing chip. These include compression of
the partial remainder's m.s.b.'s, \ldots{}",
}
@Book{Bustoz:2001:SFC,
editor = "Joaquin Bustoz and Mourad Ismail and S. K. (Sergei
Konstantinovich) Suslov",
title = "Special functions 2000: current perspective and future
directions",
volume = "30",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xi + 520",
year = "2001",
ISBN = "0-7923-7119-4, 0-7923-7120-8",
ISBN-13 = "978-0-7923-7119-9, 978-0-7923-7120-5",
LCCN = "QA351 .S694 2001",
bibdate = "Sat Oct 30 17:31:39 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "NATO science series. Series II, Mathematics, physics,
and chemistry",
acknowledgement = ack-nhfb,
subject = "functions, special; congresses",
tableofcontents = "Preface \\
Foreword \\
Bailey's transform, lemma, chains and tree / George E.
Andrews 1 \\
Riemann--Hilbert problems for multiple orthogonal
polynomials / Walter Van Assche, Jeffrey S. Geronimo,
Arno B. J. Kuijlaars 23 \\
Flowers which we cannot yet see growing in Ramanujan's
garden of hypergeometric series, elliptic functions and
$q$'s / Bruce C. Berndt 61 \\
Orthogonal rational functions and continued fractions
[et al.] 87 \\
Orthogonal polynomials and reflection groups / Charles
F. Dunkl 111 \\
The bispectral problem: an overview / F. Alberto
Grunbaum 129 \\
The Bochner--Krall problem: some new perspectives / Luc
Haine 141 \\
Lectures on $q$-orthogonal polynomials / Mourad E. H.
Ismail 179 \\
The Askey--Wilson function transform scheme / Erik
Koelink, Jasper V. Stokman 221 \\
Arithmetic of the partition function / Ken Ono 243 \\
The associated classical orthogonal polynomials / Mizan
Rahman 255 \\
Special functions defined by analytic difference
equations / S. N. M. Ruijsenaars 281 \\
The factorization method, self-similar potentials and
quantum algebras / V. P. Spiridonov 335 \\
Generalized eigenvalue problem and a new family of
rational functions biorthogonal on elliptic grids / V.
P. Spiridonov, A. S. Zhedanov 365 \\
Orthogonal polynomials and combinatorics / Dennis
Stanton 389 \\
Basic exponential functions on a $q$-quadratic grid /
Sergei K. Suslov 411 \\
Projection operator method for quantum groups / V. N.
Tolstoy 457 \\
Uniform asymptotic expansions / R. Wong 489 \\
Exponential asymptotics / R. Wong 505 \\
Index 519",
}
@InCollection{Corless:2001:RAE,
author = "Robert M. Corless and James H. Davenport and David J.
Jeffrey and Gurjeet Litt and Stephen M. Watt",
booktitle = "Artificial intelligence and symbolic computation
(Madrid, 2000)",
title = "Reasoning about the elementary functions of complex
analysis",
volume = "1930",
publisher = pub-SV,
address = pub-SV:adr,
pages = "115--126",
year = "2001",
MRclass = "68W30 (30C35)",
MRnumber = "MR1882755 (2002m:68126)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture Notes in Comput. Sci.",
acknowledgement = ack-nhfb,
}
@Book{Dunkl:2001:OPS,
author = "Charles F. Dunkl and Yuan Xu",
title = "Orthogonal Polynomials of Several Variables",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xv + 390",
year = "2001",
DOI = "https://doi.org/10.1017/CBO9780511565717",
ISBN = "0-511-56571-2 (e-book), 0-521-80043-9 (hardcover),
1-107-09582-4",
ISBN-13 = "978-0-511-56571-7 (e-book), 978-0-521-80043-3
(hardcover), 978-1-107-09582-3",
LCCN = "QA404.5 .D86 2001",
bibdate = "Sat Nov 11 07:30:57 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This is the first modern book on orthogonal
polynomials of several variables, which are valuable
tools used in multivariate analysis, including
approximations and numerical integration. The book
presents the theory in elegant form and with modern
concepts and notation. It introduces the general theory
and emphasizes the classical types of orthogonal
polynomials whose weight functions are supported on
standard domains such as the cube, the simplex, the
sphere and the ball. It also focuses on those of
Gaussian type, for which fairly explicit formulae
exist. The authors' approach blends classical analysis
and symmetry-group-theoretic methods.",
acknowledgement = ack-nhfb,
remark = "See also second edition \cite{Dunkl:2014:OPS}",
tableofcontents = "1. Background \\
2. Examples of Orthogonal Polynomials in Several
Variables \\
3. General Properties of Orthogonal Polynomials in
Several Variables \\
4. Root Systems and Coxeter groups \\
5. Spherical Harmonics Associated with Reflection
Groups \\
6. Classical and Generalized Classical Orthogonal
Polynomials \\
7. Summability of Orthogonal Expansions \\
8. Orthogonal Polynomials Associated with Symmetric
Groups \\
9. Orthogonal Polynomials Associated with Octahedral
Groups and Applications",
}
@Article{Eklund:2001:CEF,
author = "Neil Eklund",
title = "{CORDIC}: Elementary Function Computation Using
Recursive Sequences",
journal = j-COLLEGE-MATH-J,
volume = "32",
number = "5",
pages = "330--333",
month = nov,
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1080/07468342.2001.11921899",
ISSN = "0746-8342 (print), 1931-1346 (electronic)",
ISSN-L = "0746-8342",
bibdate = "Thu Feb 14 09:53:12 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/07468342.2001.11921899",
acknowledgement = ack-nhfb,
fjournal = "College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
https://www.jstor.org/journal/collmathj",
onlinedate = "30 Jan 2018",
}
@Article{Elbert:2001:CZB,
author = "{\'A}rp{\'a}d Elbert and Andrea Laforgia",
title = "A conjecture on the zeros of {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "133",
number = "1--2",
pages = "683--683",
day = "1",
month = aug,
year = "2001",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700007172",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Elbert:2001:SRR,
author = "{\'A}. Elbert",
title = "Some recent results on the zeros of {Bessel} functions
and orthogonal polynomials",
journal = j-J-COMPUT-APPL-MATH,
volume = "133",
number = "1--2",
pages = "65--83",
day = "1",
month = aug,
year = "2001",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270000635X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Giordano:2001:IMP,
author = "C. Giordano and A. Laforgia",
title = "Inequalities and monotonicity properties for the gamma
function",
journal = j-J-COMPUT-APPL-MATH,
volume = "133",
number = "1--2",
pages = "387--396",
day = "1",
month = aug,
year = "2001",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700006592",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Unpublished{Godfrey:2001:NCC,
author = "P. Godfrey",
title = "A Note on the Computation of the Convergent {Lanczos}
Complex Gamma Approximation",
year = "2001",
bibdate = "Mon Nov 24 21:04:40 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Unpublished Web file.",
URL = "http://my.fit.edu/~gabdo/gamma.txt",
acknowledgement = ack-nhfb,
}
@Article{Harris:2001:KFL,
author = "Frank E. Harris",
title = "On {Kryachko}'s formula for the leaky aquifer
function",
journal = j-IJQC,
volume = "81",
number = "5",
pages = "332--334",
month = "????",
year = "2001",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/1097-461X(2001)81:5<332::AID-QUA1002>3.0.CO%3B2-W",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Wed Apr 4 11:48:33 MDT 2001",
bibsource = "http://www.interscience.wiley.com/jpages/0020-7608;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ijqc2000.bib",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract/76507286/START;
http://www3.interscience.wiley.com/cgi-bin/fulltext/76507286/FILE?TPL=ftx_start;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=76507286&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Quantum Chem.",
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
}
@Article{Karatsuba:2001:ARE,
author = "Ekatherina A. Karatsuba",
title = "On the asymptotic representation of the {Euler} gamma
function by {Ramanujan}",
journal = j-J-COMPUT-APPL-MATH,
volume = "135",
number = "2",
pages = "225--240",
day = "15",
month = oct,
year = "2001",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:20 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700005860",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Lang:2001:CRR,
author = "Tom{\'a}s Lang and Elisardo Antelo",
booktitle = "Proceedings of the 15th {IEEE} Symposium on Computer
Arithmetic, 11--13 June 2001",
title = "Correctly Rounded Reciprocal Square-Root by Digit
Recurrence and Radix-$4$ Implementation",
crossref = "Burgess:2001:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "83--93",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
summary = "We present a reciprocal square-root algorithm by digit
recurrence and selection by a staircase function, and
the radix-$4$ implementation. As similar algorithms for
division and square-root, the results are obtained
correctly rounded in a \ldots{}",
}
@Article{Lether:2001:VPA,
author = "F. G. Lether",
title = "Variable Precision Algorithm for the Numerical
Computation of the {Fermi--Dirac} Function {$ F_j(x) $}
of Order $ j = - 3 / 2 $",
journal = j-J-SCI-COMPUT,
volume = "16",
number = "1",
pages = "69--79",
month = mar,
year = "2001",
CODEN = "JSCOEB",
DOI = "https://doi.org/10.1023/A:1011150530703",
ISSN = "0885-7474 (print), 1573-7691 (electronic)",
ISSN-L = "0885-7474",
bibdate = "Sat Dec 22 13:05:47 MST 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=16&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jscicomput.bib",
URL = "http://link.springer.com/content/pdf/10.1023/A%3A1011150530703;
http://www.springerlink.com/openurl.asp?genre=article&issn=0885-7474&volume=16&issue=1&spage=69-79",
acknowledgement = ack-nhfb,
fjournal = "Journal of Scientific Computing",
journal-URL = "http://link.springer.com/journal/10915",
}
@TechReport{Li:2001:LLF,
author = "Ren-Cang Li and Peter Markstein and Jon P. Okada and
James W. Thomas",
title = "The {\tt libm} library and floating-point arithmetic
for {HP-UX} on {Itanium}",
type = "Technical report",
institution = pub-HP,
address = pub-HP:adr,
pages = "??",
month = apr,
year = "2001",
bibdate = "Fri Jun 24 20:12:09 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
acknowledgement = ack-nhfb,
}
@Article{Loenko:2001:CEF,
author = "M. Yu. Loenko",
title = "Computation of elementary functions with guaranteed
accuracy",
journal = j-PROGRAMMIROVANIE,
volume = "2",
pages = "68--80",
year = "2001",
CODEN = "PROGD3",
ISSN = "0132-3474, 0361-7688",
MRclass = "65D15 (65G20)",
MRnumber = "MR1867584",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi\u\i skaya Akademiya Nauk. Programmirovanie",
}
@Article{Meyer:2001:JEF,
author = "Kenneth R. Meyer",
title = "{Jacobi} Elliptic Functions from a Dynamical Systems
Point of View",
journal = j-AMER-MATH-MONTHLY,
volume = "108",
number = "8",
pages = "729--737",
month = oct,
year = "2001",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jan 30 12:00:14 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/i346008;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2695616",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Muller:2001:CCH,
author = "Keith E. Muller",
title = "Computing the confluent hypergeometric function, {$
M(a, b, x) $}",
journal = j-NUM-MATH,
volume = "90",
number = "1",
pages = "179--196",
month = nov,
year = "2001",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s002110100285",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Feb 3 10:07:57 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/journals/00211/tocs/t1090001.htm;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2000.bib",
URL = "http://link.springer-ny.com/link/service/journals/00211/bibs/1090001/10900179.htm;
http://link.springer-ny.com/link/service/journals/00211/papers/1090001/10900179.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Nagel:2001:EHF,
author = "Bengt Nagel",
title = "An expansion of the hypergeometric function in
{Bessel} functions",
journal = j-J-MATH-PHYS,
volume = "42",
number = "12",
pages = "5910--5914",
month = dec,
year = "2001",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Thu Mar 28 19:47:21 MST 2002",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Plagianakos:2001:LCP,
author = "V. P. Plagianakos and N. K. Nousis and M. N.
Vrahatis",
title = "Locating and computing in parallel all the simple
roots of special functions using {PVM}",
journal = j-J-COMPUT-APPL-MATH,
volume = "133",
number = "1--2",
pages = "545--554",
day = "1",
month = aug,
year = "2001",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00675-0",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700006750",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Plofker:2001:EIT,
author = "Kim Plofker",
title = "The {``Error''} in the {Indian} ``{Taylor} Series
Approximation'' to the Sine",
journal = j-HIST-MATH,
volume = "28",
number = "4",
pages = "283--295",
month = nov,
year = "2001",
CODEN = "HIMADS",
DOI = "https://doi.org/10.1006/hmat.2001.2331",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Jun 26 06:20:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086001923316",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860",
}
@Article{Rabi:2001:OCA,
author = "J. A. Rabi and M. J. S. de Lemos",
title = "Optimization of convergence acceleration in multigrid
numerical solutions of conductive-convective problems",
journal = j-APPL-MATH-COMP,
volume = "124",
number = "2",
pages = "215--226",
day = "25",
month = oct,
year = "2001",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sun Nov 18 09:58:00 MST 2001",
bibsource = "http://www.elsevier.com/locate/issn/00963003;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "convergence acceleration",
}
@Article{Rahavachary:2001:LSS,
author = "Saty Rahavachary",
title = "Letters: Setting the {\tt sqrt()} record straight",
journal = j-DDJ,
volume = "26",
number = "4",
pages = "12--12",
month = apr,
year = "2001",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Mar 13 15:22:36 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ddj.com/",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Rappoport:2001:CVP,
author = "J. M. Rappoport",
title = "Canonical vector polynomials for the computation of
complex order {Bessel} functions with the tau method",
journal = j-COMPUT-MATH-APPL,
volume = "41",
number = "3--4",
pages = "399--406",
month = feb,
year = "2001",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:14 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122100002820",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Rump:2001:RPS,
author = "Siegfried M. Rump",
title = "Rigorous and Portable Standard Functions",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "3",
pages = "540--562",
month = jun,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021971313412",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540",
abstract = "Today's floating point implementations of elementary
transcendental functions are usually very accurate.
However, with few exceptions, the actual accuracy is
not known. In the present paper we describe a rigorous,
accurate, fast and portable implementation of the
elementary standard functions based on some existing
approximate standard functions. The scheme is outlined
for IEEE 754, but not difficult to adapt to other
floating point formats. A Matlab implementation is
available on the net. Accuracy of the proposed
algorithms can be rigorously estimated. As an example
we prove that the relative accuracy of the exponential
function is better than 2.07 eps in a slightly reduced
argument range (eps denoting the relative rounding
error unit). Otherwise, extensive computational tests
suggest for all elementary functions and all suitable
arguments an accuracy better than about 3 eps.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "elementary functions; floating-point arithmetic",
}
@Article{Smith:2001:AFS,
author = "David M. Smith",
title = "{Algorithm 814}: {Fortran 90} software for
floating-point multiple precision arithmetic, gamma and
related functions",
journal = j-TOMS,
volume = "27",
number = "4",
pages = "377--387",
month = dec,
year = "2001",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Mar 13 08:49:29 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Book{Srivastava:2001:SAZ,
author = "H. M. Srivastava and Choi Junesang",
title = "Series Associated with the Zeta and Related
Functions",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "ix + 388",
year = "2001",
DOI = "https://doi.org/10.1007/978-94-015-9672-5",
ISBN = "0-7923-7054-6",
ISBN-13 = "978-0-7923-7054-3",
LCCN = "QA351 .S74 2001",
bibdate = "Wed Jun 10 16:22:26 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0822/2001035764-d.html;
http://www.loc.gov/catdir/enhancements/fy0822/2001035764-t.html",
acknowledgement = ack-nhfb,
subject = "Functions, Zeta; Series",
tableofcontents = "Acknowledgements / ix \\
1. Introduction and Preliminaries \\
1.1. Gamma and Beta functions / 1 \\
1.2. Polygamma functions / 13 \\
1.3. The multiple Gamma functions / 24 \\
1.4. The Gaussian hypergeometric function and its
generalization / 44 \\
1.5. Stirling numbers of the first and second kind / 56
\\
1.6. Bernoulli and Euler polynomials and numbers / 59
\\
Problems / 67 \\
2. The Zeta and Related Functions \\
2.1. Multiple Hurwitz Zeta functions / 77 \\
2.2. The Hurwitz (or generalized) Zeta function / 88
\\
2.3. The Riemann Zeta function / 96 \\
2.4. Polylogarithm functions / 106 \\
2.5. Hurwitz--Lerch Zeta functions / 121 \\
Problems / 128 \\
3. Series Involving Zeta Functions \\
3.1. Historical introduction / 142 \\
3.2. Use of the Binomial theorem / 143 \\
3.3. Use of generating functions / 152 \\
3.4. Use of multiple Gamma functions / 159 \\
3.5. Use of hypergeometric identities / 250 \\
3.6. Other methods and their applications / 260 \\
Problems / 269 \\
4. Evaluations and Series Representations \\
4.1. Evaluation of $\zeta(2n)$ / 275 \\
4.2. Rapidly convergent series for $\zeta(2n + 1)$ /
280 \\
4.3. Further series representations / 289 \\
4.4. Computational results / 295 \\
Problems / 304 \\
5. Determinants of the Laplacians \\
5.1. The $n$-dimensional problem / 315 \\
5.2. Computations using the simple and multiple Gamma
functions / 318 \\
5.3. Computations using series of Zeta functions / 325
\\
5.4. Remarks and observations / 328 \\
Problems / 329 \\
6. Miscellaneous Results \\
6.1. Bernoulli and Euler polynomials at rational
arguments / 335 \\
6.2. Closed-form summation of trigonometric series /
341 \\
6.3. Integrals associated with the use of the
Euler--Maclaurin summation formula / 344 \\
Problems / 350 \\
Bibliography / 353 \\
Author Index / 379 \\
Subject Index / 383",
}
@InProceedings{Takagi:2001:HAC,
author = "N. Takagi",
booktitle = "Proceedings of the 15th {IEEE} Symposium on Computer
Arithmetic, 11--13 June 2001",
title = "A Hardware Algorithm for Computing Reciprocal Square
Root",
crossref = "Burgess:2001:ISC",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "94--100",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
summary = "A hardware algorithm for computing the reciprocal
square root which appears frequently in multimedia and
graphics applications is proposed. The reciprocal
square root is computed by iteration of
carry-propagation-free additions, shifts, and
\ldots{}",
}
@Article{Thorsley:2001:AEH,
author = "Michael D. Thorsley and Marita C. Chidichimo",
title = "An asymptotic expansion for the hypergeometric
function {$_2 F_1 (a, b; c; x)$}",
journal = j-J-MATH-PHYS,
volume = "42",
number = "4",
pages = "1921--1930",
month = apr,
year = "2001",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Wed Apr 18 05:33:53 MDT 2001",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Verdonk:2001:PRIa,
author = "Brigitte Verdonk and Annie Cuyt and Dennis
Verschaeren",
title = "A precision- and range-independent tool for testing
floating-point arithmetic {I}: {Basic} operations,
square root, and remainder",
journal = j-TOMS,
volume = "27",
number = "1",
pages = "92--118",
month = mar,
year = "2001",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/382043.382404",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://doi.acm.org/10.1145/382043.382404;
http://www.win.ua.ac.be/~cant/ieeecc754.html",
abstract = "This paper introduces a precision- and
range-independent tool for testing the compliance of
hardware or software implementations of
(multiprecision) floating-point arithmetic with the
principles of the IEEE standards 754 and 854. The tool
consists of a driver program, offering many options to
test only specific aspects of the IEEE standards, and a
large set of test vectors, encoded in a
precision-independent syntax to allow the testing of
basic and extended hardware formats as well as
multiprecision floating-point implementations. The
suite of test vectors stems on one hand from the
integration and fully precision- and range-independent
generalization of existing hardware test sets, and on
the other hand from the systematic testing of exact
rounding for all combinations of round and sticky bits
that can occur. The former constitutes only 50\% of the
resulting test set. In the latter we especially focus
on hard-to-round cases. In addition, the test suite
implicitly tests properties of floating-point
operations, following the idea of Paranoia, and it
reports which of the three IEEE-compliant underflow
mechanisms is used by the floating-point implementation
under consideration. We also check whether that
underflow mechanism is used consistently. The tool is
backward compatible with the UCBTEST package and with
Coonen's test syntax.",
accepted = "23 February 2001",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "arithmetic; floating-point; floating-point testing;
IEEE floating-point standard; multiprecision;
validation; Verification",
subject = "Primary Classification: G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
arithmetic\\
Additional Classification: D. Software D.3 PROGRAMMING
LANGUAGES D.3.0 General Subjects: Standards",
}
@Article{Weniger:2001:IID,
author = "Ernst Joachim Weniger",
title = "Irregular input data in convergence acceleration and
summation processes: {General} considerations and some
special {Gaussian} hypergeometric series as model
problems",
journal = j-COMP-PHYS-COMM,
volume = "133",
number = "2--3",
pages = "202--228",
day = "15",
month = jan,
year = "2001",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(00)00175-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Dec 01 09:12:48 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
keywords = "convergence acceleration",
remark = "This paper concentrates on $_2 F_1 (a, b; c; z)$.",
}
@InProceedings{Zheng:2001:ARE,
author = "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
booktitle = "Proceedings of the 4th International Conference on
{ASIC}",
title = "The application of redundant encoding in iterative
implementation of division and square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "603--606",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "The purpose of this paper is to discuss the speed
improvement in division and square root computation
with small area penalty. The digit recurrence SRT
algorithm and functional iteration Newton--Raphson
algorithm are generally used in modern \ldots{}",
}
@Misc{Ziv:2001:APM,
author = "Abraham Ziv and Moshe Olshansky and Ealan Henis and
Anna Reitman",
title = "Accurate Portable Mathematical Library ({IBM
APMathLib})",
howpublished = "World-Wide Web document",
publisher = pub-IBM,
address = pub-IBM:adr,
day = "20",
month = dec,
year = "2001",
bibdate = "Wed Nov 24 08:06:54 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
http://oss.software.ibm.com/mathlib/",
acknowledgement = ack-nhfb,
}
@Article{Al-Jarrah:2002:GSB,
author = "A. Al-Jarrah and K. M. Dempsey and M. L. Glasser",
title = "Generalized series of {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "143",
number = "1",
pages = "1--8",
day = "1",
month = jun,
year = "2002",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:28 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042701005052",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Bertot:2002:PGS,
author = "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
title = "A Proof of {GMP} Square Root",
journal = j-J-AUTOM-REASON,
volume = "29",
number = "3--4",
pages = "225--252",
month = sep,
year = "2002",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1023/A:1021987403425",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Sat Feb 08 08:59:09 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "https://link.springer.com/article/10.1023/A:1021987403425",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
keywords = "GNU Multiple Precision library",
}
@InCollection{Boisvert:2002:HMF,
author = "Ronald F. Boisvert and Daniel W. Lozier",
title = "Handbook of Mathematical Functions",
crossref = "Lide:2002:CEM",
pages = "135--139",
year = "2002",
bibdate = "Fri Jul 09 06:28:13 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Also printed as NIST Special Publication 958, Jan.
2001.",
URL = "https://nvlpubs.nist.gov/nistpubs/sp958-lide/135-139.pdf;
https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/135-139.html",
acknowledgement = ack-nhfb,
remark = "This article describes the history of the creation of
the famous 1964 book by Milton Abramowitz and Irene
Stegun named in the title.",
}
@Article{Bradford:2002:RAE,
author = "Russell Bradford and Robert M. Corless and James H.
Davenport and David J. Jeffrey and Stephen M. Watt",
title = "Reasoning about the elementary functions of complex
analysis",
journal = j-ANN-MATH-ARTIF-INTELL,
volume = "36",
number = "3",
pages = "303--318",
year = "2002",
CODEN = "AMAIEC",
ISSN = "1012-2443 (print), 1573-7470 (electronic)",
ISSN-L = "1012-2443",
MRclass = "30-01 (03B35 68W30)",
MRnumber = "MR1950025 (2003m:30001)",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Artificial intelligence and symbolic computation
(Madrid, 2000)",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematics and Artificial Intelligence",
journal-URL = "http://link.springer.com/journal/10472",
}
@InProceedings{Bradford:2002:TBS,
author = "Russell Bradford and James H. Davenport",
booktitle = "Proceedings of the 2002 International Symposium on
Symbolic and Algebraic Computation",
title = "Towards better simplification of elementary
functions",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "16--22 (electronic)",
year = "2002",
MRclass = "68W30 (33B10)",
MRnumber = "MR2035228",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Bryc:2002:UAR,
author = "W. Bryc",
title = "A uniform approximation to the right normal tail
integral",
journal = j-APPL-MATH-COMP,
volume = "127",
number = "2--3",
pages = "365--374",
day = "15",
month = apr,
year = "2002",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(01)00015-7",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Feb 27 08:48:29 MST 2002",
bibsource = "http://www.elsevier.com/locate/issn/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.elsevier.com/gej-ng/10/9/12/123/27/44/abstract.html;
http://www.sciencedirect.com/science/article/pii/S0096300301000157",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Ceberio:2002:HRI,
author = "M. Ceberio and L. Granvilliers",
title = "{Horner}'s Rule for Interval Evaluation Revisited",
journal = j-COMPUTING,
volume = "69",
number = "1",
pages = "51--81",
month = mar,
year = "2002",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-002-1448-y",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Nov 5 07:12:39 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/journals/00607/tocs/t2069001.htm;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.de/link/service/journals/00607/bibs/2069001/20690051.htm;
http://link.springer.de/link/service/journals/00607/papers/2069001/20690051.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "interval arithmetic; number of multiplications to
evaluate a polynomial",
}
@InProceedings{Chiani:2002:IEB,
author = "M. Chiani and D. Dardari",
booktitle = "Global Telecommunications Conference, 2002. {GLOBECOM
'02}. {IEEE}",
title = "Improved exponential bounds and approximation for the
{$Q$}-function with application to average error
probability computation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
year = "2002",
DOI = "https://doi.org/10.1109/glocom.2002.1188428",
bibdate = "Sat Dec 16 16:54:47 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/1188428/",
acknowledgement = ack-nhfb,
}
@Article{Fabijonas:2002:LMC,
author = "Bruce R. Fabijonas",
title = "{Laplace}'s method on a computer algebra system with
an application to the real valued modified {Bessel}
functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "146",
number = "2",
pages = "323--342",
day = "15",
month = sep,
year = "2002",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:30 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042702003643",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Gautschi:2002:GQA,
author = "W. Gautschi",
title = "{Gauss} quadrature approximations to hypergeometric
and confluent hypergeometric functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "139",
number = "1",
pages = "173--187",
day = "1",
month = feb,
year = "2002",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "33F05 (33C05 33C15 65D20)",
MRnumber = "MR1876879 (2002m:33029)",
bibdate = "Thu Dec 01 09:11:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
remark = "The paper treats ordinary and confluent hypergeometric
functions $_2 F_1$ and $_1 F_1$, using their integral
representations to obtain Gaussian quadrature rules.",
}
@Article{Gil:2002:AAB,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77}
routines for the computation of complex {Airy}
functions",
journal = j-TOMS,
volume = "28",
number = "3",
pages = "325--336",
month = sep,
year = "2002",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/569147.569150",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 9 11:16:50 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Two Fortran 77 routines for the evaluation of Airy
functions of complex arguments $ A i(z) $, $ B i(z) $
and their derivatives are presented. The routines are
based on the use of Gaussian quadrature, Maclaurin
series and asymptotic expansions. Comparison with a
previous code by D. E. Amos (ACM TOMS 12 (1986)) is
provided.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gil:2002:AGH,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77
routines for the computation of complex {Scorer}
functions",
journal = j-TOMS,
volume = "28",
number = "4",
pages = "436--447",
month = dec,
year = "2002",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/592843.592847",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Mar 28 08:17:55 MST 2003",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Two Fortran 77 routines for the evaluation of Scorer
functions of complex arguments $ G i(z) $, $ H i(z) $
and their derivatives are presented. The routines are
based on the use of quadrature, Maclaurin series and
asymptotic expansions. For real $z$ comparison with a
previous code by A. J. Macleod (J. Comput. Appl. Math.
53 (1994)) is provided.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@TechReport{Gil:2002:CSF,
author = "A. Gil and J. Segura and N. M. Temme",
title = "Computing special functions by using quadrature
rules",
type = "Report",
number = "MAS-R0230",
institution = pub-CWI,
address = pub-CWI:adr,
pages = "11",
year = "2002",
LCCN = "QA9.A1 R426 MAS-R0230",
bibdate = "Sat Oct 30 19:13:12 2010",
bibsource = "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Gil:2003:CSF}.",
acknowledgement = ack-nhfb,
}
@Article{Gil:2002:EMB,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Evaluation of the Modified {Bessel} Function of the
Third Kind of Imaginary Orders",
journal = j-J-COMPUT-PHYS,
volume = "175",
number = "2",
pages = "398--411",
day = "20",
month = jan,
year = "2002",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.2001.6894",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:12:13 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999101968949",
abstract = "The evaluation of the modified Bessel function of the
third kind of purely imaginary order $ \mathrm
{K}_{ia}(x) $ is discussed; we also present analogous
results for the derivative. The methods are based on
the use of Maclaurin series, nonoscillatory integral
representations, asymptotic expansions, and a continued
fraction method, depending on the ranges of x and a. We
discuss the range of applicability of the different
approaches considered and conclude that power series,
the continued fraction method, and the nonoscillatory
integral representation can be used to accurately
compute the function $ \mathrm {K}_{ia}(x) $ in the
range $ 0 \leq a \leq 200 $, $ 0 \leq x \leq 100 $;
using a similar scheme the derivative $ \mathrm
{K}'_{ia(x)} $ can also be computed within these
ranges.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Gray:2002:ARE,
author = "Norman Gray",
title = "Automatic reduction of elliptic integrals using
{Carlson}'s relations",
journal = j-MATH-COMPUT,
volume = "71",
number = "237",
pages = "311--318",
month = jan,
year = "2002",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Thu Jan 31 06:16:28 MST 2002",
bibsource = "http://www.ams.org/mcom/2002-71-237;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-01-01333-3;
http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.dvi;
http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.pdf;
http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.ps;
http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.tex",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Hassenpflug:2002:EAS,
author = "W. C. Hassenpflug",
title = "Error analysis in the series evaluation of the
exponential type integral {$ e^z E_1 (z) $}",
journal = j-COMPUT-MATH-APPL,
volume = "43",
number = "1--2",
pages = "207--266",
month = jan,
year = "2002",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:20 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122101002838",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Kilbas:2002:ARH,
author = "Anatoly A. Kilbas and Luis Rodr{\'\i}guez and Juan J.
Trujillo",
title = "Asymptotic representations for hypergeometric-{Bessel}
type function and fractional integrals",
journal = j-J-COMPUT-APPL-MATH,
volume = "149",
number = "2",
pages = "469--487",
day = "15",
month = dec,
year = "2002",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:32 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042702005629",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Book{Korenev:2002:BFT,
author = "B. G. (Boris Grigorevich) Korenev",
title = "{Bessel} Functions and Their Applications",
publisher = pub-TAYLOR-FRANCIS,
address = pub-TAYLOR-FRANCIS:adr,
pages = "ix + 276",
year = "2002",
ISBN = "0-415-28130-X (hardcover)",
ISBN-13 = "978-0-415-28130-0 (hardcover)",
LCCN = "QA408 .K67 2002",
bibdate = "Sat Oct 30 17:01:51 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
subject = "Bessel functions",
tableofcontents = "Part 1. Foundation of the theory of Bessel
functions \\
1. The Bessel equation \\
Properties of Bessel functions \\
2. Definite and improper integrals \\
Series in Bessel functions \\
Part 2. Applications of Bessel functions \\
3. Problems of the theory of plates and shells \\
4. Problems of the theory of oscillations,
hydrodynamics and heat transfer \\
Appendix A. Brief information on gamma functions",
xxaddress = pub-CRC:adr,
xxpublisher = pub-CRC,
}
@Book{Li:2002:SWF,
author = "Le-Wei Li and Xiao-Kang Kang and Mook-Seng Leong",
title = "Spheroidal Wave Functions in Electromagnetic Theory",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 295",
year = "2002",
ISBN = "0-471-03170-4 (hardcover)",
ISBN-13 = "978-0-471-03170-3 (hardcover)",
LCCN = "QC670 .L49 2002",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley series in microwave and optical engineering",
URL = "http://www.loc.gov/catdir/bios/wiley043/2001045399.html;
http://www.loc.gov/catdir/description/wiley036/2001045399.html;
http://www.loc.gov/catdir/toc/onix07/2001045399.html",
acknowledgement = ack-nhfb,
subject = "Electromagnetic theory; Spheroidal functions",
tableofcontents = "Preface \\
Acknowledgments \\
Introduction \\
Spheroidal Coordinates and Wave Functions \\
Dyadic Green's Functions in Spheroidal Systems \\
EM Scattering by a Conducting Spheroid \\
EM Scattering by a Coated Dielectric Spheroid \\
Spheroidal Antennas \\
SAR Distributions in a Spheroidal Head Model \\
Analysis of Rainfall Attenuation Using Oblate Raindrops
\\
EM Eigenfrequencies in a Spheroidal Cavity \\
Appendix A: Expressions of Spheroidal Vector Wave
Functions \\
Appendix B: Intermediates $I_{t,\ell}^{mn}(c)$ in
Closed Form \\
Appendix C: ${\cal U}^{q(i),t}$ and ${\cal V}^{(i),t}$
Used in the Matrix Equation System \\
References \\
Index",
}
@Article{McCluskey:2002:MLF,
author = "Glen McCluskey",
title = "Math Library Functions in {C9X}",
journal = j-LOGIN,
volume = "27",
number = "2",
pages = "8--13",
month = apr,
year = "2002",
CODEN = "LOGNEM",
ISSN = "1044-6397",
bibdate = "Tue Apr 11 10:52:14 MDT 2006",
bibsource = "http://www.usenix.org/publications/login/2002-04/index.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf",
acknowledgement = ack-nhfb,
fjournal = ";login: the USENIX Association newsletter",
remark = "This is a short tutorial on some of the new math
library functions in C99.",
}
@Article{Paris:2002:EBU,
author = "R. B. Paris",
title = "Error bounds for the uniform asymptotic expansion of
the incomplete gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "147",
number = "1",
pages = "215--231",
day = "1",
month = oct,
year = "2002",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:30 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270200434X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Paris:2002:UAE,
author = "R. B. Paris",
title = "A uniform asymptotic expansion for the incomplete
gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "148",
number = "2",
pages = "323--339",
month = nov,
year = "2002",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/s0377-0427(02)00553-8",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 18 09:18:08 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See related work \cite{Paris:2016:UAE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Pineiro:2002:HRL,
author = "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera",
booktitle = "{The IEEE International Conference on
Application-Specific Systems, Architectures and
Processors, 2002. Proceedings. 17--19 July 2002}",
title = "High-radix logarithm with selection by rounding",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "101--110",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "A high-radix digit-recurrence algorithm or the
computation of the logarithm is presented in this
paper. Selection by rounding is used in iterations
j/spl ges/2, and selection by table in the first
iteration is combined with a restricted digit-set
\ldots{}",
}
@Article{Pineiro:2002:HSD,
author = "J. A. Pi{\~n}eiro and J. D. Bruguera",
title = "High-Speed Double Precision Computation of Reciprocal,
Division, Square Root, and Inverse Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "12",
pages = "1377--1388",
month = dec,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2002.1146704",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A new method for the high-speed computation of
double-precision floating-point reciprocal, division,
square root, and inverse square root operations is
presented in this paper. This method employs a
second-degree minimax polynomial approximation to
\ldots{}",
}
@Book{Samko:2002:HIT,
author = "S. G. (Stefan Grigorevich) Samko",
title = "Hypersingular Integrals and Their Applications",
volume = "5",
publisher = pub-TAYLOR-FRANCIS,
address = pub-TAYLOR-FRANCIS:adr,
pages = "xvii + 359",
year = "2002",
DOI = "https://doi.org/10.1201/9781482264968",
ISBN = "0-415-27268-8",
ISBN-13 = "978-0-415-27268-1",
LCCN = "QA403.5 .S26 2002",
bibdate = "Sat Oct 30 17:22:10 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
subject = "singular integrals",
tableofcontents = "Part 1: Hypersingular integrals \\
1: Some basics from the theory of special functions and
operator theory \\
2: The Riesz potential operator and Lizorkin type
invariant spaces $\Phi_v$ \\
3: Hypersingular integrals with constant
characteristics \\
4: Potentials and hypersingular integrals with
homogeneous characteristics \\
5: Hypersingular integrals with non-homogeneous
characteristics \\
6: Hypersingular integrals on the unit sphere \\
Part 2: Applications of hypersingular integrals \\
7: Characterization of some function spaces in terms of
hypersingular integrals \\
8: Solution of multidimensional integral equations of
the first kind with a potential type kernel \\
9: Hypersingular operators as positive fractional
powers of some operators of mathematical physics \\
10: Regularization of multidimensional integral
equations of the first kind with a potential type
kernel \\
11: Some modifications of hypersingular integrals and
their applications",
}
@InProceedings{Sawada:2002:FVD,
author = "J. Sawada",
title = "Formal verification of divide and square root
algorithms using series calculation",
crossref = "Borrione:2002:TIW",
pages = "31--49",
year = "2002",
bibdate = "Fri Jun 24 15:14:00 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sawada:2002:MVS,
author = "Jun Sawada and Ruben Gamboa",
title = "Mechanical Verification of a Square Root Algorithm
Using {Taylor}'s Theorem",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2517",
pages = "274--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Nov 30 20:58:00 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm;
http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Misc{Sebah:2002:IGF,
author = "Pascal Sebah and Xavier Gourdon",
title = "Introduction to the Gamma Function",
howpublished = "World-Wide Web document",
day = "4",
month = feb,
year = "2002",
bibdate = "Sat May 01 16:07:51 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://numbers.computation.free.fr/Constants/constants.html;
http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.ps",
acknowledgement = ack-nhfb,
}
@Article{Shore:2002:RMM,
author = "Haim Shore",
title = "Response Modeling Methodology ({RMM})-Exploring the
Properties of the Implied Error Distribution",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "31",
number = "12",
pages = "2225--2249",
year = "2002",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1081/STA-120017223",
ISSN = "0361-0926 (print), 1532-415X (electronic)",
ISSN-L = "0361-0926",
bibdate = "Wed Jan 27 05:41:30 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
}
@Article{Tornaria:2002:SRM,
author = "Gonzalo Tornar{\'\i}a",
title = "Square Roots Modulo $p$",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2286",
pages = "430--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:12 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Book{Vladimirov:2002:MTG,
author = "V. S. (Vasilii Sergeevich) Vladimirov",
title = "Methods of the Theory of Generalized Functions",
volume = "6",
publisher = pub-TAYLOR-FRANCIS,
address = pub-TAYLOR-FRANCIS:adr,
pages = "xiv + 311",
year = "2002",
DOI = "https://doi.org/10.1201/9781482288162",
ISBN = "0-415-27356-0",
ISBN-13 = "978-0-415-27356-5",
LCCN = "QC20.7.T45 V53 2002",
bibdate = "Sat Oct 30 17:22:15 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
subject = "Theory of distributions (Functional analysis);
Integral transforms; Mathematical physics",
tableofcontents = "Preface / xi \\
Symbols and Definitions / 1 \\
\\
1. Generalized Functions and their Properties / 5 \\
1. Test and Generalized Functions / 5 \\
1.1. Introduction / 5 \\
1.2. The space of test functions
$\mathcal{D}(\mathcal{O})$ / 6 \\
1.3. The space of generalized functions
$\mathcal{D}'(\mathcal{O})$ / 10 \\
1.4. The completeness of the space of generalized
functions $\mathcal{D}'(\mathcal{O})$ / 12 \\
1.5. The support of a generalized function / 13 \\
1.6. Regular generalized functions / 15 \\
1.7. Measures / 16 \\
1.8. Sochozki formulae / 19 \\
1.9. Change of variables in generalized functions / 21
\\
1.10. Multiplication of generalized functions / 23 \\
\\
2. Differentiation of Generalized Functions / 25 \\
2.1. Derivatives of generalized functions / 25 \\
2.2. The antiderivative (primitive) of a generalized
function / 27 \\
2.3. Examples / 29 \\
2.4. The local structure of generalized functions / 35
\\
2.5. Generalized functions with compact support / 36
\\
2.6. Generalized functions with point support / 37 \\
2.7. Generalized functions
$\mathcal{P}(\pi_nu|x|^{\alpha - 1})$ / 39 \\
\\
3. Direct Product of Generalized Functions / 41 \\
3.1. The definition of a direct product / 41 \\
3.2. The properties of a direct product / 43 \\
3.3. Some applications / 56 \\
3.4. Generalized functions that are smooth with respect
to some of the variables / 48 \\
\\
4. The Convolution of Generalized Functions / 50 \\
4.1. The definition of convolution / 50 \\
4.2. The properties of a convolution / 53 \\
4.3. The existence of a convolution / 57 \\
4.4. Cones in $\mathcal{R}^n$ / 59 \\
4.5. Convolution algebras $\mathcal{D}'(\Gamma+)$ and
$\mathcal{D}'(\Gamma)$ / 63 \\
4.6. Mean functions of generalized functions / 64 \\
4.7. Multiplication of generalized functions / 66 \\
4.8. Convolution as a continuous linear translation
invariant operator / 66 \\
4.9. Some applications / 68 \\
\\
5. Tempered Generalized Functions / 74 \\
5.1. The space $S$ of test (rapidly decreasing)
functions / 74 \\
5.2. The space $S'$ of tempered generalized functions /
77 \\
5.3. Examples of tempered generalized functions and
elementary operations in $S$ /' 78 \\
5.4. The structure of tempered generalized functions /
80 \\
5.5. The direct product of tempered generalized
functions / 81 \\
5.6. The convolution of tempered generalized functions
/ 82 \\
5.7. Homogeneous generalized functions / 85 \\
2. Integral Transformations of Generalized Functions /
89 \\
\\
6. The Fourier Transform of Tempered Generalized
Functions / 89 \\
6.1. The Fourier transform of test functions in $S$ /
89 \\
6.2. The Fourier transform of tempered generalized
functions / 90 \\
6.3. Properties of the Fourier transform / 92 \\
6.4. The Fourier transform of generalized functions
with compact support / 93 \\
6.5. The Fourier transform of a convolution / 94 \\
6.6. Examples / 96 \\
6.7. The Mellin transform / 109 \\
\\
7. Fourier Series of Periodic Generalized Functions /
113 \\
7.1. The definition and elementary properties of
periodic generalized functions / 113 \\
7.2. Fourier series of periodic generalized functions /
116 \\
7.3. The convolution algebra $\mathcal{D}'_T$ / 117 \\
7.4. Examples / 119 \\
\\
8. Positive Definite Generalized Functions / 121 \\
8.1. The definition and elementary properties of
positive definite generalized functions / 121 \\
8.2. The Bochner--Schwartz theorem / 123 \\
8.3. Examples / 125 \\
\\
9. The Laplace Transform of Tempered Generalized
Functions / 126 \\
9.1. Definition of the Laplace transform / 126 \\
9.2. Properties of the Laplace transform / 128 \\
9.3. Examples / 130 \\
\\
10. The Cauchy Kernel and the Transforms of
Cauchy--Bochner and Hilbert / 133 \\
10.1. The space $\mathcal{H}_s$ / 133 \\
10.2. The Cauchy kernel $\mathcal{K}_(z)$ / 138 \\
10.3. The Cauchy--Bochner transform / 144 \\
10.4. The Hilbert transform / 146 \\
10.5. Holomorphic functions of the class
$\mathcal{H}_a^{(s)}(C)$ / 147 \\
10.6. The generalized Cauchy--Bochner representation /
151 \\
\\
11. Poisson Kernel and Poisson Transform / 152 \\
11.1. The definition and properties of the Poisson
kernel / 152 \\
11.2. The Poisson transform and Poisson representation
/ 155 \\
11.3. Boundary values of the Poisson integral / 157 \\
\\
12. Algebras of Holomorphic Functions / 159 \\
12.1. The definition of the $H_+(C)$ and $H(C)$
algebras / 160 \\
12.2. Isomorphism of the algebras $S'(C*+) \sim H_+(C)$
and $S'(C*) \sim H(C)$ / 160 \\
12.3. The Paley--Wiener--Schwartz theorem and its
generalizations / 165 \\
12.4. The space $H_a(C)$ is the projective limit of the
spaces $H_{a'}(C)$ / 166 \\
12.5. The Schwartz representation / 168 \\
12.6. A generalization of the Phragmen--Lindelof
theorem / 171 \\
\\
13. Equations in Convolution Algebras / 171 \\
13.1. Divisors of unity in the $H_+(C)$ and $H(C)$
algebras / 171 \\
13.2. On division by a polynomial in the $H(C)$ algebra
/ 172 \\
13.3. Estimates for holomorphic functions with
nonnegative imaginary part in $T^C$ / 174 \\
13.4. Divisors of unity in the algebra $W(C)$ / 177 \\
13.5. Example / 177 \\
\\
14. Tauberian Theorems for Generalized Functions / 179
\\
14.1. Preliminary results / 179 \\
14.2. General Tauberian theorem / 183 \\
14.3. One-dimensional Tauberian theorems / 186 \\
14.4. Tauberian and Abelian theorems for nonnegative
measures / 187 \\
14.5. Tauberian theorems for holomorphic functions of
bounded argument / 188 \\
3. Some Applications in Mathematical Physics / 191 \\
\\
15. Differential Operators with Constant Coefficients /
191 \\
15.1. Fundamental solutions in $\mathcal{D}'$ / 191 \\
15.2. Tempered fundamental solutions / 194 \\
15.3. A descent method / 196 \\
15.4. Examples / 199 \\
15.5. A comparison of differential operators / 207 \\
15.6. Elliptic and hypoelliptic operators / 210 \\
15.7. Hyperbolic operators / 212 \\
15.8. The sweeping principle / 212 \\
\\
16. The Cauchy Problem / 213 \\
16.1. The generalized Cauchy problem for a hyperbolic
equation / 213 \\
16.2. Wave potential / 216 \\
16.3. Surface wave potentials / 220 \\
16.4. The Cauchy problem for the wave equation / 222
\\
16.5. A statement of the generalized Cauchy problem for
the heat equation / 224 \\
16.6. Heat potential / 224 \\
16.7. Solution of the Cauchy problem for the heat
equation / 228 \\
\\
17. Holomorphic Functions with Nonnegative Imaginary
Part in $T^C$ / 229 \\
17.1. Preliminary remarks / 229 \\
17.2. Properties of functions of the class
$\mathcal{P}_+(T^C)$ / 231 \\
17.3. Estimates of the growth of functions of the class
$H_+(T^C)$ / 238 \\
17.4. Smoothness of the spectral function / 240 \\
17.5. Indicator of growth of functions of the class
$\mathcal{P}_+T^C$ / 242 \\
17.6. An integral representation of functions of the
class $H_+(T^C)$ / 245 \\
\\
18. Holomorphic Functions with Nonnegative Imaginary
Part in $T^n$ / 249 \\
18.1. Lemmas / 249 \\
18.2. Functions of the classes $H_+(T^1)$ and
$\mathcal{P}_+(T^1)$ / 254 \\
18.3. Functions of the class $\mathcal{P}_+(T^n)$ / 258
\\
18.4. Functions of the class $H_+(T^n)$ / 263 \\
\\
19. Positive Real Matrix Functions in $T^C$ / 266 \\
19.1. Positive real functions in $T^C$ / 267 \\
19.2. Positive real matrix functions in $T^C$ / 269 \\
\\
20. Linear Passive Systems / 271 \\
20.1. Introduction / 271 \\
20.2. Corollaries to the condition of passivity / 273
\\
20.3. The necessary and sufficient conditions for
passivity / 277 \\
20.4. Multidimensional dispersion relations / 282 \\
20.5. The fundamental solution and the Cauchy problem /
285 \\
20.6. What differential and difference operators are
passive operators? / 287 \\
20.7. Examples / 290 \\
20.8. Quasiasymptotics of the solutions of systems of
equations in convolutions / 294 \\
\\
21. Abstract Scattering Operator / 295 \\
21.1. The definition and properties of an abstract
scattering matrix / 295 \\
21.2. A description of abstract scattering matrices /
298 \\
21.3. The relationship between passive operators and
scattering operators / 299 \\
\\
Bibliography / 303 \\
Index / 309",
}
@Article{Aarts:2003:ASF,
author = "Ronald M. Aarts and Augustus J. E. M. Janssen",
title = "Approximation of the {Struve} function {$ H_1 $}
occurring in impedance calculations",
journal = j-J-ACOUST-SOC-AM,
volume = "113",
number = "5",
pages = "2635--2637",
month = may,
year = "2003",
CODEN = "JASMAN",
DOI = "https://doi.org/10.1121/1.1564019",
ISSN = "0001-4966",
ISSN-L = "0001-4966",
bibdate = "Tue Mar 28 07:23:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Acoustical Society of America",
journal-URL = "http://scitation.aip.org/content/asa/journal/jasa",
}
@Article{Abad:2003:AEQ,
author = "J. Abad and J. Sesma",
title = "Asymptotic expansion of the quasiconfluent
hypergeometric function",
journal = j-J-MATH-PHYS,
volume = "44",
number = "4",
pages = "1723--1729",
month = apr,
year = "2003",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Tue Dec 16 11:36:01 MST 2003",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Agou:2003:SPR,
author = "Simon Joseph Agou and Marc Del{\'e}glise and
Jean-Louis Nicolas",
title = "Short Polynomial Representations for Square Roots
Modulo $p$",
journal = j-DESIGNS-CODES-CRYPTOGR,
volume = "28",
number = "1",
pages = "33--44",
month = jan,
year = "2003",
CODEN = "DCCREC",
ISSN = "0925-1022 (print), 1573-7586 (electronic)",
ISSN-L = "0925-1022",
bibdate = "Thu Dec 11 06:27:20 MST 2003",
bibsource = "http://www.wkap.nl/jrnltoc.htm/0925-1022;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Designs, codes, and cryptography",
journal-URL = "http://link.springer.com/journal/10623",
}
@Article{Alzer:2003:GHM,
author = "Horst Alzer",
title = "On {Gautschi}'s harmonic mean inequality for the gamma
function",
journal = j-J-COMPUT-APPL-MATH,
volume = "157",
number = "1",
pages = "243--249",
day = "1",
month = aug,
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042703004564",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Beaumont:2003:BSE,
author = "James Beaumont and Russell Bradford and James H.
Davenport",
booktitle = "Proceedings of the 2003 International Symposium on
Symbolic and Algebraic Computation",
title = "Better simplification of elementary functions through
power series",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "30--36 (electronic)",
year = "2003",
MRclass = "33F10 (68W30)",
MRnumber = "MR2035192 (2005e:33018)",
MRreviewer = "Ekatherina A. Karatsuba",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "A new algorithm testing the correctness of
simplifications of elementary functions in the presence
of branch cuts is proposed.",
}
@Article{Buhring:2003:PSH,
author = "Wolfgang B{\"u}hring",
title = "Partial sums of hypergeometric functions of unit
argument",
journal = j-PROC-AM-MATH-SOC,
volume = "132",
number = "2",
pages = "407--415",
month = "????",
year = "2003",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "33C20",
MRnumber = "MR2022363 (2005f:33011)",
bibdate = "Thu Dec 01 09:53:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Chiani:2003:NEB,
author = "M. Chiani and D. Dardari and M. K. Simon",
title = "New exponential bounds and approximations for the
computation of error probability in fading channels",
journal = j-IEEE-TRANS-WIREL-COMMUN,
volume = "24",
number = "5",
pages = "840--845",
month = may,
year = "2003",
CODEN = "ITWCAX",
DOI = "https://doi.org/10.1109/twc.2003.814350",
ISSN = "1536-1276 (print), 1558-2248 (electronic)",
ISSN-L = "1536-1276",
bibdate = "Sat Dec 16 15:47:42 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/1210748/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Wireless Communications",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693",
}
@TechReport{Cornea:2003:DSR,
author = "M. Cornea and J. Harrison and C. Iordache and B. Norin
and S. Story",
title = "Division, Square Root and Remainder Algorithms for the
{Intel Itanium} Architecture",
type = "Report",
institution = pub-INTEL,
address = pub-INTEL:adr,
month = nov,
year = "2003",
bibdate = "Fri Jun 24 12:05:58 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Coussement:2003:AMO,
author = "Els Coussement and Walter {Van Assche}",
title = "Asymptotics of multiple orthogonal polynomials
associated with the modified {Bessel} functions of the
first kind",
journal = j-J-COMPUT-APPL-MATH,
volume = "153",
number = "1--2",
pages = "141--149",
day = "1",
month = apr,
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:34 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042702005964",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Dominici:2003:NDS,
author = "Diego Dominici",
title = "Nested derivatives: a simple method for computing
series expansions of inverse functions",
journal = j-INT-J-MATH-MATH-SCI,
volume = "58",
pages = "3699--3715",
year = "2003",
CODEN = "????",
ISSN = "0161-1712 (print), 1687-0425 (electronic)",
ISSN-L = "0161-1712",
MRclass = "41A58 (33F10)",
MRnumber = "MR2031140 (2005f:41079)",
MRreviewer = "Tord H. Ganelius",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www2.newpaltz.edu/~dominicd/NESTED14.pdf",
abstract = "We give an algorithm to compute the series expansion
for the inverse of a given function. The algorithm is
extremely easy to implement and gives the first $N$
terms of the series. We show several examples of its
application in calculating the inverses of some special
functions.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
journal-URL = "https://www.hindawi.com/journals/ijmms/",
keywords = "error function, erf(x); incomplete beta function,
B(nu,mu,x); incomplete gamma function, gamma(nu,x);
logarithm integral, li(x); Maple; sine integral,
Si(x)",
}
@InProceedings{Ercegovac:2003:DRA,
author = "M. D. Ercegovac and J.-M. Muller",
booktitle = "Conference Record of the Thirty-Seventh Asilomar
Conference on Signals, Systems and Computers, 2003",
title = "Digit-recurrence algorithms for division and square
root with limited precision primitives",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1440--1444",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "We propose a digit-recurrence algorithm for square
root using limited-precision multipliers, adders, and
table-lookups. The algorithm, except in the
initialization, uses the digit-recurrence algorithm for
division with limited-precision primitives \ldots{}",
}
@Article{Fabijonas:2003:ACM,
author = "B. R. Fabijonas and Daniel W. Lozier and J. M.
Rappoport",
title = "Algorithms and Codes for the {Macdonald} Function:
Recent Progress and Comparisons",
journal = j-J-COMPUT-APPL-MATH,
volume = "161",
number = "1",
pages = "179--192",
month = "????",
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "33F05 (33C10 65D20)",
MRnumber = "MR2018582",
bibdate = "Fri Jul 09 06:21:51 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Galue:2003:FRG,
author = "L. Galu{\'e} and A. Al-Zamel and Shyam L. Kalla",
title = "Further results on generalized hypergeometric
functions",
journal = j-APPL-MATH-COMP,
volume = "136",
number = "1",
pages = "17--25",
day = "25",
month = mar,
year = "2003",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Jan 9 08:40:52 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Gautschi:2003:EEI,
author = "W. Gautschi and F. E. Harris and N. M. Temme",
title = "Expansions of the exponential integral in incomplete
gamma functions",
journal = j-APPL-MATH-LETT,
volume = "16",
number = "7",
pages = "1095--1099",
month = oct,
year = "2003",
CODEN = "AMLEEL",
DOI = "https://doi.org/10.1016/S0893-9659(03)90100-5",
ISSN = "0893-9659 (print), 1873-5452 (electronic)",
ISSN-L = "0893-9659",
MRclass = "33B20",
bibdate = "Wed Dec 4 10:29:43 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "1058.33002",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/08939659",
}
@Article{Gil:2003:CMB,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Computation of the modified {Bessel} function of the
third kind of imaginary orders: uniform {Airy}-type
asymptotic expansion",
journal = j-J-COMPUT-APPL-MATH,
volume = "153",
number = "1--2",
pages = "225--234",
day = "1",
month = apr,
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:34 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042702006088",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Gil:2003:CSF,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Computing Special Functions by Using Quadrature
Rules",
journal = j-NUMER-ALGORITHMS,
volume = "33",
number = "1--4",
pages = "265--275",
month = aug,
year = "2003",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Sep 29 08:37:11 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Harrison:2003:FVS,
author = "John Harrison",
title = "Formal verification of square root algorithms",
journal = j-FORM-METHODS-SYST-DES,
volume = "22",
number = "2",
pages = "143--153",
month = mar,
year = "2003",
CODEN = "FMSDE6",
DOI = "https://doi.org/10.1023/A:1022973506233",
ISSN = "0925-9856 (print), 1572-8102 (electronic)",
ISSN-L = "0925-9856",
bibdate = "Sat Feb 08 08:47:21 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib",
URL = "https://dl.acm.org/doi/abs/10.1023/A:1022973506233",
abstract = "We discuss the formal verification of some low-level
mathematical software for the Intel Itanium
architecture. A number of important algorithms have
been proven correct using the HOL Light theorem prover.
After briefly surveying some of our formal verification
work, we discuss in more detail the verification of a
square root algorithm, which helps to illustrate why
some features of HOL Light, in particular
programmability, make it especially suitable for these
applications.",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
journal-URL = "https://dl.acm.org/loi/fmsd",
}
@Misc{Intel:2003:DSR,
author = "{Intel}",
title = "Divide, Square Root, and Remainder Algorithms for the
{Itanium} Architecture",
howpublished = "Intel Software Development Products",
day = "18",
month = dec,
year = "2003",
bibdate = "Tue Nov 18 16:23:36 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm",
acknowledgement = ack-nhfb,
}
@Misc{Intel:2003:NID,
author = "{Intel}",
title = "Non-{IEEE} Division, Square Root, Reciprocal, and
Reciprocal Square Root Algorithms for the {Intel
Itanium} Architecture",
howpublished = "Intel Software Development Products",
day = "18",
month = dec,
year = "2003",
bibdate = "Tue Nov 18 16:23:36 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm",
acknowledgement = ack-nhfb,
}
@Article{Kzaz:2003:CAG,
author = "M. Kzaz and M. Pr{\'e}vost",
title = "Convergence Acceleration of {Gauss--Chebyshev}
Quadrature Formulae",
journal = j-NUMER-ALGORITHMS,
volume = "34",
number = "2--4",
pages = "379--391",
month = dec,
year = "2003",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Tue Jan 13 17:32:50 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "convergence acceleration",
}
@Article{Lang:2003:RRS,
author = "Tom{\'a}s Lang and Elisardo Antelo",
title = "Radix-$4$ Reciprocal Square-root and Its Combination
with Division and Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "9",
pages = "1100--1114",
month = sep,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1228508",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In this work, we present a reciprocal square root
algorithm by digit recurrence and selection by a
staircase function and the radix-$4$ implementation. As
in similar algorithms for division and square root, the
results are obtained correctly rounded in a
straightforward manner (in contrast to existing methods
to compute the reciprocal square root). Although,
apparently, a single selection function can only be
used for $ j \geq 2 $ (the selection constants are
different for $ j = 0 $, $ j = 1 $, and $ j \geq 2 $ ),
we show that it is possible to use a single selection
function for all iterations. We perform a rough
comparison with existing methods and we conclude that
our implementation is a low hardware complexity
solution with moderate latency, especially for exactly
rounded results. We also extend the unit to support
division and square root with the same selection
function and with slight modifications in the
initialization of the reciprocal square root unit.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Lefevre:2003:WCC,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller",
title = "Worst Cases for Correct Rounding for the Elementary
Functions in Double Precision",
type = "Technical report",
institution = "INRIA, Projet Spaces, LORIA, Campus Scientifique",
address = "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
France",
day = "14",
month = aug,
year = "2003",
bibdate = "Thu Jul 08 08:27:53 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf",
abstract = "We give the results of our search for the worst cases
for correct rounding of the major elementary functions
in double precision floating-point arithmetic. These
results allow the design of reasonably fast routines
that will compute these functions with correct
rounding, at least in some interval, for any of the
four rounding modes specified by the IEEE-754 standard.
They will also allow one to easily test libraries that
are claimed to provide correctly rounded functions.",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic; elementary functions;
floating-point arithmetic; Table Maker's Dilemma",
}
@Article{Lozier:2003:NDL,
author = "Daniel W. Lozier",
title = "{NIST Digital Library of Mathematical Functions}",
journal = j-ANN-MATH-ARTIF-INTELL,
volume = "38",
number = "1--3",
pages = "105--119",
month = may,
year = "2003",
CODEN = "AMAIEC",
ISSN = "1012-2443 (print), 1573-7470 (electronic)",
ISSN-L = "1012-2443",
bibdate = "Fri Jul 09 06:23:08 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematics and Artificial Intelligence",
journal-URL = "http://link.springer.com/journal/10472",
}
@InProceedings{Markstein:2003:FQP,
author = "Peter Markstein",
title = "A fast quad precision elementary function library for
{Itanium}",
crossref = "Anonymous:2003:CRN",
pages = "5--12",
year = "2003",
bibdate = "Fri Jun 24 20:14:39 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This talk will describe Itanium's floating point
architecture and how it has been used to produce a high
performance, highly accurate quad precision elementary
function library.\par
Itanium's floating-point features will first be
described, from the point of view of a computer
architect. Many conflicting requirements vie for
consideration during the design of a new computer
architecture. These include instruction word size,
number of registers, the set of operations, arithmetic
precisions supported, and memory access. Some of the
trade-offs during the design phase will be
discussed.\par
One of the objectives of the original Itanium design
was to accelerate quad precision arithmetic. The talk
will describe how the Itanium elementary function
library was constructed, with attention to performance
and accuracy. Because a pair of double-extended
floating point words are used for internal operations
involving quad precision numbers, intermediate results,
holding 128 bits, provide 15 guard bits during
intermediate calculations, resulting in a very low
percentage of misrounded results.",
acknowledgement = ack-nhfb,
}
@Book{Mason:2003:CP,
author = "J. C. Mason and D. C. Handscomb",
title = "{Chebyshev} Polynomials",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
pages = "xiii + 341",
year = "2003",
ISBN = "0-8493-0355-9",
ISBN-13 = "978-0-8493-0355-5",
LCCN = "QA404.5 .M37 2003",
bibdate = "Fri Apr 17 09:45:35 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Chebyshev polynomials",
tableofcontents = "1 Definitions / 1 \\
1.1 Preliminary remarks / 1 \\
1.2 Trigonometric definitions and recurrences / 1 \\
1.2.1 The first-kind polynomial $T_n$ / 2 \\
1.2.2 The second-kind polynomial $U_n$ / 3 \\
1.2.3 The third- and fourth-kind polynomials $V_n$ and
$W_n$ (the airfoil polynomials) / 5 \\
1.2.4 Connections between the four kinds of polynomial
/ 7 \\
1.3 Shifted Chebyshev polynomials / 9 \\
1.3.1 The shifted polynomials $T_n^*$, $U_n^*$,
$V_n^*$, $W_n^*$ / 9 \\
1.3.2 Chebyshev polynomials for the general range $[a,
b]$ / 11 \\
1.4 Chebyshev polynomials of a complex variable / 11
\\
1.4.1 Conformal mapping of a circle to and from an
ellipse / 12 \\
1.4.2 Chebyshev polynomials in $z$ / 14 \\
1.4.3 Shabat polynomials / 17 \\
1.5 Problems for Chapter 1 / 17 \\
2 Basic Properties and Formulae / 19 \\
2.1 Introduction / 19 \\
2.2 Chebyshev polynomial zeros and extrema / 19 \\
2.3 Relations between Chebyshev polynomials and powers
of x / 22 \\
2.3.1 Powers of $x$ in terms of $\{T_n(x)\}$ / 22 \\
2.3.2 $T_n(x)$ in terms of powers of $x$ / 23 \\
2.3.3 Ratios of coefficients in $T_n(x)$ / 25 \\
2.4 Evaluation of Chebyshev sums, products, integrals
and derivatives / 25 \\
2.4.1 Evaluation of a Chebyshev sum / 25 \\
2.4.2 Stability of the evaluation of a Chebyshev sum /
29 \\
2.4.3 Evaluation of a product / 31 \\
2.4.4 Evaluation of an integral / 32 \\
2.4.5 Evaluation of a derivative / 34 \\
6.3.1 Aliasing / 152 \\
6.3.2 Second-kind interpolation / 155 \\
6.3.3 Third- and fourth-kind interpolation / 156 \\
6.3.4 Conditioning / 158 \\
6.4 Best $\mathcal{L}_1$ approximation by Chebyshev
interpolation / 158 \\
6.5 Near-minimax approximation by Chebyshev
interpolation / 160 \\
6.6 Problems for Chapter 6 / 162 \\
7 Near-Best $\mathcal{L}_\infty$, $\mathcal{L}_1$ and
$\mathcal{L}_p$ Approximations / 165 \\
7.1 Near-best $\mathcal{L}_\infty$ (near-minimax)
approximations / 165 \\
7.1.1 Second-kind expansions in $\mathcal{L}_\infty$ /
165 \\
7.1.2 Third-kind expansions in $\mathcal{L}_\infty$ /
167 \\
7.2 Near-best $\mathcal{L}_1$ approximations / 169 \\
7.3 Best and near-best $\mathcal{L}_p$ approximations /
170 \\
7.3.1 Complex variable results for elliptic-type
regions / 172 \\
7.4 Problems for Chapter 7 / 173 \\
8 Integration Using Chebyshev Polynomials / 177 \\
8.1 Indefinite integration with Chebyshev series / 177
\\
8.2 Gauss--Chebyshev quadrature / 180 \\
8.3 Quadrature methods of Clenshaw--Curtis type / 186
\\
8.3.1 Introduction / 186 \\
8.3.2 First-kind formulae / 187 \\
8.3.3 Second-kind formulae / 189 \\
8.3.4 Third-kind formulae / 191 \\
8.3.5 General remark on methods of Clenshaw--Curtis
type / 192 \\
8.4 Error estimation for Clenshaw--Curtis methods / 192
\\
8.4.1 First-kind polynomials / 193 \\
8.4.2 Fitting an exponential curve / 195 \\
8.4.3 Other abscissae and polynomials / 196 \\
8.5 Some other work on Clenshaw--Curtis methods / 200
\\
8.6 Problems for Chapter 8 / 201 \\
9 Solution of Integral Equations / 203 \\
9.1 Introduction / 203 \\
9.2 Fredholm equations of the second kind / 204 \\
9.3 Fredholm equations of the third kind / 206 \\
9.4 Fredholm equations of the first kind / 207 \\
9.5 Singular kernels / 209 \\
9.5.1 Hilbert-type kernels and related kernels / 209
\\
9.5.2 Symm's integral equation / 212 \\
9.6 Regularisation of integral equations / 214 \\
9.6.1 Discrete data with second derivative
regularisation / 214 \\
9.6.2 Details of a smoothing algorithm (second
derivative regularisation) / 215 \\
9.6.3 A smoothing algorithm with weighted function
regularisation / 217 \\
9.6.4 Evaluation of $V(\lambda)$ / 220 \\
9.6.5 Other basis functions / 221 \\
9.7 Partial differential equations and boundary
integral equation methods / 222 \\
9.7.1 A hypersingular integral equation derived from a
mixed boundary value problem for Laplace's equation /
222 \\
9.8 Problems for Chapter 9 / 227 \\
10 Solution of Ordinary Differential Equations / 231
\\
10.1 Introduction / 231 \\
10.2 A simple example / 232 \\
10.2.1 Collocation methods / 234 \\
10.2.2 Error of the collocation method / 237 \\
10.2.3 Projection (tau) methods / 239 \\
10.2.4 Error of the preceding projection method / 241
\\
10.3 The original Lanczos tau ($\tau$) method / 242 \\
10.4 A more general linear equation / 244 \\
10.4.1 Collocation method / 244 \\
10.4.2 Projection method / 245 \\
10.5 Pseudospectral methods --- another form of
collocation / 245 \\
10.5.1 Differentiation matrices / 246 \\
10.5.2 Differentiation matrix for Chebyshev points /
247 \\
10.5.3 Collocation using differentiation matrices / 249
\\
10.6 Nonlinear equations / 251 \\
10.7 Eigenvalue problems / 252 \\
10.7.1 Collocation methods / 252 \\
10.7.2 Collocation using the differentiation matrix /
254 \\
10.8 Differential equations in one space and one time
dimension / 256 \\
10.8.1 Collocation methods / 257 \\
10.8.2 Collocation using the differentiation matrix /
258 \\
10.9 Problems for Chapter 10 / 259 \\
11 Chebyshev and Spectral Methods for Partial
Differential Equations / 261 \\
11.1 Introduction / 261 \\
11.2 Interior, boundary and mixed methods / 262 \\
11.2.1 Interior methods / 262 \\
11.2.2 Boundary methods / 263 \\
11.2.3 Mixed methods / 265 \\
11.3 Differentiation matrices and nodal representation
/ 265 \\
11.4 Method of weighted residuals / 265 \\
11.4.1 Continuous MWR / 265 \\
11.4.2 Discrete MWR --- a new nomenclature / 266 \\
11.5 Chebyshev series and Galerkin methods / 267 \\
11.6 Collocation/interpolation and related methods /
269 \\
11.7 PDE methods / 271 \\
11.7.1 Error analysis / 272 \\
11.8 Some PDE problems and various methods / 272 \\
11.8.1 Power basis: collocation for Poisson problem /
273 \\
11.8.2 Power basis: interior collocation for the
L-membrane / 275 \\
11.8.3 Chebyshev basis and discrete orthogonalisation /
278 \\
11.8.4 Differentiation matrix approach: Poisson problem
/ 281 \\
11.8.5 Explicit collocation for the quasilinear
Dirichlet problem: Chebyshev basis / 283 \\
11.9 Computational fluid dynamics / 295 \\
11.10 Particular issues in spectral methods / 296 \\
11.11 More advanced problems / 297 \\
11.12 Problems for Chapter 11 / 298 \\
12 Conclusion / 303 \\
Bibliography / 305 \\
Appendices: \\
A Biographical Note / 321 \\
B Summary of Notations, Definitions and Important
Properties / 323 \\
B.I Miscellaneous notations / 323 \\
B.2 The four kinds of Chebyshev polynomial / 325 \\
C Tables of Coefficients / 329 \\
Index / 335",
xxauthor = "J. C. Mason and D. C. (David Christopher) Handscomb",
xxURL = "http://www.loc.gov/catdir/enhancements/fy0646/2002073578-d.html",
}
@InProceedings{Meunier:2003:EAG,
author = "Ludovic Meunier and Bruno Salvy",
editor = "Hoon Hong",
booktitle = "Proceedings of the 2003 International Symposium on
Symbolic and Algebraic Computation: {Philadelphia, PA,
USA, August 3--6, 2003}",
title = "{ESF}: an automatically generated encyclopedia of
special functions",
publisher = pub-ACM,
address = pub-ACM:adr,
month = aug,
year = "2003",
DOI = "https://doi.org/10.1145/860854.860898",
ISBN = "1-58113-641-2 (paperback)",
ISBN-13 = "978-1-58113-641-8 (paperback)",
LCCN = "QA76.5 S98 2003; QA76.95.I59 2003",
bibdate = "Sat Nov 11 06:21:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "We present our on-going work on the automatic
generation of an encyclopedia of special functions on
the web, called The Encyclopedia of Special Functions
(ESF) (\url{http://algo.inria.fr/esf}). All
mathematical formulae in the ESF are computed, typeset
and displayed without any human intervention. This is
achieved by exploiting a collection of computer algebra
algorithms in a systematic way, on top of a specially
designed data structure for a class of special
functions.",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1145/860854",
book-URL = "https://dl.acm.org/doi/proceedings/10.1145/860854",
}
@Article{Ovtchinnikov:2003:CEGb,
author = "E. Ovtchinnikov",
title = "Convergence Estimates for the Generalized {Davidson}
Method for Symmetric Eigenvalue Problems {II}: The
Subspace Acceleration",
journal = j-SIAM-J-NUMER-ANAL,
volume = "41",
number = "1",
pages = "272--286",
month = feb,
year = "2003",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/S0036142902411768",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Aug 15 05:57:09 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SINUM/41/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41176",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "convergence acceleration",
}
@Article{Paris:2003:AEG,
author = "R. B. Paris",
title = "The asymptotic expansion of a generalised incomplete
gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "151",
number = "2",
pages = "297--306",
day = "15",
month = feb,
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:33 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042702008099",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Paszkowski:2003:CAS,
author = "Stefan Paszkowski",
title = "Convergence Acceleration of Some Continued Fractions",
journal = j-NUMER-ALGORITHMS,
volume = "32",
number = "2--4",
pages = "193--247",
month = apr,
year = "2003",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Sep 29 08:37:11 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "convergence acceleration",
}
@Article{Pedersen:2003:DGF,
author = "Henrik L. Pedersen",
title = "The double gamma function and related {Pick}
functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "153",
number = "1--2",
pages = "361--369",
day = "1",
month = apr,
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:34 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042702006040",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Petropoulou:2003:CZB,
author = "Eugenia N. Petropoulou and Panayiotis D. Siafarikas
and Ioannis D. Stabolas",
title = "On the common zeros of {Bessel} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "153",
number = "1--2",
pages = "387--393",
day = "1",
month = apr,
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:34 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042702006416",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Pineiro:2003:LHR,
author = "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac",
booktitle = "{ISCAS '03. Proceedings of the 2003 International
Symposium on Circuits and Systems. 25--28 May 2003}",
title = "On-line high-radix exponential with selection by
rounding",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "IV-121--IV-124",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "An on-line high-radix algorithm for computing the
exponential function (e/sup x/) with arbitrary
precision n is presented. Selection by rounding and a
redundant digit-set for the digits e/sub j/ are used,
with selection by table in the first \ldots{}",
}
@Book{Sidi:2003:PEM,
author = "Avram Sidi",
title = "Practical Extrapolation Methods: Theory and
Applications",
volume = "10",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xxii + 519",
year = "2003",
DOI = "https://doi.org/10.1017/CBO9780511546815",
ISBN = "0-521-66159-5 (hardcover), 0-511-54681-5 (e-book),
0-511-06018-1 (Adobe Reader), 0-511-06649-X (e-book)",
ISBN-13 = "978-0-521-66159-1 (hardcover), 978-0-511-54681-5
(e-book), 978-0-511-06018-2 (Adobe Reader),
978-0-511-06649-8 (e-book)",
LCCN = "QA281 .S555 2003",
bibdate = "Mon Jul 5 16:49:09 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Cambridge monographs on applied and computational
mathematics",
acknowledgement = ack-nhfb,
subject = "extrapolation",
tableofcontents = "Preface / xix--xxii \\
Introduction / 1--18 \\
I: The Richardson Extrapolation Process and Its
Generalizations / 19--20 \\
1: The Richardson Extrapolation Process / 21--41 \\
2: Additional Topics in Richardson Extrapolation /
42--56 \\
3: First Generalization of the Richardson Extrapolation
Process / 57--80 \\
4: GREP: Further Generalization of the Richardson
Extrapolation Process / 81--94 \\
5: The $D$-Transformation: A GREP for Infinite-Range
Integrals / 95--120 \\
6: The $d$-Transformation: A GREP for Infinite Series
and Sequences / 121--157 \\
7: Recursive Algorithms for GREP / 158--175 \\
8: Analytic Study of GREP(1): Slowly Varying $A(y) \in
F^{(1)}$ / 176--202 \\
9: Analytic Study of GREP(1): Quickly Varying $A(y) \in
F^{(1)}$ / 203--211 \\
10: Efficient Use of GREP(1): Applications to the
$D(1)$-, $d(1)$-, and $d(m)$-Transformations / 212--217
\\
11: Reduction of the $D$-Transformation for Oscillatory
Infinite-Range Integrals: The $\bar{D}$-, $D'$-, $W$-,
and $mW$-Transformations / 218--237 \\
12: Acceleration of Convergence of Power Series by the
$d$-Transformation: Rational $d$-Approximants /
238--252 \\
13: Acceleration of Convergence of Fourier and
Generalized Fourier Series by the $d$-Transformation:
The Complex Series Approach with APS / 253--262 \\
14: Special Topics in Richardson Extrapolation /
263--276 \\
II: Sequence Transformations / 277--278 \\
15: The Euler Transformation, Aitken 2-Process, and
Lubkin W-Transformation / 279--296 \\
16: The Shanks Transformation / 297--322 \\
17: The Pad{\'e} Table / 323--347 \\
18: Generalizations of Pad{\'e} Approximants / 348--362
\\
19: The Levin- and Sidi $S$-Transformations / 363--374
\\
20: The Wynn- and Brezinski-Algorithms / 375--383 \\
21: The $G$-Transformation and Its Generalizations /
384--389 \\
22: The Transformations of Overholt and Wimp / 390--395
\\
23: Confluent Transformations / 396--406 \\
24: Formal Theory of Sequence Transformations /
407--412 \\
III: Further Applications / 413--414 \\
25: Further Applications of Extrapolation Methods and
Sequence Transformations / 415--456 \\
IV: Appendices / 457--458 \\
A: Review of Basic Asymptotics / 459--462 \\
B: The Laplace Transform and Watson's Lemma / 463--464
\\
C: The Gamma Function / 465--466 \\
D: Bernoulli Numbers and Polynomials and the Euler
Maclaurin Formula / 467--476 \\
E: The Riemann Zeta Function and the Generalized Zeta
Function / 477--479 \\
F: Some Highlights of Polynomial Approximation Theory /
480--482 \\
G: A Compendium of Sequence Transformations / 483--487
\\
H: Efficient Application of Sequence Transformations:
Summary / 488--492 \\
I: FORTRAN 77 Program for the $d(m)$-Transformation /
493--500 \\
Bibliography / 501--514 \\
Index / 515--519",
xxURL = "http://www.loc.gov/catdir/samples/cam033/2002024669.html;
http://www.loc.gov/catdir/description/cam022/2002024669.html;
http://www.loc.gov/catdir/toc/cam024/2002024669.html",
}
@Misc{Tkachev:2003:EFI,
author = "Vladimir G. Tkachev",
title = "Elliptic functions: Introduction course",
howpublished = "Web lecture notes.",
day = "25",
month = nov,
year = "2003",
bibdate = "Wed Mar 15 08:43:21 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://users.mai.liu.se/vlatk48/teaching/lect2-agm.pdf",
acknowledgement = ack-nhfb,
tableofcontents = "Chapter 1. Elliptic integrals and Jacobi's theta
functions / 5 \\
1.1. Elliptic integrals and the AGM: real case / 5 \\
1.1.3. The arithmetic-geometric mean iteration / 7 \\
1.2. Lemniscates and elastic curves / 11 \\
1.3. Euler's addition theorem / 18 \\
1.4. Theta functions: preliminaries 5 / 24 \\
Chapter 2. General theory of doubly periodic functions
/ 31 \\
2.1. Preliminaries / 31 \\
2.2. Periods of analytic functions / 33 \\
2.3. Existence of doubly periodic functions / 36 \\
2.4. Liouville's theorems / 38 \\
2.5. The Weierstrass function $\wp(z)$ / 43 \\
2.6. Modular forms / 51 \\
Bibliography / 61",
}
@InProceedings{Wang:2003:TDF,
author = "Xiaojun Wang and B. E. Nelson",
booktitle = "{FCCM 2003}: 11th Annual {IEEE} Symposium on
Field-Programmable Custom Computing Machines, 9--11
April 2003",
title = "Tradeoffs of designing floating-point division and
square root on {Virtex FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "195--203",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "Low latency, high throughput and small area are three
major design considerations of an FPGA (field
programmable gate array) design. In this paper, we
present a high radix SRT division algorithm and a
binary restoring square root algorithm. We \ldots{}",
}
@Article{Yousif:2003:CBF,
author = "Hashim A. Yousif and Richard Melka",
title = "Computing {Bessel} functions of the second kind in
extreme parameter regimes",
journal = j-COMP-PHYS-COMM,
volume = "151",
number = "1",
pages = "25--34",
day = "1",
month = mar,
year = "2003",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(02)00697-5",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 23:41:27 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465502006975",
abstract = "A useful method of computing the integral order Bessel
functions of the second kind $ Y_n(x + i y) $ when
either, the absolute value of the real part, or the
imaginary part of the argument $ z = x + i y $ is
small, is described. This method is based on computing
the Bessel functions for extreme parameter regimes when
$ x \sim 0 $ (or $ y \sim 0 $ ) and is useful because a
number existing algorithms and methods fail to give
correct results for small $x$ or small $y$. The
approximating equations are derived by expanding the
Bessel function in Taylor series, are tested and
discussed. The present work is a continuation of the
previous one conducted in regard to the Bessel function
of the first kind. The results of our formalism are
compared to the available existing numerical methods
used in Mathematica, IMSL, MATLAB, and the Amos
library. Our numerical method is easy to implement,
efficient, and produces reliable results. In addition,
this method reduces the computation of the Bessel
functions of the second complex argument to that of
real argument which simplify the computation
considerably.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Book{Zwillinger:2003:CSM,
editor = "Daniel Zwillinger",
title = "{CRC} Standard Mathematical Tables and Formulae",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
edition = "31st",
pages = "xiv + 910",
year = "2003",
ISBN = "1-58488-291-3 (hardcover), 1-4200-3534-7 (e-book)",
ISBN-13 = "978-1-58488-291-6 (hardcover), 978-1-4200-3534-6
(e-book)",
LCCN = "QA47 .M315 2003",
bibdate = "Thu Nov 25 11:07:20 MST 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
prodorbis.library.yale.edu:7090/voyager",
acknowledgement = ack-nhfb,
subject = "mathematics; tables",
tableofcontents = "Preface \\
Contributors \\
Table of Contents \\
1 Analysis \\
2 Algebra \\
3 Discrete Mathematics \\
4 Geometry \\
5 Continuous Mathematics \\
6 Special Functions \\
7 Probability and Statistics \\
8 Scientific Computing \\
9 Financial Analysis \\
10 Miscellaneous \\
List of References \\
List of Figures \\
List of Notation \\
Index",
}
@Book{Bell:2004:SFS,
author = "W. W. (William Wallace) Bell",
title = "Special Functions for Scientists and Engineers",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xiv + 247",
year = "2004",
ISBN = "0-486-43521-0",
ISBN-13 = "978-0-486-43521-3",
LCCN = "QA351 .B4 2004",
bibdate = "Sat Oct 30 16:30:44 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Dover books on mathematics",
acknowledgement = ack-nhfb,
remark = "Reprinting of \cite{Bell:1968:SFS}.",
subject = "Functions, Special",
tableofcontents = "Preface / v List of Symbols / ix Series Solution of
Differential Equations Method of Frobenius / 1 \\
Examples / 8 \\
Problems / 21 \\
Gamma and Beta Functions Definitions / 23 \\
Properties of the beta and gamma functions / 24 \\
Definition of the gamma function for negative values of
the argument / 30 \\
Examples / 37 \\
Problems / 40 \\
Legendre Polynomials and Functions Legendre's equation
and its solution / 42 \\
Generating function for the Legendre polynomials / 46
\\
Further expressions for the Legendre polynomials / 48
\\
Explicit expressions for and special values of the
Legendre polynomials / 50 \\
Orthogonality properties of the Legendre polynomials /
52 \\
Legendre series / 55 \\
Relations between the Legendre polynomials and their
derivatives; / 58 \\
recurrence relations Associated Legendre functions / 62
\\
Properties of the associated Legendre functions / 65
\\
Legendre functions of the second kind / 70 \\
Spherical harmonics / 78 \\
Graphs of the Legendre functions / 82 \\
Examples / 85 \\
Problems / 90 \\
Bessel Functions Bessel's equation and its solutions;
Bessel functions of the first and second kind / 92 \\
Generating function for the Bessel functions / 99 \\
Integral representations for Bessel functions / 101 \\
Recurrence relations / 104 \\
Hankel functions / 107 \\
Equations reducible to Bessel's equation / 108 \\
Modified Bessel functions / 110 \\
Recurrence relations for the modified Bessel functions
/ 113 \\
Integral representations for the modified Bessel
functions / 116 \\
Kelvin's functions / 120 \\
Spherical Bessel functions / 121 \\
Behaviour of the Bessel functions for large and small
values of the argument / 127 \\
Graphs of the Bessel functions / 133 \\
Orthonormality of the Bessel functions; Bessel series /
137 \\
Integrals involving Bessel functions / 141 \\
Examples / 148 \\
Problems / 154 \\
Hermite Polynomials Hermite's equation and its solution
/ 156 \\
Generating function / 157 \\
Other expressions for the Hermite polynomials / 158 \\
Explicit expressions for, and special values of, the
Hermite polynomials / 160 \\
Orthogonality properties of the Hermite polynomials /
161 \\
Relations between Hermite polynomials and their
derivatives; recurrence relations / 162 \\
Weber--Hermite functions / 163 \\
Examples / 164 \\
Problems / 166 \\
Laguerre Polynomials Laguerre's equation and its
solution / 168 \\
Generating function / 169 \\
Alternative expression for the Laguerre polynomials /
170 \\
Explicit expressions for, and special values of, the
Laguerre polynomials / 171 \\
Orthogonality properties of the Laguerre polynomials /
172 \\
Relations between Laguerre polynomials and their
derivatives; recurrence relations / 173 \\
Associated Laguerre polynomials / 176 \\
Properties of the associated Laguerre polynomials / 177
\\
Notation / 182 \\
Examples / 182 \\
Problems / 185 \\
Chebyshev Polynomials Definition of Chebyshev
polynomials; Chebyshev's equation / 187 \\
Generating function / 190 \\
Orthogonality properties / 192 \\
Recurrence relations / 193 \\
Examples / 194 \\
Problems / 196 \\
Gegenbauer and Jacobi Polynomials Gegenbauer
polynomials / 197 \\
Jacobi polynomials / 198 \\
Examples / 200 \\
Problems / 201 \\
Hypergeometric Functions Definition of hypergeometric
functions / 203 \\
Properties of the hypergeometric function / 207 \\
Properties of the confluent hypergeometric function /
210 \\
Examples / 212 \\
Problem / 216 \\
Other Special Functions Incomplete gamma functions /
218 \\
Exponential integral and related functions / 218 \\
The error function and related functions / 221 \\
Riemann's zeta function / 223 \\
Debye functions / 224 \\
Elliptic integrals / 224 \\
Examples / 225 \\
Problems / 228 \\
Appendices Convergence of Legendre series / 230 \\
Euler's constant / 231 \\
Differential equations / 233 \\
Orthogonality relations / 234 \\
Generating functions / 236 \\
Hints and Solutions to Problems / 237 \\
Bibliography / 243 \\
Index / 245",
}
@Article{Berrut:2004:APS,
author = "Jean-Paul Berrut and Hans D. Mittelmann",
title = "Adaptive Point Shifts in Rational Approximation with
Optimized Denominator",
journal = j-J-COMPUT-APPL-MATH,
volume = "164--165",
number = "??",
pages = "81--92",
day = "1",
month = mar,
year = "2004",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(03)00485-0",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Tue Mar 24 21:10:48 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the 10th International Congress on
Computational and Applied Mathematics University of
Leuven, Belgium, 22--26 July 2002. Edited by M. J.
Goovaerts, S. Vandewalle, and L. Wuytack.",
abstract = "Classical rational interpolation is known to suffer
from several drawbacks, such as unattainable points and
randomly located poles for a small number of nodes, as
well as an erratic behavior of the error as this number
grows larger. In a former article, we have suggested to
obtain rational interpolants by a procedure that
attaches optimally placed poles to the interpolating
polynomial, using the barycentric representation of the
interpolants. In order to improve upon the condition of
the derivatives in the solution of differential
equations, we have then experimented with a conformal
point shift suggested by Kosloff and Tal-Ezer. As it
turned out, such shifts can achieve a spectacular
improvement in the quality of the approximation itself
for functions with a large gradient in the center of
the interval. This leads us to the present work which
combines the pole attachment method with shifts
optimally adjusted to the interpolated function. Such
shifts are also constructed for functions with several
shocks away from the extremities of the interval.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "interpolation; optimal interpolation; point shifts;
rational approximation",
}
@InCollection{Borwein:2004:AGMa,
author = "J. M. Borwein and P. B. Borwein",
title = "The Arithmetic--Geometric Mean and Fast Computation of
Elementary Functions",
crossref = "Berggren:2004:PSB",
pages = "537--552",
year = "2004",
DOI = "https://doi.org/10.1007/978-1-4757-4217-6_56",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Reprint of \cite{Borwein:1984:AGM}.",
URL = "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Brisebarre:2004:ACR,
author = "N. Brisebarre and J.-M. Muller and Saurabh Kumar
Raina",
title = "Accelerating correctly rounded floating-point division
when the divisor is known in advance",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "8",
pages = "1069--1072",
month = aug,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.37",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "We present techniques for accelerating the
floating-point computation of $ x / y $ when $y$ is
known before $x$. The proposed algorithms are oriented
toward architectures with available fused-mac
operations. The goal is to get exactly the same result
as with \ldots{}",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "We present techniques for accelerating the
floating-point computation of x/y when y is known
before x. The proposed algorithms are oriented toward
architectures with available fused-mac operations. The
goal is to get exactly the same result as with
\ldots{}",
}
@Article{Chaudhry:2004:EHC,
author = "M. Aslam Chaudhry and Asghar Qadir and H. M.
Srivastava and R. B. Paris",
title = "Extended hypergeometric and confluent hypergeometric
functions",
journal = j-APPL-MATH-COMP,
volume = "159",
number = "2",
pages = "589--602",
day = "6",
month = dec,
year = "2004",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Jul 4 09:15:38 MDT 2005",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Croot:2004:ACC,
author = "Ernie Croot and Ren-Cang Li and H. J. Hui June Zhu",
title = "The {\em abc\/} conjecture and correctly rounded
reciprocal square roots",
journal = j-THEOR-COMP-SCI,
volume = "315",
number = "2--3",
pages = "405--417",
day = "6",
month = may,
year = "2004",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Thu Nov 4 10:19:15 MST 2004",
bibsource = "http://www.sciencedirect.com/science/journal/03043975;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tcs2000.bib",
abstract = "The reciprocal square root calculation $ \alpha = 1 /
\sqrt {x} $ is very common in scientific computations.
Having a correctly rounded implementation of it is of
great importance in producing numerically predictable
code among today's heterogeneous computing environment.
Existing results suggest that to get the correctly
rounded $ \alpha $ in a floating point number system
with $p$ significant bits, we may have to compute up to
$ 3 p + 1 $ leading bits of $ \alpha $. However,
numerical evidence indicates the actual number may be
as small as $ 2 p $ plus a few more bits. This paper
attempts to bridge the gap by showing that this is
indeed true, assuming the {\em abc\/} conjecture which
is widely purported to hold. (But our results do not
tell exactly how many more bits beyond the $ 2 p $
bits, due to the fact that the constants involved in
the conjecture are ineffective.) Along the way, rough
bounds which are comparable to the existing ones are
also proven. The technique used here is a combination
of the classical Liouville's estimation and
contemporary number theory.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@InProceedings{deDinechin:2004:PCR,
author = "Florent de Dinechin and Catherine Loirat and
Jean-Michel Muller",
title = "A proven correctly rounded logarithm in
double-precision",
crossref = "Frougny:2004:RCR",
pages = "71--85",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_07_dinechin.pdf",
abstract = "This article is a case study in the implementation of
a proven, portable, and efficient correctly rounded
elementary function in double-precision. We describe
the methodology used in the implementation of the
natural logarithm in the crlibm library. The discipline
required to prove a tight bound on the overall
evaluation error allows to design a very efficient
implementation with moderate effort.",
acknowledgement = ack-nhfb,
keywords = "arithmetic; correct rounding; elementary functions;
floating-point; libm; logarithm",
}
@Article{Defour:2004:PSM,
author = "David Defour and Guillaume Hanrot and Vincent
Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol
and Paul Zimmermann",
title = "Proposal for a Standardization of Mathematical
Function Implementation in Floating-Point Arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "367--375",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 07:00:28 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm;
http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf;
http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "Special Issue: SCAN'2002 International Conference
(Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}
@InProceedings{Doss:2004:FBI,
author = "C. C. Doss and R. L. {Riley, Jr.}",
booktitle = "{FCCM 2004}. 12th Annual {IEEE} Symposium on
Field-Programmable Custom Computing Machines, 20--23
April 2004",
title = "{FPGA}-based implementation of a robust {IEEE-754}
exponential unit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "229--238",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 17:14:11 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
summary = "This work explores the feasibility of implementing a
floating-point exponentiation unit on reconfigurable
computing systems. A table-driven exponentiation unit
was implemented using synthesizable VHDL. The project
included creating pipelined \ldots{}",
}
@TechReport{Ercegovac:2004:CSRa,
author = "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
title = "Complex Square Root with Operand Prescaling",
type = "Research Report",
number = "RR2004-42",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 12",
month = sep,
year = "2004",
bibdate = "Mon Dec 06 11:07:40 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-42.pdf",
abstract = "We propose a radix-$r$ digit-recurrence algorithm for
complex square-root. The operand is prescaled to allow
the selection of square-root digits by rounding of the
residual. This leads to a simple hardware
implementation. Moreover, the use of digit recurrence
approach allows correct rounding of the result. The
algorithm, compatible with the complex division, and
its design are described at a high-level. We also give
rough comparisons of its latency and cost with respect
to implementation based on standard floating-point
instructions as used in software routines for complex
square root.",
acknowledgement = ack-nhfb,
keywords = "complex square-root; Computer arithmetic;
digit-recurrence algorithm; operand prescaling.",
}
@InProceedings{Ercegovac:2004:CSRb,
author = "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
booktitle = "{Proceedings of the 15th IEEE International Conference
on Application-Specific Systems, Architectures and
Processors, 2004}",
title = "Complex square root with operand prescaling",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "52--62",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1109/ASAP.2004.1342458",
ISBN = "0-7695-2226-2",
ISBN-13 = "978-0-7695-2226-5",
ISSN = "1063-6862",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We propose a radix-r digit-recurrence algorithm for
complex square-root. The operand is prescaled to allow
the selection of square-root digits by rounding of the
residual. This leads to a simple hardware
implementation. Moreover, the use of digit \ldots{}",
}
@Article{Fabijonas:2004:AAF,
author = "B. R. Fabijonas",
title = "{Algorithm 838}: {Airy} Functions",
journal = j-TOMS,
volume = "30",
number = "4",
pages = "491--501",
month = dec,
year = "2004",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1039813.1039819",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Apr 12 06:34:31 MDT 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We present a Fortran 90 module, which computes the
solutions and their derivatives of Airy's differential
equation, both on the real line and in the complex
plane. The module also computes the zeros and
associated values of the solutions and their
derivatives, and the modulus and phase functions on the
negative real axis. The computational methods are
numerical integration of the differential equation and
summation of asymptotic expansions for large argument.
These methods were chosen because they are simple,
adaptable to any precision, and amenable to rigorous
error analysis. The module can be used to validate
other codes or as a component in programs that require
Airy functions.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Fabijonas:2004:CCA,
author = "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver",
title = "Computation of complex {Airy} functions and their
zeros using asymptotics and the differential equation",
journal = j-TOMS,
volume = "30",
number = "4",
pages = "471--490",
month = dec,
year = "2004",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1039813.1039818",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Apr 12 06:34:31 MDT 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We describe a method by which one can compute the
solutions of Airy's differential equation, and their
derivatives, both on the real line and in the complex
plane. The computational methods are numerical
integration of the differential equation and summation
of asymptotic expansions for large argument. We give
details involved in obtaining all of the parameter
values, and we control the truncation errors
rigorously. Using the same computational methods, we
describe an algorithm that computes the zeros and
associated values of the Airy functions and their
derivatives, and the modulus and phase functions on the
negative real axis.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Gebali:2004:EAF,
author = "Fayez Gebali and Mohamed Watheq El-Kharashi",
title = "{ERL}: an algorithm for fast evaluation of
exponential, reciprocal, and logarithmic functions",
crossref = "Wahdan:2004:IHE",
pages = "269--272",
year = "2004",
bibdate = "Sat Jul 16 18:04:58 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A fast algorithm (ERL) is proposed for evaluating
Exponential, Reciprocal, and Logarithmic functions. The
algorithm requires two to three iterations to complete
using simple operations such as multiply, accumulate,
and table lookup. The algorithm is independent of the
number format used by the machine. Thus it can be
implemented using the IEEE 754 floating-point standard
or any other special format used by special-purpose
processors. The dynamic range of the algorithm is
limited only by the dynamic range of the machine on
which it is implemented Numerical simulations are
performed which verifies the speed and accuracy of the
algorithm.",
acknowledgement = ack-nhfb,
}
@Article{Gil:2004:AMB,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 831}: {Modified} {Bessel} functions of
imaginary order and positive argument",
journal = j-TOMS,
volume = "30",
number = "2",
pages = "159--164",
month = jun,
year = "2004",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/992200.992204",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Jun 10 07:24:58 MDT 2004",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Fortran 77 programs for the computation of modified
Bessel functions of purely imaginary order are
presented. The codes compute the functions $ K_{ia}(x)
$, $ L_{ia}(x) $ and their derivatives for real $a$ and
positive $x$; these functions are independent solutions
of the differential equation $ x^2 w'' + x w' + (a^2 -
x^2)w = 0 $. The code also computes exponentially
scaled functions. The range of computation is $ (x, a)
\in (0, 1500] \times [ - 1500, 1500] $ when scaled
functions are considered and it is larger than $ (0,
500] \times [ - 400, 400] $ for standard IEEE double
precision arithmetic. The relative accuracy is better
than $ 10^{-13} $ in the range $ (0, 200] \times [ -
200, 200] $ and close to $ 10^{-12} $ in $ (0, 1500]
\times [ - 1500, 1500] $.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gil:2004:CRZ,
author = "Amparo Gil and Wolfram Koepf and Javier Segura",
title = "Computing the Real Zeros of Hypergeometric Functions",
journal = j-NUMER-ALGORITHMS,
volume = "36",
number = "2",
pages = "113--134",
month = jun,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 07:00:32 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/54/A/2/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Gil:2004:CSM,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Computing solutions of the modified {Bessel}
differential equation for imaginary orders and positive
arguments",
journal = j-TOMS,
volume = "30",
number = "2",
pages = "145--158",
month = jun,
year = "2004",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/992200.992203",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Jun 10 07:24:58 MDT 2004",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We describe a variety of methods to compute the
functions $ K_{ia}(x) $, $ L_{ia}(x) $ and their
derivatives for real $a$ and positive $x$. These
functions are numerically satisfactory independent
solutions of the differential equation $ x^2 w'' + x w'
+ (a^2 - x^2)w = 0 $. In the accompanying paper [Gil et
al. 2004], we describe the implementation of these
methods in Fortran 77 codes.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Guseinov:2004:EIG,
author = "I. I. Guseinov and B. A. Mamedov",
title = "Evaluation of Incomplete Gamma Functions Using
Downward Recursion and Analytical Relations",
journal = j-J-MATH-CHEM,
volume = "36",
number = "4",
pages = "341--346",
month = aug,
year = "2004",
CODEN = "JMCHEG",
DOI = "https://doi.org/10.1023/B:JOMC.0000044521.18885.d3",
ISSN = "0259-9791 (print), 1572-8897 (electronic)",
ISSN-L = "0259-9791",
bibdate = "Thu Apr 9 18:14:03 MDT 2015",
bibsource = "http://link.springer.com/journal/10910/36/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
URL = "http://link.springer.com/article/10.1023/B:JOMC.0000044521.18885.d3",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Chemistry",
journal-URL = "http://link.springer.com/journal/10910",
journalabr = "J. Math. Chem.",
}
@Book{Jeffrey:2004:HMF,
author = "Alan Jeffrey",
title = "Handbook of Mathematical Formulas and Integrals",
publisher = pub-ELSEVIER-ACADEMIC,
address = pub-ELSEVIER-ACADEMIC:adr,
edition = "Third",
pages = "xxvi + 453",
year = "2004",
ISBN = "0-12-382256-4",
ISBN-13 = "978-0-12-382256-7",
LCCN = "QA47 .J38 2004",
bibdate = "Thu May 8 16:02:52 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "mathematics; tables; formulae",
tableofcontents = "0. Quick Reference List of Frequently Used Data 1
\\
1. Numerical, Algebraic, and Analytical Results for
Series and Calculus 25 \\
2. Functions and Identities 101 \\
3. Derivatives of Elementary Functions 139 \\
4. Indefinite Integrals of Algebraic Functions 145 \\
5. Indefinite Integrals of Exponential Functions 167
\\
6. Indefinite Integrals of logarithmic Functions 173
\\
7. Indefinite Integrals of Hyperbolic Functions 179 \\
8. Indefinite Integrals Involving Inverse Hyperbolic
Functions 191 \\
9. Indefinite Integrals of Trigonometric Functions 197
\\
10. Indefinite Integrals of Inverse Trigonometric
Functions 215 \\
11. The Gamma, Beta, Pi, and Psi Functions 221 \\
12. Elliptic Integrals and Functions 229 \\
13. Probability Integrals and the Error Function 239
\\
14. Fresnel Integrals, Sine and Cosine Integrals 245
\\
15. Definite Integrals 249 \\
16. Different Forms of Fourier Series 257 \\
17. Bessel Functions 269 \\
18. Orthogonal Polynomials 285 \\
19. Laplace Transformation 299 \\
20. Fourier Transforms 307 \\
21. Numerical Integration 315 \\
22. Solutions of Standard Ordinary Differential
Equations 321 \\
23. Vector Analysis 353 \\
24. Systems of Orthogonal Coordinates 369 \\
25. Partial Differential Equations and Special
Functions 381 \\
26. the z-Transform 403 \\
27. Numerical Approximation 409 \\
28. Solutions of Elliptic, Parabolic, and Hyperbolic
Equations 419 \\
29. Qualitative Properties of the Heat and Laplace
Equation 437",
xxURL = "http://www.loc.gov/catdir/description/els041/2003049507.html;
http://www.loc.gov/catdir/toc/els041/2003049507.html;
http://www.e-streams.com/es0710/es0710_3628.html",
}
@Misc{Kahan:2004:LTC,
author = "W. Kahan",
title = "A Logarithm Too Clever by Half",
howpublished = "World-Wide Web document",
pages = "9",
day = "9",
month = aug,
year = "2004",
bibdate = "Mon Apr 25 17:39:08 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT",
acknowledgement = ack-nhfb,
remark = "Careful analysis of the problem of computing {\tt
log10(x)} accurately from {\tt log(x)}.",
}
@Article{Kalmykov:2004:SEH,
author = "M. Y. Kalmykov",
title = "Series and $ \epsilon $-expansion of the
hypergeometric functions",
journal = j-NUCL-PHYS-B-PROC-SUPPL,
volume = "135",
number = "??",
pages = "280--284",
month = "????",
year = "2004",
CODEN = "NPBSE7",
ISSN = "0920-5632 (print), 1873-3832 (electronic)",
ISSN-L = "0920-5632",
bibdate = "Thu Dec 01 09:14:29 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Nuclear Physics B, Proceedings Supplements",
journal-URL = "http://www.sciencedirect.com/science/journal/09205632",
}
@Book{Kilbas:2004:TTA,
author = "A. A. (Anatolii Aleksandrovich) Kilbas and Megumi
Saigo",
title = "{$H$}-transforms: theory and applications",
volume = "9",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
pages = "xii + 389",
year = "2004",
ISBN = "0-203-48737-0, 0-415-29916-0, 1-58488-116-X",
ISBN-13 = "978-0-203-48737-2, 978-1-58488-116-2,
978-0-415-29916-9",
LCCN = "????",
bibdate = "Sat Oct 30 17:20:21 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.bibsys.no:2100/BIBSYS",
series = "Analytical methods and special functions",
acknowledgement = ack-nhfb,
subject = "$H$-functions; integral transforms",
tableofcontents = "1. Definition, representations and expansions of
the H-function \\
2. Properties of the H-function \\
3. H-transform on the space [symbol] \\
4. H-transform on the space [symbol] \\
5. Modified H-transforms on the space [symbol] \\
6. G-transform and modified G-transforms on the space
[symbol] \\
7. Hypergeometric type integral transforms on the space
[symbol] \\
8. Bessel type integral transforms on the space
[symbol] \\
Bibliography \\
Author Index \\
Subject Index \\
Symbol Index",
}
@Article{Kyurkchiev:2004:FCN,
author = "N. Kyurkchiev and A. Iliev",
title = "Failure of convergence of the {Newton--Weierstrass}
iterative method for simultaneous root finding of
generalized polynomials",
journal = j-COMPUT-MATH-APPL,
volume = "47",
number = "2--3",
pages = "441--446",
month = jan # "\slash " # feb,
year = "2004",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:35 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122104900363",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Book{Lau:2004:NLJ,
author = "H. T. (Hang Tong) Lau",
title = "A Numerical Library in {Java} for Scientists and
Engineers",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
pages = "xxiii + 1063",
year = "2004",
DOI = "https://doi.org/10.1201/9780203507643",
ISBN = "1-58488-430-4",
ISBN-13 = "978-1-58488-430-9",
LCCN = "QA76.73.J38 L363 2004",
bibdate = "Fri Sep 26 14:28:47 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0646/2003055149-d.html",
acknowledgement = ack-nhfb,
subject = "Java (Computer program language)",
tableofcontents = "1: Elementary Procedures \\
1.1: Real vector and matrix \\
Initialization \\
1.2: Real vector and matrix \\
Duplication \\
1.3: Real vector and matrix \\
Multiplication \\
1.4: Real vector vector products \\
1.5: Real matrix vector products \\
1.6: Real matrix matrix products \\
1.7: Real vector and matrix \\
Elimination \\
1.8: Real vector and matrix \\
Interchanging \\
1.9: Real vector and matrix \\
Rotation \\
1.10: Real vector and matrix \\
Norms \\
1.11: Real vector and matrix \\
Scaling \\
1.12: Complex vector and matrix \\
Multiplication \\
1.13: Complex vector and matrix \\
Scalar products \\
1.14: Complex vector and matrix \\
Elimination \\
1.15: Complex vector and matrix \\
Rotation \\
1.16: Complex vector and matrix \\
Norms \\
1.17: Complex vector and matrix \\
Scaling \\
1.18: Complex monadic operations \\
1.19: Complex dyadic operations \\
1.20: Long integer arithmetic \\
2: Algebraic Evaluations \\
2.1: Evaluation of polynomials in Grunert form \\
2.2: Evaluation of general orthogonal polynomials \\
2.3: Evaluation of Chebyshev polynomials \\
2.4: Evaluation of Fourier series \\
2.5: Evaluation of continued fractions \\
2.6: Transformation of polynomial representation \\
2.7: Operations on orthogonal polynomials \\
3: Linear Algebra \\
3.1: Full real general matrices \\
3.2: Real symmetric positive definite matrices \\
3.3: General real symmetric matrices \\
3.4: Real full rank overdetermined systems \\
3.5: Other real matrix problems \\
3.6: Real sparse nonsymmetric band matrices \\
3.7: Real sparse nonsymmetric tridiagonal matrices \\
3.8: Sparse symmetric positive definite band matrices
\\
3.9: Symmetric positive definite tridiagonal matrices
\\
3.10: Sparse real matrices \\
Iterative methods \\
3.11: Similarity transformation \\
3.12: Other transformations \\
3.13: The (ordinary) eigenvalue problem \\
3.14: The generalized eigenvalue problem \\
3.15: Singular values \\
3.16: Zeros of polynomials \\
4: Analytic Evaluations \\
4.1: Evaluation of an infinite series \\
4.2: Quadrature \\
4.3: Numerical differentiation \\
5: Analytic Problems \\
5.1: Nonlinear equations \\
5.2: Unconstrained optimization \\
5.3: Overdetermined nonlinear systems \\
5.4: Differential equations \\
Initial value problems \\
5.5: Two point boundary value problems \\
5.6: Two-dimensional boundary value problems \\
5.7: Parameter estimation in differential equations \\
6: Special Functions \\
6.1: Elementary functions \\
6.2: Exponential Integral \\
6.3: Gamma function \\
6.4: Error function \\
6.5: Bessel functions of integer order \\
6.6: Bessel functions of real order \\
7: Interpolation and Approximation \\
7.1: Real data in one dimension \\
I: Fast Fourier transforms \\
II: Time series analysis \\
Worked Examples \\
Examples for chapter 1 procedures \\
Examples for chapter 2 procedures \\
Examples for chapter 3 procedures \\
Examples for chapter 4 procedures \\
Examples for chapter 5 procedures \\
Examples for chapter 6 procedures \\
Examples for chapter 7 procedures \\
App. B: Procedures Description",
}
@InProceedings{Markstein:2004:SDS,
author = "Peter Markstein",
title = "Software Division and Square Root Using
{Goldschmidt}'s Algorithms",
crossref = "Frougny:2004:RCR",
pages = "146--157",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_12_markstein.pdf",
abstract = "Goldschmidt's Algorithms for division and square root
are often characterized as being useful for hardware
implementation, and lacking self-correction. A
reexamination of these algorithms show that there are
good software counterparts that retain the speed
advantage of Goldschmidt's Algorithm over the
Newton--Raphson iteration. A final step is needed,
however, to get the last bit rounded correctly.",
acknowledgement = ack-nhfb,
keywords = "division; floating-point; Goldschmidt; square root",
}
@Article{Marsaglia:2004:END,
author = "George Marsaglia",
title = "Evaluating the Normal Distribution",
journal = j-J-STAT-SOFT,
volume = "11",
number = "4",
pages = "1--7",
month = "????",
year = "2004",
CODEN = "JSSOBK",
ISSN = "1548-7660",
bibdate = "Sat Dec 04 09:18:40 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/cphi.pdf&ct=1",
accepted = "2004-07-18",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
remark = "This article exhibits accurate, compact, and fast
algorithms for computation of the normal distribution
function and the complementary normal distribution,
which have a simple relation to the error function and
the complementary error function. They appear to be
improvements on almost all previously-published
algorithms for these functions. However, closer study
shows that the complementary normal distribution
function has an unchecked out-of-bounds array access
for $ |x| \geq 17 $, and its Taylor series sum has poor
convergence because the tabulated intervals are twice
too wide. The Taylor series sum for the normal
distribution function is expanded around $ x = 0 $, and
thus has poor convergence for large $ |x| $. Neither
function takes into account the accuracy loss when the
computed result is the larger of the two (their sum is
one, and their range is $ [ - \infty, + \infty] $ ),
although the text discusses the problem. The article
also discusses the historical origin of the term
``error function'', tracing it to J. W. Glaisher in
1871.",
submitted = "2004-06-05",
}
@Article{Mathar:2004:NRI,
author = "Richard J. Mathar",
title = "Numerical Representations of the Incomplete Gamma
Function of Complex-Valued Argument",
journal = j-NUMER-ALGORITHMS,
volume = "36",
number = "3",
pages = "247--264",
month = jul,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 07:00:32 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/57/A/4/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Misc{Miller:2004:AMF,
author = "Alan Miller",
title = "{Alan Miller}'s {Fortran} Software",
howpublished = "Web site",
day = "4",
month = feb,
year = "2004",
bibdate = "Tue Jun 13 12:03:37 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
note = "From the Web site: All code written by Alan Miller is
released into the public domain.",
URL = "https://jblevins.org/mirror/amiller/",
acknowledgement = ack-nhfb,
remark = "The Web site contains a section ``Code converted from
the Naval Surface Warfare Center Math. Library'' with
links to individual Fortran 90 source files.",
}
@Article{Moore:2004:PSW,
author = "Ian C. Moore and Michael Cada",
title = "Prolate spheroidal wave functions, an introduction to
the {Slepian} series and its properties",
journal = j-APPL-COMPUT-HARMON-ANAL,
volume = "16",
number = "3",
pages = "208--230",
month = may,
year = "2004",
DOI = "https://doi.org/10.1016/j.acha.2004.03.004",
ISSN = "1063-5203 (print), 1096-603x (electronic)",
ISSN-L = "1063-5203",
bibdate = "Sun Oct 31 09:58:00 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "For decades mathematicians, physicists, and engineers
have relied on various orthogonal expansions such as
Fourier, Legendre, and Chebyschev to solve a variety of
problems. In this paper we exploit the orthogonal
properties of prolate spheroidal wave functions (PSWF)
in the form of a new orthogonal expansion which we have
named the Slepian series. We empirically show that the
Slepian series is potentially optimal over more
conventional orthogonal expansions for discontinuous
functions such as the square wave among others. With
regards to interpolation, we explore the connections
the Slepian series has to the Shannon sampling theorem.
By utilizing Euler's equation, a relationship between
the even and odd ordered PSWFs is investigated. We also
establish several other key advantages the Slepian
series has such as the presence of a free tunable
bandwidth parameter.",
acknowledgement = ack-nhfb,
fjournal = "Applied and Computational Harmonic Analysis.
Time-Frequency and Time-Scale Analysis, Wavelets,
Numerical Algorithms, and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/10635203",
keywords = "Interpolation; Orthogonal expansion; Prolate
spheroidal wave function",
}
@Article{Muller:2004:CSR,
author = "Siguna M{\"u}ller",
title = "On the Computation of Square Roots in Finite Fields",
journal = j-DESIGNS-CODES-CRYPTOGR,
volume = "31",
number = "3",
pages = "301--312",
month = mar,
year = "2004",
CODEN = "DCCREC",
ISSN = "0925-1022 (print), 1573-7586 (electronic)",
ISSN-L = "0925-1022",
bibdate = "Tue Aug 3 16:38:18 MDT 2004",
bibsource = "http://www.wkap.nl/jrnltoc.htm/0925-1022;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp008.kluweronline.com/IPS/content/ext/x/J/4630/I/61/A/8/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Designs, codes, and cryptography",
journal-URL = "http://link.springer.com/journal/10623",
}
@Article{Nagel:2004:CEG,
author = "Bengt Nagel",
title = "Confluence expansions of the generalized
hypergeometric function",
journal = j-J-MATH-PHYS,
volume = "45",
number = "1",
pages = "495--508",
month = jan,
year = "2004",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1629777",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Tue Oct 25 18:16:52 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v45/i1/p495_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "19 December 2003",
pagecount = "14",
}
@InProceedings{Ortiz:2004:SPI,
author = "I. Ortiz and M. Jimenez",
booktitle = "{MWSCAS '04. The 2004 47th Midwest Symposium on
Circuits and Systems. 25--28 July 2004}",
title = "Scalable pipeline insertion in floating-point division
and square root units",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-225--II-228",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Division and square root are important operations in a
number of data processing algorithms. They are
inherently time consuming operations and can require a
significant amount of resources when implemented in
hardware. This work reports the development of
scalable, floating-point (FP) division and square root
operators with adjustable precision, range, and
pipeline granularity. An algorithm for pipeline
insertion was used for both operators, enabling speeds
up to 204MFLOPS when implemented on a Xilinx Virtex II
FPGA.",
acknowledgement = ack-nhfb,
summary = "Division and square root are important operations in a
number of data processing algorithms. They are
inherently time consuming operations and can require a
significant amount of resources when implemented in
hardware. This work reports the \ldots{}",
}
@Article{Petkovic:2004:GCS,
author = "M. S. Petkovi{\'c} and L. Ranci{\'c}",
title = "On the guaranteed convergence of the square-root
iteration method",
journal = j-J-COMPUT-APPL-MATH,
volume = "170",
number = "1",
pages = "169--179",
day = "1",
month = sep,
year = "2004",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:00:00 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042704000184",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Pineiro:2004:AAL,
author = "J. A. Pi{\~n}eiro and M. D. Ercegovac and J. D.
Bruguera",
title = "Algorithm and Architecture for Logarithm, Exponential
and Powering Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "9",
pages = "1085--1096",
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.53",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 10:05:48 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j05.ps",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Pugh:2004:ALG,
author = "Glendon Ralpha Pugh",
title = "An Analysis of the {Lanczos} Gamma Approximation",
type = "Ph.D. thesis",
school = "Department of Mathematics, University of British
Columbia",
address = "Vancouver, BC, Canada",
pages = "viii + 154",
month = "????",
year = "2004",
ISBN = "0-612-99536-4",
ISBN-13 = "978-0-612-99536-9",
LCCN = "AW5 .B7 2005-995364",
bibdate = "Mon Nov 24 20:55:30 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Raade:2004:MHS,
author = "Lennart R{\aa}de and Bertil Westergren",
title = "Mathematics Handbook for Science and Engineering",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Fifth",
pages = "562",
year = "2004",
ISBN = "3-540-21141-1 (hardcover)",
ISBN-13 = "978-3-540-21141-9 (hardcover)",
LCCN = "QA41 .R34 2004",
bibdate = "Sat May 15 09:15:39 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0818/2006286513-d.html;
http://www.loc.gov/catdir/toc/fy0704/2006286513.html",
acknowledgement = ack-nhfb,
libnote = "Not in my library.",
subject = "mathematics; formulae; tables; handbooks, manuals,
etc.",
tableofcontents = "1. Fundamentals \\
Discrete Mathematics / 9 \\
1.1 Logic / 9 \\
1.2 Set Theory / 14 \\
1.3 Binary Relations and Functions / 17 \\
1.4 Algebraic Structures / 21 \\
1.5 Graph Theory / 33 \\
1.6 Codes / 37 \\
2: Algebra / 43 \\
2.1 Basic Algebra of Real Numbers / 43 \\
2.2 Number Theory / 49 \\
2.3 Complex Numbers / 61 \\
2.4 Algebraic Equations / 63 \\
3: Geometry and Trigonometry / 66 \\
3.1 Plane Figures / 66 \\
3.2 Solids / 71 \\
3.3 Spherical Trigonometry / 75 \\
3.4 Geometrical Vectors / 77 \\
3.5 Plane Analytic Geometry / 79 \\
3.6 Analytic Geometry in Space / 83 \\
3.7 Fractals / 87 \\
4: Linear Algebra / 90 \\
4.1 Matrices / 90 \\
4.2 Determinants / 93 \\
4.3 Systems of Linear Equations / 95 \\
4.4 Linear Coordinate Transformations / 97 \\
4.5 Eigenvalues. Diagonalization / 98 \\
4.6 Quadratic Forms / 103 \\
4.7 Linear Spaces / 106 \\
4.8 Linear Mappings / 108 \\
4.9 Tensors / 114 \\
4.10 Complex matrices / 114 \\
5: The Elementary Functions / 118 \\
5.1 A Survey of the Elementary Functions / 118 \\
5.2 Polynomials and Rational Functions / 119 \\
5.3 Logarithmic, Exponential, Power and Hyperbolic
Functions / 121 \\
5.4 Trigonometric and Inverse Trigonometric Functions /
125 \\
6: Differential Calculus (one variable) / 132 \\
6.1 Some Basic Concepts / 132 \\
6.2 Limits and Continuity / 133 \\
6.3 Derivatives / 136 \\
6.4 Monotonicity. Extremes of Functions / 139 \\
7: Integral Calculus / 141 \\
7.1 Indefinite Integrals / 141 \\
7.2 Definite Integrals / 146 \\
7.3 Applications of Differential and Integral Calculus
/ 148 \\
7.4 Table of Indefinite Integral / 153 \\
7.5 Tables of Definite Integrals / 178 \\
8: Sequences and Series / 183 \\
8.1 Sequences of Numbers / 183 \\
8.2 Sequences of Functions / 184 \\
8.3 Series of Constant Terms / 185 \\
8.4 Series of Functions / 187 \\
8.5 Taylor Series / 189 \\
8.6 Special Sums and Series / 192 \\
9: Ordinary Differential Equations (ODE) / 200 \\
9.1 Differential Equations of the First Order / 200 \\
9.2 Differential Equations of the Second Order / 202
\\
9.3 Linear Differential Equations / 205 \\
9.4 Autonomous systems / 2313 \\
9.5 General Concepts and Results / 216 \\
9.6 Linear Difference Equations / 218 \\
10: Multidimensional Calculus / 221 \\
10.1 The Space Rn / 221 \\
10.2 Surfaces. Tangent Planes / 222 \\
10.3 Limits and Continuity / 223 \\
10.4 Partial Derivatives / 224 \\
10.5 Extremes of Functions / 227 \\
10.6 Functions $f: R^n \to R^m (R^n \to R^n)$ / 229 \\
10.7 Double Integrals / 231 \\
10.8 Triple Integrals / 234 \\
10.9 Partial Differential Equations / 239 \\
11: Vector Analysis / 246 \\
11.1 Curves / 246 \\
11.2 Vector Fields / 248 \\
11.3 Line Integrals / 253 \\
11.4 Surface Integrals / 256 \\
12: Orthogonal Series and Special Functions / 259 \\
12.1 Orthogonal Systems / 259 \\
12.2 Orthogonal Polynomials / 263 \\
12.3 Bernoulli and Euler Polynomials / 269 \\
12.4 Bessel Functions / 270 \\
12.5 Functions Defined by Transcendental Integrals /
287 \\
12.6 Step and Impulse Functions / 297 \\
12.7 Functional Analysis / 298 \\
12.8 Lebesgue Integrals / 303 \\
12.9 Generalized functions (Distributions) / 308 \\
13: Transforms / 310 \\
13.1 Trigonometric Fourier Series / 310 \\
13.2 Fourier Transforms / 315 \\
13.3 Discrete Fourier Transforms / 325 \\
13.4 The $z$-transform / 327 \\
13.5 Laplace Transforms / 330 \\
13.6 Dynamical Systems (Filters) / 338 \\
13.7 Hankel and Hilbert transforms / 341 \\
13.8 Wavelets / 344 \\
14: Complex Analysis / 349 \\
14.1 Functions of a Complex Variable / 349 \\
14.2 Complex Integration / 352 \\
14.3 Power Series Expansions / 354 \\
14.4 Zeros and Singularities / 355 \\
14.5 Conformal Mappings / 356 \\
15: Optimization / 365 \\
15.1 Calculus of Variations / 365 \\
15.2 Linear Optimization / 371 \\
15.3 Integer and Combinatorial Optimization / 379 \\
15.4 Nonlinear Optimization / 383 \\
15.5 Dynamic Optimization / 389 \\
16: Numerical Analysis / 391 \\
16.1 Approximations and Errors / 391 \\
16.2 Numerical Solution of Equations / 392 \\
16.3 Perturbation analysis / 397 \\
16.4 Interpolation / 398 \\
16.5 Numerical Integration and Differentiation / 404
\\
16.6 Numerical Solutions of Differential Equations /
412 \\
16.7 Numerical summation / 421 \\
17: Probability Theory / 424 \\
17.1 Basic Probability Theory / 424 \\
17.2 Probability Distributions / 434 \\
17.3 Stochastic Processes / 439 \\
17.4 Algorithms for Calculation of Probability
Distributions / 443 \\
17.5 Simulation / 445 \\
17.6 Queueing Systems / 449 \\
17.7 Reliability / 452 \\
17.8 Tables / 459 \\
18: Statistics / 479 \\
18.1 Descriptive Statistics / 479 \\
18.2 Point Estimation / 488 \\
18.3 Confidence Intervals / 491 \\
18.4 Tables for Confidence Intervals / 495 \\
18.5 Tests of Significance / 501 \\
18.6 Linear Models / 507 \\
18.7 Distribution-free Methods / 512 \\
18.8 Statistical Quality Control / 518 \\
18.9 Factorial Experiments / 522 \\
18.10 Analysis of life time (failure time) data / 525
\\
18.11 Statistical glossary / 526 \\
19: Miscellaneous / 530",
}
@Article{Skorokhodov:2004:STP,
author = "S. L. Skorokhodov",
title = "Symbolic transformations in the problem of analytic
continuation of the hypergeometric function {$_p F_{p -
1}(z)$} in the neighborhood of the point $ z = 1 $ in
the logarithmic case",
journal = j-PROG-COMP-SOFT,
volume = "30",
number = "3",
pages = "150--156",
month = "????",
year = "2004",
CODEN = "PCSODA",
ISSN = "0361-7688 (print), 1608-3261 (electronic)",
ISSN-L = "0361-7688",
MRclass = "3C20 (33B15 33C05 33F05 33F10)",
MRnumber = "MR2082811 (2005f:33013)",
bibdate = "Thu Dec 01 09:18:16 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Programming and Computer Software; translation of
Programmirovaniye (Moscow, USSR) Plenum",
journal-URL = "http://link.springer.com/journal/11086",
}
@Article{Thompson:2004:EBB,
author = "I. J. Thompson",
title = "Erratum to {{\booktitle{Modified Bessel functions $ I
\_ n u(z) $ and $ K_\nu (z) $ of real order and complex
argument}} [Comput. Phys. Commun. {\bf 47} (1987)
245--257]}",
journal = j-COMP-PHYS-COMM,
volume = "159",
number = "3",
pages = "243--244",
day = "1",
month = jun,
year = "2004",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2004.02.007",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Apr 24 10:35:27 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Thompson:1987:MBF}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465504001067",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Book{Vallee:2004:AFA,
author = "Olivier Vall{\'e}e and Manuel Soares",
title = "{Airy} Functions and Applications to Physics",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "x + 194",
year = "2004",
ISBN = "1-86094-478-7 (hardcover)",
ISBN-13 = "978-1-86094-478-9 (hardcover)",
LCCN = "QA351 .V35 2004",
bibdate = "Tue Dec 5 10:16:05 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The use of special functions, and in particular Airy
functions, is rather common in physics. The reason may
be found in the need, and even in the necessity, to
express a physical phenomenon in terms of an effective
and comprehensive analytical form for the whole
scientific community. However, for the past twenty
years, many physical problems have been resolved by
computers. This trend is now becoming the norm as the
importance of computers continues to grow. As a last
resort, the special functions employed in physics will
have to be calculated numerically, even if the analytic
formulation of physics is of primary
importance.\par
Airy functions have periodically been the subject of
many review articles, but no noteworthy compilation on
this subject has been published since the 1950s. In
this work, we provide an exhaustive compilation of the
current knowledge on the analytical properties of Airy
functions, developing with care the calculus implying
the Airy functions.",
acknowledgement = ack-nhfb,
remark = "See also second edition \cite{Vallee:2010:AFA}.",
shorttableofcontents = "1: A historical introduction: Sir George
Biddell Airy / 1 \\
2: Definitions and properties / 5 \\
3: Primitives and integrals of Airy functions / 37 \\
4: Transformations of Airy functions / 71 \\
5: The uniform approximation / 91 \\
6: Generalisation of Airy functions / 101 \\
7: Applications to classical physics / 115 \\
8: Applications to quantum physics / 137 \\
Appendix A: Numerical computation of the Airy functions
/ 177 \\
Bibliography / 183 \\
Index / 193",
tableofcontents = "Preface / v \\
1. A Historical Introduction: Sir George Biddell Airy /
1 \\
2. Definitions and Properties / 5 \\
2.1 The Homogeneous Airy Functions / 5 \\
2.1.1 The Airy's equation / 5 \\
2.1.2 Elementary properties / 8 \\
2.1.2.1 Wronskians of homogeneous Airy functions / 8
\\
2.1.2.2 Particular values of Airy functions / 8 \\
2.1.2.3 Relations between Airy functions / 9 \\
2.1.3 Integral representations / 9 \\
2.1.4 Ascending and asymptotic series / 11 \\
2.1.4.1 Expansion of $\Ai$ near the origin / 11 \\
2.1.4.2 Ascending series of $\Ai$ and $\Bi$ / 12 \\
2.1.4.3 Asymptotic series of $\Ai$ and $\Bi$ / 13 \\
2.2 Properties of Airy Functions / 15 \\
2.2.1 Zeros of Airy functions / 15 \\
2.2.2 The spectral zeta function / 18 \\
2.2.3 Inequalities / 20 \\
2.2.4 Connection with Bessel functions / 20 \\
2.2.5 Modulus and phase of Airy functions / 21 \\
2.2.5.1 Definitions / 21 \\
2.2.5.2 Differential equations / 22 \\
2.2.5.3 Asymptotic expansions / 23 \\
2.2.5.4 Functions of positive arguments / 24 \\
2.3 The Inhomogeneous Airy Functions / 25 \\
2.3.1 Definitions / 25 \\
2.3.2 Properties of inhomogeneous Airy functions / 27
\\
2.3.2.1 Values at the origin / 27 \\
2.3.2.2 Other integral representations / 27 \\
2.3.3 Ascending and asymptotic series / 28 \\
2.3.3.1 Ascending series / 28 \\
2.3.3.2 Asymptotic series / 29 \\
2.3.4 Zeros of the Scorer functions / 29 \\
2.4 Squares and Products of Airy Functions / 30 \\
2.4.1 Differential equation and integral representation
/ 30 \\
2.4.2 A remarkable identity / 32 \\
2.4.3 The product $\Ai(x) \Ai(-x)$: Airy wavelets / 32
\\
3. Primitives and Integrals of Airy Functions / 37 \\
3.1 Primitives Containing One Airy Function / 37 \\
3.1.1 In terms of Airy functions / 37 \\
3.1.2 Ascending series / 38 \\
3.1.3 Asymptotic series / 38 \\
3.1.4 Primitive of Scorer functions / 39 \\
3.1.5 Repeated primitives / 40 \\
3.2 Product of Airy Functions / 40 \\
3.2.1 The method of Albright / 41 \\
3.2.2 Some primitives / 43 \\
3.3 Other Primitives / 48 \\
3.4 Miscellaneous / 49 \\
3.5 Elementary Integrals / 50 \\
3.5.1 Particular integrals / 50 \\
3.5.2 Integrals containing a single Airy function / 51
\\
3.5.2.1 Integrals involving algebraic functions / 51
\\
3.5.2.2 Integrals involving transcendental functions /
54 \\
3.5.3 Integrals of products of two Airy functions / 56
\\
3.6 Other Integrals / 60 \\
3.6.1 Integrals involving the Volterra $\mu$-function /
60 \\
3.6.2 Canonisation of cubic form / 64 \\
3.6.3 Integrals with three Airy functions / 65 \\
3.6.4 Integrals with four Airy functions / 67 \\
3.6.5 Double integrals / 68 \\
4. Transformations of Airy Functions / 71 \\
4.1 Causal Properties of Airy Functions / 71 \\
4.1.1 Causal relations / 71 \\
4.1.2 Green function of the Airy equation / 73 \\
4.2 The Airy Transform / 74 \\
4.2.1 Definitions and elementary properties / 74 \\
4.2.2 Some examples / 77 \\
4.2.3 Airy polynomials / 82 \\
4.2.4 Summary of Airy transform / 84 \\
4.2.5 Airy averaging / 85 \\
4.3 Other Kinds of Transformations / 85 \\
4.3.1 Laplace transform of Airy functions / 85 \\
4.3.2 Mellin transform of Airy function / 86 \\
4.3.3 Fourier transform of Airy functions / 87 \\
4.4 Expansion into Fourier-Airy Series / 88 \\
5. The Uniform Approximation / 91 \\
5.1 Oscillating Integrals / 91 \\
5.1.1 The method of stationary phase / 91 \\
5.1.2 The uniform approximation of oscillating
integrals / 93 \\
5.1.3 The Airy uniform approximation / 94 \\
5.2 Differential Equation of the Second Order / 95 \\
5.2.1 The JWKB method / 95 \\
5.2.2 The generalisation of Langer / 97 \\
5.3 Inhomogeneous Differential Equations / 98 \\
6. Generalisation of Airy Functions / 101 \\
6.1 Generalisation of the Airy Integral / 101 \\
6.2 Third Order Differential Equations / 105 \\
6.2.1 The linear third order differential equation /
105 \\
6.2.2 Asymptotic solutions / 106 \\
6.2.3 The comparison equation / 107 \\
6.3 Differential Equation of the Fourth Order / 111 \\
7. Applications to Classical Physics / 115 \\
7.1 Optics and Electromagnetism / 115 \\
7.2 Fluid Mechanics / 119 \\
7.2.1 The Tricomi equation / 119 \\
7.2.2 The Orr--Sommerfeld equation / 121 \\
7.3 Elasticity / 124 \\
7.4 The Heat Equation / 127 \\
7.5 Nonlinear Physics / 129 \\
7.5.1 Korteweg--de Vries equation / 129 \\
7.5.1.1 The linearised Korteweg--de Vries equation /
129 \\
7.5.1.2 Similarity solutions / 131 \\
7.5.2 The second Painlev{\'e} equation / 132 \\
7.5.2.1 The Painlev{\'e} equations / 132 \\
7.5.2.2 An integral equation / 134 \\
7.5.2.3 Rational solutions 135 \\
8. Applications to Quantum Physics / 137 \\
8.1 The Schr{\"o}dinger Equation / 137 \\
8.1.1 Particle in a uniform field / 137 \\
8.1.2 The $|x|$ potential / 140 \\
8.1.3 Uniform approximation of the Schr{\"o}dinger
equation / 144 \\
8.1.3.1 The JWKB approximation / 145 \\
8.1.3.2 The Airy uniform approximation / 146 \\
8.1.3.3 Exact vs approximate wave functions / 148 \\
8.2 Evaluation of the Franck--Condon Factors / 152 \\
8.2.1 The Franck--Condon principle / 153 \\
8.2.2 The JWKB approximation / 154 \\
8.2.3 The uniform approximation / 157 \\
8.3 The Semiclassical Wigner Distribution / 162 \\
8.3.1 The Weyl--Wigner formalism / 163 \\
8.3.2 The one-dimensional Wigner distribution / 164 \\
8.3.3 The two-dimensional Wigner distribution / 166 \\
8.3.4 Configuration of the Wigner distribution / 169
\\
8.4 Airy Transform of the Schr{\"o}dinger Equation /
173 \\
Appendix A: Numerical Computation of the Airy Functions
/ 177 \\
A.1 The Homogeneous Functions / 177 \\
A.2 The Inhomogeneous Functions / 180 \\
Bibliography / 183 \\
Index / 193",
}
@Article{VanDeun:2004:IAO,
author = "J. {Van Deun} and A. Bultheel",
title = "An Interpolation Algorithm for Orthogonal Rational
Functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "164--165",
number = "??",
pages = "749--762",
month = mar,
year = "2004",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(03)00493-X",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Tue Mar 24 21:14:11 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the 10th International Congress on
Computational and Applied Mathematics University of
Leuven, Belgium, 22--26 July 2002. Edited by M. J.
Goovaerts, S. Vandewalle, and L. Wuytack.",
abstract = "Let $ A = \{ \alpha_1, \alpha_2, \ldots {} \} $ be a
sequence of numbers on the extended real line $
\mathcal {R} = \mathcal {R} \union \{ \infty \} $ and $
\mu $ a positive bounded Borel measure with support in
(a subset of) $ \mathcal {R} $. We introduce rational
functions n with poles $ \{ \alpha_1, \ldots {},
\alpha_n \} $ that are orthogonal with respect to $ \mu
$ (if all poles are at infinity, we recover the
polynomial situation). It is well known that under
certain conditions on the location of the poles, the
system $ \{ \phi_n \} $ is regular such that the
orthogonal functions satisfy a three-term recurrence
relation similar to the one for orthogonal polynomials.
To compute the recurrence coefficients one can use
explicit formulas involving inner products. We present
a theoretical alternative to these explicit formulas
that uses certain interpolation properties of the
Riesz--Herglotz--Nevanlinna transform $ \Omega_\mu $ of
the measure $ \mu $. Error bounds are derived and some
examples serve as illustration.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "interpolation; orthogonal polynomials; orthogonal
rational functions; three-term recurrence",
}
@Article{Wang:2004:CHP,
author = "Ren-Hong Wang and Cheng-de Zheng",
title = "Cubic {Hermite--Pad{\'e}} approximation to the
exponential function",
journal = j-J-COMPUT-APPL-MATH,
volume = "163",
number = "1",
pages = "259--268",
day = "1",
month = feb,
year = "2004",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:59:56 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042703008124",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Zeng:2004:AMM,
author = "Zhonggang Zeng",
title = "Algorithm 835: {MultRoot}---a {Matlab} package for
computing polynomial roots and multiplicities",
journal = j-TOMS,
volume = "30",
number = "2",
pages = "218--236",
month = jun,
year = "2004",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/992200.992209",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65H05",
MRnumber = "MR2075984 (2005c:65041)",
bibdate = "Tue Mar 30 16:16:28 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "MultRoot is a collection of Matlab modules for
accurate computation of polynomial roots, especially
roots with non-trivial multiplicities. As a
blackbox-type software, MultRoot requires the
polynomial coefficients as the only input, and outputs
the computed roots, multiplicities, backward error,
estimated forward error, and the structure-preserving
condition number. The most significant features of
MultRoot are the multiplicity identification capability
and high accuracy on multiple roots without using
multiprecision arithmetic, even if the polynomial
coefficients are inexact. A comprehensive test suite of
polynomials that are collected from the literature is
included for numerical experiments and performance
comparison.",
acknowledgement = ack-nhfb,
fjournal = "Association for Computing Machinery. Transactions on
Mathematical Software",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Zhu:2004:ISR,
author = "Hufei Zhu and Zhongding Lei and F. P. S. Chin",
title = "An improved square-root algorithm for {BLAST}",
journal = j-IEEE-SIGNAL-PROCESS-LETT,
volume = "11",
number = "9",
pages = "772--775",
month = sep,
year = "2004",
CODEN = "ISPLEM",
DOI = "https://doi.org/10.1109/LSP.2004.833483",
ISSN = "1070-9908 (print), 1558-2361 (electronic)",
ISSN-L = "1070-9908",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Signal Processing Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
summary = "In this letter, an improved square-root algorithm for
Bell Labs Layered Space-Time (BLAST) system is
proposed. It speeds up the original square-root
algorithm by 36\% in terms of the number of
multiplications and additions. Compared with the
\ldots{}",
}
@Article{Abad:2005:TNA,
author = "Julio Abad and Javier Sesma",
title = "Two new asymptotic expansions of the ratio of two
gamma functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "173",
number = "2",
pages = "359--363",
day = "15",
month = jan,
year = "2005",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:00:02 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042704001669",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Antelo:2005:LLD,
author = "Elisardo Antelo and Tom{\'a}s Lang and Paolo Montuschi
and Alberto Nannarelli",
title = "Low Latency Digit-Recurrence Reciprocal and
Square-Root Reciprocal Algorithm and Architecture",
crossref = "IEEE:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arith17.polito.it/final/paper-116.pdf",
abstract = "The reciprocal and square-root reciprocal operations
are important in several applications. For the
operations, we present algorithms that combine a
digit-by-digit module and one iteration of a
quadratic-convergence approximation. The latter is
implemented by a digit-recurrence, which uses the
digits produced by the digit-by-digit part. In this
way, both parts execute in an overlapped manner, so
that the total number of cycles is about half the
number that would be required by the digit-by-digit
part alone. Because of the approximation, correct
rounding of the result cannot be obtained directly in
all cases; we propose a variable-time implementation
that produces the correctly rounded result with a small
average overhead. Radix-4 implementations are described
and have been synthesized. They achieve the same cycle
time as the standard digit-by-digit implementation,
resulting in a speed-up of about 2 and, because of the
approximation part, the area factor is also about 2. We
also show a combined implementation for both operations
that has essentially the same complexity as that for
square-root reciprocal alone.",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@Book{Arfken:2005:MMP,
author = "George B. Arfken and Hans-J{\"u}rgen Weber",
title = "Mathematical Methods for Physicists",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
edition = "Sixth",
pages = "xii + 1182",
year = "2005",
ISBN = "0-12-059876-0, 0-12-088584-0 (paperback)",
ISBN-13 = "978-0-12-059876-2, 978-0-12-088584-8 (paperback)",
LCCN = "QA37.3 .A74 2005",
bibdate = "Tue Feb 17 18:23:45 MST 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Mathematics; Mathematical physics",
tableofcontents = "1. Vector Analysis \\
2. Vector Analysis in Curved Coordinates and Tensors
\\
3. Determinants and Matrices \\
4. Group Theory \\
5. Infinite Series \\
6. Functions of a Complex Variable I: Analytic
Properties, Mapping \\
7. Functions of a Complex Variable II \\
8. The Gamma Function (Factorial Function) \\
9. Differential Equations \\
10. Sturm--Liouville Theory-Orthogonal Functions \\
11. Bessel Functions \\
12. Legendre Functions \\
13. More Special Functions \\
14. Fourier Series \\
15. Integral Transforms \\
16. Integral Equations \\
17. Calculus of Variations \\
18. Nonlinear Methods and Chaos \\
19. Probability",
xxauthor = "George B. (George Brown) Arfken and Hans-J{\"u}rgen
Weber",
xxURL = "http://www.loc.gov/catdir/enhancements/fy0625/2005049844-d.html;
http://www.loc.gov/catdir/enhancements/fy0625/2005049844-t.html",
}
@Article{Bonan-Hamada:2005:SCF,
author = "Catherine M. Bonan-Hamada and William B. Jones",
title = "{Stieltjes} continued fractions for polygamma
functions; speed of convergence",
journal = j-J-COMPUT-APPL-MATH,
volume = "179",
number = "1--2",
pages = "47--55",
day = "1",
month = jul,
year = "2005",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:00:05 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270400442X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Brisebarre:2005:NRR,
author = "Nicolas Brisebarre and David Defour and Peter Kornerup
and Jean-Michel Muller and Nathalie Revol",
title = "A New Range-Reduction Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "331--339",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.36",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Apr 27 18:04:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0331abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0331.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0331.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf?isnumber=30205&prod=JNL&arnumber=1388197&arSt=+331&ared=+339&arAuthor=Brisebarre%2C+N.%3B+Defour%2C+D.%3B+Kornerup%2C+P.%3B+Muller%2C+J.-M.%3B+Revol%2C+N.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388197&count=13&index=8;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388197",
abstract = "Range-reduction is a key point for getting accurate
elementary function routines. We introduce a new
algorithm that is fast for input arguments belonging to
the most common domains, yet accurate over the full
double-precision range.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Carlson:2005:JEF,
author = "B. C. Carlson",
title = "{Jacobian} elliptic functions as inverses of an
integral",
journal = j-J-COMPUT-APPL-MATH,
volume = "174",
number = "2",
pages = "355--359",
day = "15",
month = feb,
year = "2005",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:00:02 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042704002201",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Cheng:2005:SEEa,
author = "Howard Cheng and Barry Gergel and Ethan Kim and Eugene
Zima",
title = "Space-efficient evaluation of hypergeometric series",
journal = j-SIGSAM,
volume = "39",
number = "2",
pages = "41--52",
month = jun,
year = "2005",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Tue Nov 29 06:11:40 MST 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin (ACM Special Interest Group on
Symbolic and Algebraic Manipulation)",
issue = "152",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Cheng:2005:SEEb,
author = "Howard Cheng and Barry Gergel and Ethan Kim and Eugene
Zima",
title = "Space-efficient evaluation of hypergeometric series",
journal = j-SIGSAM,
volume = "39",
number = "3",
pages = "81--83",
year = "2005",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Sat Feb 4 09:52:36 MST 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
note = "ISSAC 2005 poster abstract.",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin (ACM Special Interest Group on
Symbolic and Algebraic Manipulation)",
issue = "153",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@InProceedings{deDinechin:2005:TPU,
author = "Florent de Dinechin and Alexey Ershov and Nicolas
Gast",
title = "Towards the Post-ultimate {\tt libm}",
crossref = "IEEE:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arith17.polito.it/final/paper-165.pdf",
abstract = "This article presents advances on the subject of
correctly rounded elementary functions since the
publication of the {\tt libultim} mathematical library
developed by Ziv at IBM. This library showed that the
average performance and memory overhead of correct
rounding could be made negligible. However, the
worst-case overhead was still a factor 1000 or more. It
is shown here that, with current processor technology,
this worst-case overhead can be kept within a factor of
2 to 10 of current best libms. This low overhead has
very positive consequences on the techniques for
implementing and proving correctly rounded functions,
which are also studied. These results lift the last
technical obstacles to a generalisation of (at least
some) correctly rounded double precision elementary
functions.",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@Article{Freitas:2005:IPF,
author = "Pedro Freitas",
title = "Integrals of polylogarithmic functions, recurrence
relations, and associated {Euler} sums",
journal = j-MATH-COMPUT,
volume = "74",
number = "251",
pages = "1425--1440",
month = jul,
year = "2005",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Aug 2 10:37:19 MDT 2005",
bibsource = "http://www.ams.org/mcom/2005-74-251;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib",
URL = "http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/home.html;
http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.dvi;
http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.pdf;
http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.ps;
http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.tex",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Hernandez:2005:ACN,
author = "M. A. Hern{\'a}ndez and N. Romero",
title = "Accelerated convergence in {Newton}'s method for
approximating square roots",
journal = j-J-COMPUT-APPL-MATH,
volume = "177",
number = "1",
pages = "225--229",
day = "1",
month = may,
year = "2005",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2004.09.025",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:00:04 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042704004315",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Misc{IBM:2005:MAS,
author = "{IBM Corporation}",
title = "{Mathematical Acceleration Subsystem} for {Linux}",
howpublished = "World Wide Web document",
year = "2005",
bibdate = "Mon Dec 05 18:59:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www-306.ibm.com/software/awdtools/mass/linux/mass-linux.html",
abstract = "Mathematical Acceleration Subsystem (MASS) for Linux
consists of libraries of mathematical intrinsic
functions tuned specifically for optimum performance on
POWER architectures.",
acknowledgement = ack-nhfb,
keywords = "Mathematical Acceleration Subsystem (MASS)",
remark = "Scalar library functions: atan, atan2, cos, cosh,
dnint, exp, log, pow [Fortran **], rsqrt, sin, sinh,
sqrt, tan, and tanh.\par
Vector library double-precision function: vacos, vasin,
vatan2, vcbrt, vcos, vcosh, vcosisin, vdint, vdiv,
vdnint, vexp, vexpm1, vlog, vlog10, vlog1p, vpow,
vrcbrt, vrec, vrsqrt, vsin, vsincos, vsinh, vsqrt,
vtan, and vtanh.\par
Vector library single-precision functions: vsacos,
vsasin, vsatan2, vscbrt, vscos, vscosh, vscosisin,
vsdiv, vsexp, vsexpm1, vslog, vslog10, vslog1p, vspow,
vsrcbrt, vsrec, vsrsqrt, vssin, vssincos, vssinh,
vssqrt, vstan, and vstanh.",
}
@Article{Kornerup:2005:DSS,
author = "Peter Kornerup",
title = "Digit Selection for {SRT} Division and Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "294--303",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.47",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 19 09:20:54 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0294abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0294.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0294.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388194.pdf?isnumber=30205&prod=JNL&arnumber=1388194&arSt=+294&ared=+303&arAuthor=Kornerup%2C+P.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388194&count=13&index=5;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388194",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "The quotient digit selection in the SRT division
algorithm is based on a few most significant bits of
the remainder and divisor, where the remainder is
usually represented in a redundant representation. The
number of leading bits needed depends on \ldots{}",
}
@Article{Ledoux:2005:CME,
author = "V. Ledoux and M. {Van Daele} and G. {Vanden Berghe}",
title = "{CP} methods and the evaluation of negative energy
{Coulomb} {Whittaker} functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "183",
number = "1",
pages = "168--176",
day = "1",
month = nov,
year = "2005",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:00:34 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042705000233",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Lee:2005:OHF,
author = "Dong-U. Lee and Altaf Abdul Gaffar and Oskar Mencer
and Wayne Luk",
title = "Optimizing hardware function evaluation",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "12",
pages = "1520--1531",
month = dec,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.201",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:04:26 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
abstract = "We present a methodology and an automated system for
function evaluation unit generation. Our system selects
the best function evaluation hardware for a given
function, accuracy requirements, technology mapping,
and optimization metrics, such as area, throughput, and
latency. Function evaluation $ f(x) $ typically
consists of range reduction and the actual evaluation
on a small convenient interval such as $ [0, \pi / 2) $
for $ \sin (x) $. We investigate the impact of hardware
function evaluation with range reduction for a given
range and precision of $x$ and $ f(x) $ on area and
speed. An automated bit-width optimization technique
for minimizing the sizes of the operators in the data
paths is also proposed. We explore a vast design space
for fixed-point $ \sin (x) $, $ \log (x) $, and $ \sqrt
{x} $ accurate to one unit in the last place using
MATLAB and ASC, a stream compiler for
field-programmable gate arrays (FPGAs). In this study,
we implement over 2,000 placed-and-routed FPGA designs,
resulting in over 100 million application-specific
integrated circuit (ASIC) equivalent gates. We provide
optimal function evaluation results for range and
precision combinations between 8 and 48 bits.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "application specific integrated circuits;
application-specific integrated circuit equivalent
gates; ASC; ASIC; automated bit-width optimization
technique; circuit optimisation; computer arithmetic;
elementary function approximation; field programmable
gate arrays; field-programmable gate arrays; fixed
point arithmetic; fixed-point arithmetic; FPGA;
hardware function evaluation optimisation; logic
design; MATLAB; minimax approximation; range reduction;
stream compiler",
}
@InProceedings{Lefevre:2005:NRD,
author = "Vincent Lef{\`e}vre",
title = "New Results on the Distance Between a Segment and {$
Z^2 $}. {Application} to the Exact Rounding",
crossref = "IEEE:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arith17.polito.it/final/paper-147.pdf",
abstract = "This paper presents extensions to Lef{\'e}vre's
algorithm that computes a lower bound on the distance
between a segment and a regular grid $ Z^2 $. This
algorithm and, in particular, the extensions are useful
in the search for worst cases for the exact rounding of
unary elementary functions or base-conversion
functions. The proof that is presented here is simpler
and less technical than the original proof. This paper
also gives benchmark results with various optimization
parameters, explanations of these results, and an
application to base conversion.",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@InProceedings{Markstein:2005:FSM,
author = "Peter Markstein",
title = "A Fast-Start Method for Computing the Inverse
Tangent",
crossref = "IEEE:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arith17.polito.it/final/paper-112.pdf",
abstract = "In a search for an algorithm to compute $ \atan (x) $
which has both low latency and few floating point
instructions, an interesting variant of familiar
trigonometry formulas was discovered that allow the
start of argument reduction to commence before any
references to tables stored in memory are needed. Low
latency makes the method suitable for a closed
subroutine, and few floating point operations make the
method advantageous for a software-pipelined
implementation.",
acknowledgement = ack-nhfb,
keywords = "IA-64; Itanium-2",
pagecount = "6",
}
@Article{Merkle:2005:GRG,
author = "M. Merkle",
title = "{Gurland}'s ratio for the gamma function",
journal = j-COMPUT-MATH-APPL,
volume = "49",
number = "2--3",
pages = "389--406",
month = jan # "\slash " # feb,
year = "2005",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:42 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122105000416",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Perram:2005:EFW,
author = "John W. Perram and Edgar R. Smith",
title = "Elliptic Functions of the Worst Kind: Non-linear
Quantisation of the Classical Spherical Pendulum",
journal = j-ADV-QUANTUM-CHEM,
volume = "48",
pages = "111--125",
year = "2005",
CODEN = "AQCHA9",
DOI = "https://doi.org/10.1016/S0065-3276(05)48008-9",
ISSN = "0065-3276",
ISSN-L = "0065-3276",
bibdate = "Thu Oct 13 11:45:04 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/bookseries/00653276;
https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0065327605480089",
acknowledgement = ack-nhfb,
ajournal = "Adv. Quantum Chem.",
fjournal = "Advances in Quantum Chemistry",
journal-URL = "http://www.sciencedirect.com/science/bookseries/00653276",
}
@Article{Pineiro:2005:HSF,
author = "Jose-Alejandro Pi{\~n}eiro and Stuart F. Oberman and
Jean-Michel Muller and Javier D. Bruguera",
title = "High-Speed Function Approximation Using a Minimax
Quadratic Interpolator",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "304--318",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.52",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 19 09:20:54 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0304abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0304.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0304.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388195.pdf?isnumber=30205&prod=JNL&arnumber=1388195&arSt=+304&ared=+318&arAuthor=Pineiro%2C+J.-A.%3B+Oberman%2C+S.F.%3B+Muller%2C+J.-M.%3B+Bruguera%2C+J.D.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388195&count=13&index=6;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388195",
abstract = "A table-based method for high-speed function
approximation in single-precision floating-point format
is presented in this paper. Our focus is the
approximation of reciprocal, square root, square root
reciprocal, exponentials, logarithms, trigonometric
functions, powering (with a fixed exponent $p$ ), or
special functions. The algorithm presented here
combines table look-up, an enhanced minimax quadratic
approximation, and an efficient evaluation of the
second-degree polynomial (using a specialized squaring
unit, redundant arithmetic, and multioperand addition).
The execution times and area costs of an architecture
implementing our method are estimated, showing the
achievement of the fast execution times of linear
approximation methods and the reduced area requirements
of other second-degree interpolation algorithms.
Moreover, the use of an enhanced minimax approximation
which, through an iterative process, takes into account
the effect of rounding the polynomial coefficients to a
finite size allows for a further reduction in the size
of the look-up tables to be used, making our method
very suitable for the implementation of an elementary
function generator in state-of-the-art DSPs or graphics
processing units (GPUs).",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Shore:2005:ARB,
author = "Haim Shore",
title = "Accurate {RMM}-Based Approximations for the {CDF} of
the Normal Distribution",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "34",
number = "3",
pages = "507--513",
year = "2005",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1081/STA-200052102",
ISSN = "0361-0926 (print), 1532-415X (electronic)",
ISSN-L = "0361-0926",
bibdate = "Wed Jan 27 05:42:00 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
}
@Book{Simon:2005:DCF,
author = "Marvin Kenneth Simon and Mohamed-Slim Alouini",
title = "Digital Communication over Fading Channels",
publisher = pub-WI,
address = pub-WI:adr,
edition = "Second",
pages = "xxxiv + 900",
year = "2005",
DOI = "https://doi.org/10.1002/0471715220",
ISBN = "0-471-64953-8 (hardcover)",
ISBN-13 = "978-0-471-64953-3 (hardcover)",
LCCN = "TK5103.7 .S523 2005",
bibdate = "Sat Dec 16 17:34:06 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley series in telecommunications and signal
processing",
URL = "http://www.loc.gov/catdir/description/wiley042/2004042040.html;
http://www.loc.gov/catdir/enhancements/fy0617/2004042040-b.html;
http://www.loc.gov/catdir/toc/wiley041/2004042040.html",
acknowledgement = ack-nhfb,
author-dates = "1939--",
subject = "Digital communications; Reliability; Mathematics;
Radio; Transmitters and transmission; Fading",
tableofcontents = "Preface \\
Nomenclature \\
Part 1: Fundamentals \\
1. Introduction \\
2. Fading Channel Characterization and Modeling \\
3. Types of Communication \\
Part 2: Mathematical TOOLS \\
4. Alternative Representations of Classical Functions
\\
5. Some Useful Expressions for Evaluating Average Error
Probability Performance \\
6. New Representations of Some Probability Density and
Cumulative Distribution Functions for Correlative
Fading Applications \\
Part 3: Optimum Reception and Performance Evaluation
\\
7. Optimum Receivers for Fading Channels. \\
8. Performance of Single-Channel Receivers. \\
9. Performance of Multichannel Receivers. \\
Part 4: Multiuser Communication Systems \\
10. Outage Performance of Multiuser Communication
Systems \\
11. Optimum Combining --- A Diversity Technique for
Communication Over Fading Channels in the Presence of
Interference \\
12. Direct-Sequence Code-Division Multiple Access
(DS-CDMA) \\
Part 5: Coded Communication Systems \\
13. Coded Communicatuion over Fading Channels. \\
14. Multichannel Transmission-Transmit Diversity and
Space-Time Coding \\
15. Capacity of Fading Channels \\
Index",
}
@Article{Skorokhodov:2005:MCG,
author = "S. L. Skorokhodov",
title = "A method for computing generalized hypergeometric
function {$_p F_{p - 1}(a_1, \ldots {}, a_p; b_1,
\ldots {}, b_{p - 1}; 1)$} in terms of the {Riemann}
zeta function",
journal = j-COMPUT-MATH-MATH-PHYS,
volume = "45",
number = "4",
pages = "550--562",
month = "????",
year = "2005",
CODEN = "????",
ISSN = "0965-5425 (print), 1555-6662 (electronic)",
ISSN-L = "0965-5425",
bibdate = "Thu Dec 01 09:31:40 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "1077.33008",
acknowledgement = ack-nhfb,
classmath = "33C20 (Generalized hypergeometric series, ${}_pF_q$)",
fjournal = "Computational Mathematics and Mathematical Physics",
keywords = "generalized hypergeometric functions; Hurwitz zeta
function; hypergeometric function; Riemann zeta
function",
xxnote = "Is the journal name correct??",
}
@InProceedings{Stehle:2005:GAT,
author = "Damien Stehl{\'e} and Paul Zimmermann",
title = "{Gal}'s Accurate Tables Method Revisited",
crossref = "IEEE:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arith17.polito.it/final/paper-152.pdf",
abstract = "Gal's accurate tables algorithm aims at providing an
efficient implementation of mathematical functions with
correct rounding as often as possible. This method
requires an expensive pre-computation of the values
taken by the function or by several related functions
at some distinguished points. Our improvements of Gal's
method are two-fold: on the one hand we describe what
is the arguably best set of distinguished values and
how it improves the efficiency and accuracy of the
function implementation, and on the other hand we give
an algorithm which drastically decreases the cost of
the pre-computation. These improvements are related to
the worst cases for the correct rounding of
mathematical functions and to the algorithms for
finding them. We demonstrate how the whole method can
be turned into practice for $ 2^x $ and $ \sin x $ for
$ x \in [1 / 2, 1) $, in double precision.",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@Article{Stehle:2005:SWC,
author = "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
Zimmermann",
title = "Searching Worst Cases of a One-Variable Function Using
Lattice Reduction",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "340--346",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.55",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 19 09:20:54 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0340abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0340.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0340.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388198.pdf?isnumber=30205&prod=JNL&arnumber=1388198&arSt=+340&ared=+346&arAuthor=Stehle%2C+D.%3B+Lefevre%2C+V.%3B+Zimmermann%2C+P.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388198&count=13&index=9;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388198",
abstract = "We propose a new algorithm to find worst cases for the
correct rounding of a mathematical function of one
variable. We first reduce this problem to the real
small value problem---i.e., for polynomials with real
coefficients. Then, we show that this second problem
can be solved efficiently by extending Coppersmith's
work on the integer small value problem---for
polynomials with integer coefficients---using lattice
reduction. For floating-point numbers with a mantissa
less than $N$ and a polynomial approximation of degree
$d$, our algorithm finds all worst cases at distance
less than $ N^{\frac {-d^2}{2d + 1}} $ from a machine
number in time $ O(N^{{\frac {d + 12d + 1}} +
\varepsilon }) $. For $ d = 2 $, a detailed study
improves on the $ O(N^{2 / 3 + \varepsilon }) $
complexity from Lef{\`e}vre's algorithm to $ O(N^{4 / 7
+ \varepsilon }) $. For larger $d$, our algorithm can
be used to check that there exist no worst cases at
distance less than $ N^{-k} $ in time $ O(N^{1 / 2 +
\varepsilon }) $.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Computer arithmetic; correct rounding; multiple
precision arithmetic; special function approximations",
}
@Article{Uzer:2005:CAS,
author = "A. Uzer and T. Ege",
title = "On the Convergence Acceleration of Slowly Convergent
Sums Involving Oscillating Terms",
journal = j-COMPUTING,
volume = "75",
number = "4",
pages = "311--318",
month = aug,
year = "2005",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-005-0126-2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65F05; 65F30; 65F50",
bibdate = "Tue Jul 8 22:32:46 MDT 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=75&issue=4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=75&issue=4&spage=311",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "convergence acceleration; Fourier series; infinite
sums; slowly convergent sums; zeta functions",
}
@InProceedings{Walters:2005:EFA,
author = "George Walters and Michael Schulte",
title = "Efficient Function Approximation Using Truncated
Multipliers and Squarers",
crossref = "IEEE:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arith17.polito.it/final/paper-190.pdf",
abstract = "This paper presents a technique for designing linear
and quadratic interpolators for function approximation
using truncated multipliers and squarers. Initial
coefficient values are found using a Chebyshev series
approximation, and then adjusted through exhaustive
simulation to minimize the maximum absolute error of
the interpolator output. This technique is suitable for
any function and any precision up to 24-bits (IEEE
single precision). Designs for linear and quadratic
interpolators that implement the reciprocal function, $
f(x) = 1 / x, $ are presented and analyzed as an
example. We show that a 24-bit truncated reciprocal
quadratic interpolator with a design specification of $
\pm 1 $ ulp error requires 24.1\% fewer partial
products to implement than a comparable standard
interpolator with the same error specification.",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@InProceedings{Wang:2005:DFPa,
author = "L.-K. Wang and M. J. Schulte",
title = "Decimal Floating-Point Square Root Using
{Newton--Raphson} Iteration",
crossref = "Vassiliadis:2005:IIC",
pages = "309--315",
year = "2005",
bibdate = "Sun Mar 04 10:19:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2005-05.pdf",
abstract = "With continued reductions in feature size, additional
functionality may be added to future microprocessors to
boost the performance of important application domains.
Due to growth in commercial, financial, and
Internet-based applications, decimal floating point
arithmetic is now attracting more attention and
hardware support for decimal operations is being
considered by various computer manufacturers. In order
to standardize decimal number formats and operations,
specifications for decimal floating-point arithmetic
have been added to the draft revision of the IEEE-754
Standard for Floating-Point Arithmetic (IEEE-754R).
This paper presents an efficient arithmetic algorithm
and hardware design for decimal floating-point square
root. This design uses an optimized piecewise linear
approximation, a modified Newton--Raphson iteration, a
specialized rounding technique, and a modified decimal
multiplier. Synthesis results show that a 64-bit
(16-digit) implementation of decimal square root, which
is compliant with IEEE-754R, has an estimated critical
path delay of 0.95 ns and a maximum latency of 210
clock cycles when implemented using a sequential
multiplier and LSI Logic's 0.11 micron Gflx-P standard
cell library.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Weber:2005:MIG,
author = "Kenneth Weber and Vilmar Trevisan and Luiz Felipe
Martins",
title = "A modular integer {GCD} algorithm",
journal = j-J-ALG,
volume = "54",
number = "2",
pages = "152--167",
month = feb,
year = "2005",
CODEN = "JOALDV",
DOI = "https://doi.org/10.1016/j.jalgor.2004.06.006",
ISSN = "0196-6774 (print), 1090-2678 (electronic)",
ISSN-L = "0196-6774",
bibdate = "Tue Dec 11 09:21:34 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jalg.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0196677404001075",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms",
journal-URL = "http://www.sciencedirect.com/science/journal/01966774",
}
@Article{West:2005:BAC,
author = "G. West",
title = "Better approximations to cumulative normal functions",
journal = "Wilmott Magazine",
volume = "??",
number = "??",
pages = "70--76",
month = "????",
year = "2005",
ISSN = "1540-6962 (print), 1541-8286 (electronic)",
ISSN-L = "1540-6962",
bibdate = "Sat Dec 16 17:59:43 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1541-8286;
https://www.wilmott.com/category/magazine/",
remark = "No issues online at Wiley before year 2011, or at
Wilmott before 2006.",
}
@TechReport{Zimmermann:2005:XXX,
author = "Paul Zimmermann",
title = "5,341,321",
type = "Technical report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "2",
day = "8",
month = jun,
year = "2005",
bibdate = "Sun Sep 10 07:32:04 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/5341321.ps.gz",
abstract = "This short note shows the nasty effects of patents for
the development of free software, even for patents that
were not written with software applications in mind.",
acknowledgement = ack-nhfb,
keywords = "floating-point division; Karp--Markstein patent on
modified Newton--Raphson iteration",
remark = "The title is the number of the U.S. Patent on the
algorithm described in the article, which is a
completely trivial modification of Newton--Raphson
iteration, published in \cite{Karp:1997:HPD}. The
patent itself is \cite{Karp:1994:FPA}, and it expired
on 5 May 2013.",
}
@InProceedings{Anderson:2006:AMF,
author = "Cristina S. Anderson and Shane Story and Nikita
Astafiev",
title = "Accurate Math Functions on the {Intel IA-32}
Architecture: a Performance-Driven Design",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@TechReport{Bertot:2006:PGS,
author = "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
title = "A proof of {GMP} square root using the {Coq}
assistant",
type = "Research Report",
number = "RR-4475",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "28",
year = "2006",
bibdate = "Sun Sep 10 08:34:35 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4475.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4475.ps.gz;
http://www.inria.fr/rrrt/rr-4475.html",
abstract = "We present a formal proof (at the implementation
level) of an efficient algorithm proposed in to compute
square roots of arbitrarily large integers. This
program, which is part of the GNU Multiple Precision
Arithmetic Library (GMP), is completely proven within
the system. Proofs are developed using the Correctness
tool to deal with imperative features of the program.
The formalization is rather large (more than 13000
lines) and requires some advanced techniques for proof
management and reuse.",
acknowledgement = ack-nhfb,
}
@Article{Bogolubsky:2006:FEH,
author = "A. I. Bogolubsky and S. L. Skorokhodov",
title = "Fast evaluation of the hypergeometric function {$_p
F_{p - 1}(a; b; z)$} at the singular point $ z = 1 $ by
means of the {Hurwitz} zeta function $ \zeta (\alpha,
s) $",
journal = j-PROG-COMP-SOFT,
volume = "32",
number = "??",
pages = "145--153",
month = "????",
year = "2006",
CODEN = "PCSODA",
ISSN = "0361-7688 (print), 1608-3261 (electronic)",
ISSN-L = "0361-7688",
bibdate = "Thu Dec 01 09:34:31 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Programming and Computer Software; translation of
Programmirovaniye (Moscow, USSR) Plenum",
journal-URL = "http://link.springer.com/journal/11086",
}
@Article{Boldo:2006:PFF,
author = "Sylvie Boldo",
editor = "Ulrich Furbach and Natarajan Shankar",
booktitle = "{Automated Reasoning: Third International Joint
Conference, IJCAR 2006, Seattle, WA, USA, August
17--20, 2006, Proceedings}",
title = "Pitfalls of a full floating-point proof: Example on
the formal proof of the {Veltkamp\slash Dekker}
algorithms",
journal = j-LECT-NOTES-COMP-SCI,
bookpages = "xv + 680",
pages = "52--66",
year = "2006",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/11814771_6",
ISBN = "3-540-37187-7 (paperback), 3-540-37188-5",
ISBN-13 = "978-3-540-37187-8 (paperback), 978-3-540-37188-5",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.9.A96 I33 2006eb",
MRnumber = "MR2354672",
bibdate = "Mon Jun 12 16:14:21 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/11814771",
book-URL = "http://www.springer.com/us/book/9783540371878",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@TechReport{Brent:2006:FAH,
author = "Richard P. Brent",
title = "Fast Algorithms for High-Precision Computation of
Elementary Functions",
type = "Report",
number = "??",
institution = "Australian National University",
address = "Canberra, ACT 0200, Australia",
pages = "61",
day = "12",
month = jul,
year = "2006",
bibdate = "Fri Sep 04 16:33:10 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://rnc7.loria.fr/brent_invited.pdf;
https://maths-people.anu.edu.au/~brent/pd/RNC7t.pdf",
acknowledgement = ack-nhfb,
keywords = "arithmetic-geometric mean",
remark = "From page 57: ``This talk is based on a chapter of a
book that Paul Zimmermann and I are writing''. That
book is entry \cite{Brent:2011:MCA}.",
}
@TechReport{Crandall:2006:NFP,
author = "Richard E. Crandall",
title = "Note on fast polylogarithm computation",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "6",
month = jan,
year = "2006",
bibdate = "Tue Mar 19 09:03:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://people.reed.edu/~crandall/papers/Polylog.pdf;
https://web.archive.org/web/20120916145721/http://people.reed.edu/~crandall/papers/Polylog.pdf",
abstract = "The polylogarithm function $ \Li_n(z) = \sum_{k =
1}^\infty z^k / k^n $, manifestly convergent for $ |z|
\eq 1 $, integer $ n > 1 $, is sometimes
numerically\slash symbolically relevant for $ |z| > 1
$, i.e., the analytic continuation may be required. By
exploiting analytic symmetry relations, we give, for
integer $n$, simple and efficient algorithms for
complete continuation in complex $z$.",
acknowledgement = ack-nhfb,
}
@Article{Cuyt:2006:ERM,
author = "Annie Cuyt and Brigitte Verdonk and Haakon Waadeland",
title = "Efficient and Reliable Multiprecision Implementation
of Elementary and Special Functions",
journal = j-SIAM-J-SCI-COMP,
volume = "28",
number = "4",
pages = "1437--1462",
month = jan,
year = "2006",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/050629203",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:43:41 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/28/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{deDinechin:2006:STP,
author = "Florent de Dinechin and Sergey Maidanov",
title = "Software techniques for perfect elementary functions
in floating-point interval arithmetic",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Book{ElAttar:2006:SFO,
author = "Refaat A. {El Attar}",
title = "Special functions and orthogonal polynomials",
volume = "3",
publisher = "Lulu Press",
address = "Morrisville, NC, USA",
pages = "vi + 302",
year = "2006",
ISBN = "1-4116-6690-9 (paperback)",
ISBN-13 = "978-1-4116-6690-0 (paperback)",
LCCN = "QA404.5 .E5 2006; QA351 .E5 2006",
bibdate = "Sat Oct 30 17:42:31 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
series = "Mathematical series",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Orthogonal polynomials; Polinomios
ortogonales; Series ortogonales",
tableofcontents = "Series solutions of differential equations \\
Gamma and beta functions and others \\
Legendre polynomials \\
Hermite polynomials \\
Laguerre and other orthogonal polynomials \\
Bessel functions",
}
@Article{Ferreira:2006:GHF,
author = "C. Ferreira and J. L. L{\'o}pez and E. P.
Sinus{\'\i}a",
title = "The {Gauss} hypergeometric function {$ F(a; b; c; z)
$} for large $c$",
journal = j-J-COMPUT-APPL-MATH,
volume = "197",
number = "2",
pages = "568--577",
day = "15",
month = jan,
year = "2006",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "33C05 (33F05 41A60)",
MRnumber = "MR2260426 (2007i:33012)",
bibdate = "Thu Dec 01 09:20:59 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
remark = "$ F(a; b; c; z) = {}_2 F_1 (a, b + 1; c + 2; z) $",
}
@Article{Gil:2006:ARP,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 850}: {Real} parabolic cylinder functions
{$ U(a, x) $, $ V(a, x) $}",
journal = j-TOMS,
volume = "32",
number = "1",
pages = "102--112",
month = mar,
year = "2006",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1132973.1132978",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri May 26 06:32:19 MDT 2006",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Fortran 90 programs for the computation of real
parabolic cylinder functions are presented. The code
computes the functions $ U(a, x) $, $ V(a, x) $ and
their derivatives for real $a$ and $ x (x \geq 0) $.
The code also computes scaled functions. The range of
computation for scaled PCFs is practically
unrestricted. The aimed relative accuracy for scaled
functions is better than $ 5 \times 10^{14} $.
Exceptions to this accuracy are the evaluation of the
functions near their zeros and the error caused by the
evaluation of trigonometric functions of large
arguments when $ |a| > x $. The routines always give
values for which the Wronskian relation for scaled
functions is verified with a relative accuracy better
than $ 5 \times 10^{14} $. The accuracy of the unscaled
functions is also better than $ 5 \times 10^{14} $ for
moderate values of $x$ and $a$ (except close to the
zeros), while for large $x$ and $a$ the error is
dominated by exponential and trigonometric function
evaluations. For IEEE standard double precision
arithmetic, the accuracy is better than $ 5 \times
10^{13} $ in the computable range of unscaled PCFs
(except close to the zeros).",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gil:2006:CRP,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Computing the real parabolic cylinder functions {$
U(a, x) $, $ V(a, x) $}",
journal = j-TOMS,
volume = "32",
number = "1",
pages = "70--101",
month = mar,
year = "2006",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1132973.1132977",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri May 26 06:32:19 MDT 2006",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Methods for the computation of real parabolic cylinder
functions $ U(a, x) $, and $ V(a, x) $ and their
derivatives are described. We give details on power
series, asymptotic series, recursion and quadrature. A
combination of these methods can be used for computing
parabolic cylinder functions for unrestricted values of
the order $a$ and the variable $x$ except for the
overflow\slash underflow limitations. By factoring the
dominant exponential factor, scaled functions can be
computed without practical overflow\slash underflow
limitations. In an accompanying article we describe the
precise domains for these methods and we present the
Fortran 90 codes for the computation of these
functions.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Jones:2006:PCF,
author = "D. S. Jones",
title = "Parabolic cylinder functions of large order",
journal = j-J-COMPUT-APPL-MATH,
volume = "190",
number = "1--2",
pages = "453--469",
day = "1",
month = jun,
year = "2006",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:11:58 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042705002463",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Kong:2006:IGA,
author = "Fanyu Kong and Zhun Cai and Jia Yu and Daxing Li",
title = "Improved generalized {Atkin} algorithm for computing
square roots in finite fields",
journal = j-INFO-PROC-LETT,
volume = "98",
number = "1",
pages = "1--5",
day = "15",
month = apr,
year = "2006",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Thu Mar 31 18:41:08 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@InProceedings{Muller:2006:GFA,
author = "Jean-Michel Muller",
editor = "Michael B. Matthews",
booktitle = "{2006 Fortieth Asilomar Conference on Signals, Systems
and Computers. October 29--November 1, 2006. Pacific
Grove, California}",
title = "Generating function approximations at compile time",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "328--331",
year = "2006",
DOI = "https://doi.org/10.1109/ACSSC.2006.354761",
ISBN = "1-4244-0785-0",
ISBN-13 = "978-1-4244-0785-9",
bibdate = "Fri Sep 29 10:57:58 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Nowak:2006:MCA,
author = "Rafal Nowak",
title = "A method of convergence acceleration of some continued
fractions",
journal = j-NUMER-ALGORITHMS,
volume = "41",
number = "3",
pages = "297--317",
month = mar,
year = "2006",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-005-9013-3",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "subject classification; 30B70; 40A15; 65B99",
bibdate = "Tue Jul 8 19:14:28 MDT 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=41&issue=3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=41&issue=3&spage=297",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "continued fraction; convergence acceleration; modified
approximant; tail",
}
@Article{Ozban:2006:NMA,
author = "Ahmet Ya{\c{s}}ar {\"O}zban",
title = "New methods for approximating square roots",
journal = j-APPL-MATH-COMP,
volume = "175",
number = "1",
pages = "532--540",
day = "1",
month = apr,
year = "2006",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:02:54 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@InProceedings{Parks:2006:UTS,
author = "Michael Parks",
title = "Unifying Tests for Square Root",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Article{Qian:2006:HMP,
author = "Jianbo Qian and Cao An Wang",
title = "How much precision is needed to compare two sums of
square roots of integers?",
journal = j-INFO-PROC-LETT,
volume = "100",
number = "5",
pages = "194--198",
day = "16",
month = dec,
year = "2006",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Thu Mar 31 15:52:31 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Shi:2006:NAS,
author = "Xiquan Shi and Fengshan Liu and Minghan Hu",
title = "A new asymptotic series for the Gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "195",
number = "1--2",
pages = "134--154",
day = "15",
month = oct,
year = "2006",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2005.03.081",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:12:01 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042705004802",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Sidi:2006:CTC,
author = "Avram Sidi",
title = "A challenging test for convergence accelerators:
Summation of a series with a special sign pattern",
journal = "App. Math. E-Notes",
volume = "6",
number = "??",
pages = "225--234",
month = "????",
year = "2006",
CODEN = "????",
ISSN = "????",
MRclass = "40A99 (11M41 40A05 65B10)",
MRnumber = "MR2231748 (2007h:40009)",
bibdate = "Thu Dec 01 10:33:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration; Shanks transformation",
}
@InProceedings{Thakkar:2006:PDP,
author = "Anuja J. Thakkar and Abdel Ejnioui",
title = "Pipelining of double precision floating point division
and square root operations",
crossref = "Menezes:2006:PAS",
pages = "488--493",
year = "2006",
DOI = "https://doi.org/10.1145/1185448.1185555",
bibdate = "Sat Oct 9 13:04:49 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Space applications rely increasingly on high data rate
DSP algorithms. These algorithms use double precision
floating point arithmetic operations. While most DSP
applications can be compiled on DSP processors, high
data rate DSP computations require novel implementation
technologies to support their high throughputs. Only
recently, gate densities in FPGAs have reached a level
which makes them attractive platforms to implement
compute-intensive DSP applications. In this context,
this paper presents the sequential and pipelined
designs of a double precision floating point divider
and square root unit on FPGAs. Contrary to pipelined
parallel implementations, the pipelining of these units
is based on unrolling the iterations in low-radix digit
recurrence algorithms. These units are mapped on
generic FPGA reconfigurable fabric without taking
advantage of any advanced architectural components
available in high capacity FPGAs. The implementations
of these designs show that their performances are
comparable to, and sometimes higher than, the
performances of non-iterative designs based of high
radix numbers. The iterative divider and square root
unit occupy less than 1\% of an XC2V6000 FPGA chip
while their pipelined counterparts can produce
throughputs that reach the 100 MFLOPS mark by consuming
a modest 8\% of the chip area.",
acknowledgement = ack-nhfb,
}
@Article{VanDeun:2006:ACI,
author = "Joris {Van Deun} and Ronald Cools",
title = "{Algorithm 858}: {Computing} infinite range integrals
of an arbitrary product of {Bessel} functions",
journal = j-TOMS,
volume = "32",
number = "4",
pages = "580--596",
month = dec,
year = "2006",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1186785.1186790",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Apr 14 09:48:57 MDT 2007",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We present an algorithm to compute integrals of the
form $ \int_0^\infty x^m \prod^k_i = 1 J_{\nu_i}(a_i
x)d x $ with $ J_{\nu_i}(x) $ the Bessel function of
the first kind and (real) order $ \nu_i $. The
parameter $m$ is a real number such that $ \sum_i \nu_i
+ m > - 1 $ and the coefficients $ a_i $ are strictly
positive real numbers. The main ingredients in this
algorithm are the well-known asymptotic expansion for $
J_{\nu_i}(x) $ and the observation that the infinite
part of the integral can be approximated using the
incomplete Gamma function $ \Gamma (a, z) $. Accurate
error estimates are included in the algorithm, which is
implemented as a MATLAB program.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{VanDeun:2006:SRI,
author = "Joris {Van Deun} and Ronald Cools",
title = "A stable recurrence for the incomplete gamma function
with imaginary second argument",
journal = j-NUM-MATH,
volume = "104",
number = "4",
pages = "445--456",
month = oct,
year = "2006",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-006-0026-1",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Tue Jul 8 10:28:23 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wires:2006:RRS,
author = "Kent E. Wires and Michael J. Schulte",
title = "Reciprocal and Reciprocal Square Root Units with
Operand Modification and Multiplication",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "42",
number = "3",
pages = "257--272",
month = mar,
year = "2006",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/s11265-006-4186-0",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Mar 05 08:26:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://springerlink.metapress.com/content/t6027p6713727606/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Barnett:2007:HPV,
author = "Ross Barnett and J. A. Youngman",
booktitle = "{1st Joint Meeting of the American Mathematical
Society and the New Zealand Mathematical Society,
Victoria University of Wellington, Wellington, New
Zealand, December 12--15, 2007}",
title = "High-Precision Values of the Gamma Function of real
argument",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "????",
year = "2007",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Mon Jul 14 11:57:00 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://homepages.mcs.vuw.ac.nz/~mathmeet/amsnzms2007/abstracts.pdf",
abstract = "A method is described to calculate values of $ \Gamma
(\nu) $, $ 0 \leq \nu \leq 1 $ to arbitrary precision
by combining a Bessel function with a $_0 F_1$
function. Steed's algorithm is used to compute the
regular Bessel function $ J_\nu (x) $, for a suitable
argument $x$ and real $ \nu $, to arbitrary accuracy.
Hence the gamma function is obtained. Example values
are given to 200D. Verification is by the 80D-results
of Frans{\'e}n and Wrigge, by the use of the
duplication formula, and by computing the closed form
results of Borwein and Zucker. A caveat is offered
concerning the coding of the Bessel functions in
Numerical Recipes and in the GSL library.",
acknowledgement = ack-nhfb,
}
@Article{Batterman:2007:SSF,
author = "Robert W. Batterman",
title = "On the Specialness of Special Functions (The Nonrandom
Effusions of the Divine Mathematician)",
journal = j-BRITISH-J-PHILOS-SCI,
volume = "58",
number = "2",
pages = "263--286",
month = jun,
year = "2007",
CODEN = "BJPIA5",
DOI = "https://doi.org/10.1093/bjps/axm007",
ISSN = "0007-0882 (print), 1464-3537 (electronic)",
ISSN-L = "0007-0882",
bibdate = "Thu Oct 7 14:03:55 MDT 2010",
bibsource = "http://bjps.oxfordjournals.org/content/58/2.toc;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bjps.oxfordjournals.org/content/58/2/263.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "British Journal for the Philosophy of Science",
journal-URL = "http://www.jstor.org/journals/00070882.html",
onlinedate = "May 18, 2007",
}
@InProceedings{Burgess:2007:DAV,
author = "Neil Burgess and Chris N. Hinds",
title = "Design of the {ARM VFP11} Divide and Square Root
Synthesisable Macrocell",
crossref = "Kornerup:2007:PIS",
pages = "87--96",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.15",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents the detailed design of the ARM
VFP11 Divide and Square Root synthesisable macrocell.
The macrocell was designed using the minimum-redundancy
radix-4 SRT digit recurrence algorithm, and this paper
describes a novel acceleration technique employed to
achieve the required processor clock frequency of up to
750MHz in 90nm CMOS. Logical Effort theory is used to
provide a delay analysis of the unit, which
demonstrates the balanced nature of the two critical
paths therein.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Cerone:2007:SFA,
author = "Pietro Cerone",
title = "Special functions: approximations and bounds",
journal = "Applicable Analysis and Discrete Mathematics",
volume = "1",
number = "1",
pages = "72--91",
year = "2007",
DOI = "https://doi.org/10.2298/AADM0701072C",
ISSN = "1452-8630 (print), 2406-100X (electronic)",
ISSN-L = "1452-8630",
MRclass = "26D15 (26D20 33B15 33C05)",
MRnumber = "2316589",
MRreviewer = "Pierpaolo Natalini",
bibdate = "Thu Jul 29 07:41:55 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://pefmath.etf.rs/accepted/AADM-Vol1-No1-72-91.pdf",
abstract = "The Steffensen inequality and bounds for the
{\v{C}}eby{\v{s}}ev functional are utilised to obtain
bounds for some classical special functions. The
technique relies on determining bounds on integrals of
products of functions. The above techniques are used to
obtain novel and useful bounds for the Bessel function
of the first kind, the Beta function, and the Zeta
function.",
acknowledgement = ack-nhfb,
ajournal = "Appl. Anal. Discrete Math.",
fjournal = "Applicable Analysis and Discrete Mathematics",
}
@Book{Chakraborty:2007:VSF,
author = "Kalyan Chakraborty and Shigeru Kanemitsu and Haruo
Tsukada",
title = "Vistas of special functions {II}",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xii + 215",
year = "2007",
ISBN = "981-270-774-3",
ISBN-13 = "978-981-270-774-1",
LCCN = "QA351 .K35 2007",
bibdate = "Sat Oct 30 17:02:07 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
prodorbis.library.yale.edu:7090/voyager",
abstract = "This is a unique book for studying special functions
through zeta-functions. Many important formulas of
special functions scattered throughout the literature
are located in their proper positions and readers get
enlightened access to them in this book. The areas
covered include: Bernoulli polynomials, the gamma
function (the beta and the digamma function), the
zeta-functions (the Hurwitz, the Lerch, and the Epstein
zeta-function), Bessel functions, an introduction to
Fourier analysis, finite Fourier series, Dirichlet
L-functions, the rudiments of complex functions and
summation formulas. The Fourier series for the (first)
periodic Bernoulli polynomial is effectively used,
familiarizing the reader with the relationship between
special functions and zeta-functions.",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Bernoulli polynomials",
tableofcontents = "The theory of Bernoulli and allied polynomials \\
The theory of the gamma and related functions \\
The theory of the Hurwitz--Lerch zeta-functions \\
The theory of Bernoulli polynomials via zeta-functions
\\
The theory of the gamma and related functions via
zeta-functions \\
The theory of Bessel functions and the Epstein
zeta-functions \\
Fourier series and Fourier transforms \\
Around Dirichlet's $L$-functions \\
Appendix A: Complex functions \\
Appendix B: Summation formulas and convergence
theorems",
}
@Article{Dyer:2007:AEF,
author = "Stephen Dyer and Justin Dyer",
title = "Approximations to Error Functions",
journal = "IEEE Instrumentation \& Measurement Magazine",
volume = "10",
number = "6",
pages = "45--48",
month = dec,
year = "2007",
DOI = "https://doi.org/10.1109/mim.2007.4428581",
bibdate = "Sat Dec 16 16:26:38 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/abstract/document/4428581/",
acknowledgement = ack-nhfb,
}
@Article{Ercegovac:2007:CSR,
author = "Milo{\v{s}} D. Ercegovac and Jean-Michel Muller",
title = "Complex Square Root with Operand Prescaling",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "49",
number = "1",
pages = "19--30",
month = oct,
year = "2007",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/s11265-006-0029-2",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Nov 05 19:24:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We propose a radix-$r$ digit-recurrence algorithm for
complex square-root. The operand is prescaled to allow
the selection of square-root digits by rounding of the
residual. This leads to a simple hardware
implementation of digit selection. Moreover, the use of
digit recurrence approach allows correct rounding of
the result if needed. The algorithm, compatible with
the complex division presented in Ercegovac and Muller
(``Complex Division with Prescaling of the Operands,''
in Proc. Application-Specific Systems, Architectures,
and Processors (ASAP'03), The Hague, The Netherlands,
June 24---26, 2003), and its design are described. We
also give rough estimates of its latency and cost with
respect to implementation based on standard
floating-point instructions as used in software
routines for complex square root.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@Article{Ferraro:2007:FAG,
author = "Giovanni Ferraro",
title = "The foundational aspects of {Gauss}'s work on the
hypergeometric, factorial and digamma functions",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "61",
number = "5",
pages = "457--518",
month = sep,
year = "2007",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/s00407-007-0004-8",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "33-03 (01A50 33B15 33C05)",
MRnumber = "2329096 (2009d:33002)",
MRreviewer = "M. E. Muldoon",
bibdate = "Fri Feb 4 21:50:42 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=61&issue=5;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=61&issue=5&spage=457",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
MRtitle = "The foundational aspects of {Gauss}'s work on the
hypergeometric, factorial and digamma functions",
}
@Article{Fousse:2007:MMP,
author = "Laurent Fousse and Guillaume Hanrot and Vincent
Lef{\`e}vre and Patrick P{\'e}lissier and Paul
Zimmermann",
title = "{MPFR}: a multiple-precision binary floating-point
library with correct rounding",
journal = j-TOMS,
volume = "33",
number = "2",
pages = "1--15",
month = jun,
year = "2007",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1236463.1236468",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G99",
MRnumber = "MR2326955",
bibdate = "Thu Jul 26 17:36:59 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "This article presents a multiple-precision binary
floating-point library, written in the ISO C language,
and based on the GNU MP library. Its particularity is
to extend to arbitrary-precision, ideas from the IEEE
754 standard, by providing correct rounding and
exceptions. We demonstrate how these strong semantics
are achieved---with no significant slowdown with
respect to other arbitrary-precision tools---and
discuss a few applications where such a library can be
useful.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Book{Gil:2007:NMS,
author = "Amparo Gil and Javier Segura and N. M. Temme",
title = "Numerical Methods for Special Functions",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xvi + 415",
year = "2007",
DOI = "https://doi.org/10.1137/1.9780898717822",
ISBN = "0-89871-634-9",
ISBN-13 = "978-0-89871-634-4",
LCCN = "QA351 .G455 2007",
bibdate = "Fri Sep 14 10:24:22 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$99.00",
acknowledgement = ack-nhfb,
shorttableofcontents = "Preface \\
1. Introduction \\
I. Basic methods \\
2. Convergent and divergent series \\
3. Chebyshev expansions \\
4. Linear recurrence relations and associated continued
fractions \\
5. Quadrature methods \\
II. Further tools and methods \\
6. Numerical aspects of continued fractions \\
7. Computation of the zeros of special functions \\
8. Uniform asymptotic expansions \\
9. Other methods \\
III. Related topics and examples \\
10. Inversion of cumulative distribution functions \\
11. Further examples \\
12. Associated algorithms \\
List of algorithms \\
Bibliography \\
Index",
subject = "functions, special; data processing; numerical
analysis; asymptotic expansions; approximation theory",
tableofcontents = "Preface xiii 1 Introduction / 1 \\
I Basic Methods / 13 \\
2 Convergent and Divergent Series / 15 \\
2.1 Introduction / 15 \\
2.1.1 Power series: First steps / 15 \\
2.1.2 Further practical aspects / 17 \\
2.2 Differential equations and Frobenius series
solutions / 18 \\
2.2.1 Singular points / 19 \\
2.2.2 The solution near a regular point / 20 \\
2.2.3 Power series expansions around a regular singular
point / 22 \\
2.2.4 The Liouville transformation / 25 \\
2.3 Hypergeometric series / 26 \\
2.3.1 The Gauss hypergeometric function / 28 \\
2.3.2 Other power series for the Gauss hypergeometric
function / 30 \\
2.3.3 Removable singularities / 33 \\
2.4 Asymptotic expansions / 34 \\
2.4.1 Watson's lemma / 36 \\
2.4.2 Estimating the remainders of asymptotic
expansions / 38 \\
2.4.3 Exponentially improved asymptotic expansions / 39
\\
2.4.4 Alternatives of asymptotic expansions / 40 \\
3 Chebyshev Expansions / 51 \\
3.1 Introduction / 51 \\
3.2 Basic results on interpolation / 52 \\
3.2.1 The Runge phenomenon and the Chebyshev nodes / 54
\\
3.3 Chebyshev polynomials: Basic properties / 56 \\
3.3.1 Properties of the Chebyshev polynomials $T_n(x)$
/ 56 \\
3.3.2 Chebyshev polynomials of the second, third, and
fourth kinds / 60 \\
vii 3.4 Chebyshev interpolation / 62 \\
3.4.1 Computing the Chebyshev interpolation polynomial
/ 64 \\
3.5 Expansions in terms of Chebyshev polynomials / 66
\\
3.5.1 Convergence properties of Chebyshev expansions /
68 \\
3.6 Computing the coefficients of a Chebyshev expansion
/ 69 \\
3.6.1 Clenshaw's method for solutions of linear
differential equations with polynomial coefficients /
70 \\
3.7 Evaluation of a Chebyshev sum / 75 \\
3.7.1 Clenshaw's method for the evaluation of a
Chebyshev sum / 75 \\
3.8 Economization of power series / 80 \\
3.9 Example: Computation of Airy functions of real
variable / 80 \\
3.10 Chebyshev expansions with coefficients in terms of
special functions / 83 \\
4 Linear Recurrence Relations and Associated Continued
Fractions / 87 \\
4.1 Introduction / 87 \\
4.2 Condition of three-term recurrence relations / 88
\\
4.2.1 Minimal solutions / 89 \\
4.3 Perron's theorem / 92 \\
4.3.1 Scaled recurrence relations / 94 \\
4.4 Minimal solutions of TTRRs and continued fractions
/ 95 \\
4.5 Some notable recurrence relations / 96 \\
4.5.1 The confluent hypergeometric family / 96 \\
4.5.2 The Gauss hypergeometric family / 102 \\
4.6 Computing the minimal solution of a TTRR / 105 \\
4.6.1 Miller's algorithm when a function value is known
/ 105 \\
4.6.2 Miller's algorithm with a normalizing sum / 107
\\
4.6.3 ``Anti-Miller'' algorithm / 110 \\
4.7 Inhomogeneous linear difference equations / 112 \\
4.7.1 Inhomogeneous first order difference equations.
Examples / 112 \\
4.7.2 Inhomogeneous second order difference equations /
115 \\
4.7.3 Olver's method / 116 \\
4.8 Anomalous behavior of some second order homogeneous
and first order inhomogeneous recurrences / 118 \\
4.8.1 A canonical example: Modified Bessel function /
118 \\
4.8.2 Other examples: Hypergeometric recursions / 120
\\
4.8.3 A first order inhomogeneous equation / 121 \\
4.8.4 A warning / 122 \\
5 Quadrature Methods / 123 \\
5.1 Introduction / 123 \\
5.2 Newton--Cotes quadrature: The trapezoidal and
Simpson's rule / 124 \\
5.2.1 The compound trapezoidal rule / 126 \\
5.2.2 The recurrent trapezoidal rule / 129 \\
5.2.3 Euler's summation formula and the trapezoidal
rule / 130 \\
5.3 Gauss quadrature / 132 \\
5.3.1 Basics of the theory of orthogonal polynomials
and Gauss quadrature / 133 \\
5.3.2 The Golub--Welsch algorithm / 141 \\
5.3.3 Example: The Airy function in the complex plane /
145 \\
5.3.4 Further practical aspects of Gauss quadrature /
146 \\
5.4 The trapezoidal rule on $\mathbb{R}$ / 147 \\
5.4.1 Contour integral formulas for the truncation
errors / 148 \\
5.4.2 Transforming the variable of integration / 153
\\
5.5 Contour integrals and the saddle point method / 157
\\
5.5.1 The saddle point method / 158 \\
5.5.2 Other integration contours / 163 \\
5.5.3 Integrating along the saddle point contours and
examples / 165 \\
II Further Tools and Methods / 171 \\
6 Numerical Aspects of Continued Fractions / 173 \\
6.1 Introduction / 173 \\
6.2 Definitions and notation / 173 \\
6.3 Equivalence transformations and contractions / 175
\\
6.4 Special forms of continued fractions / 178 \\
6.4.1 Stieltjes fractions / 178 \\
6.4.2 Jacobi fractions / 179 \\
6.4.3 Relation with Pad{\'e} approximants / 179 \\
6.5 Convergence of continued fractions / 179 \\
6.6 Numerical evaluation of continued fractions / 181
\\
6.6.1 Steed's algorithm / 181 \\
6.6.2 The modified Lentz algorithm / 183 \\
6.7 Special functions and continued fractions / 185 \\
6.7.1 Incomplete gamma function / 186 \\
6.7.2 Gauss hypergeometric functions / 187 \\
7 Computation of the Zeros of Special Functions / 191
\\
7.1 Introduction / 191 \\
7.2 Some classical methods / 193 \\
7.2.1 The bisection method / 193 \\
7.2.2 The fixed point method and the Newton--Raphson
method / 193 \\
7.2.3 Complex zeros / 197 \\
7.3 Local strategies: Asymptotic and other
approximations / 197 \\
7.3.1 Asymptotic approximations for large zeros / 199
\\
7.3.2 Other approximations / 202 \\
7.4 Global strategies I: Matrix methods / 205 \\
7.4.1 The eigenvalue problem for orthogonal polynomials
/ 206 \\
7.4.2 The eigenvalue problem for minimal solutions of
TTRRs / 207 \\
7.5 Global strategies II: Global fixed point methods /
213 \\
7.5.1 Zeros of Bessel functions / 213 \\
7.5.2 The general case / 219 \\
7.6 Asymptotic methods: Further examples / 224 \\
7.6.1 Airy functions / 224 \\
7.6.2 Scorer functions / 227 \\
7.6.3 The error functions / 229 \\
7.6.4 The parabolic cylinder function / 233 \\
7.6.5 Bessel functions / 233 \\
7.6.6 Orthogonal polynomials / 234 \\
8 Uniform Asymptotic Expansions / 237 \\
8.1 Asymptotic expansions for the incomplete gamma
functions / 237 \\
8.2 Uniform asymptotic expansions / 239 \\
8.3 Uniform asymptotic expansions for the incomplete
gamma functions / 240 \\
8.3.1 The uniform expansion / 242 \\
8.3.2 Expansions for the coefficients / 244 \\
8.3.3 Numerical algorithm for small values of $\eta$ /
245 \\
8.3.4 A simpler uniform expansion / 247 \\
8.4 Airy-type expansions for Bessel functions / 249 \\
8.4.1 The Airy-type asymptotic expansions / 250 \\
8.4.2 Representations of $a_s()$, $b_s()$, $c_s()$,
$d_s()$ / 253 \\
8.4.3 Properties of the functions $A_\nu$, $B_\nu$,
$C_\nu$, $D_\nu$ / 254 \\
8.4.4 Expansions for $a_s()$, $b_s()$, $c_s()$, $d_s()$
/ 256 \\
8.4.5 Evaluation of the functions $A_\nu()$, $B_\nu()$
by iteration / 258 \\
8.5 Airy-type asymptotic expansions obtained from
integrals / 263 \\
8.5.1 Airy-type asymptotic expansions / 264 \\
8.5.2 How to compute the coefficients $\alpha_n$,
$\beta_n$ / 267 \\
8.5.3 Application to parabolic cylinder functions / 270
\\
9 Other Methods / 275 \\
9.1 Introduction / 275 \\
9.2 Pad{\'e} approximations / 276 \\
9.2.1 Pad{\'e} approximants and continued fractions /
278 \\
9.2.2 How to compute the Pad{\'e} approximants / 278
\\
9.2.3 Pad{\'e} approximants to the exponential function
/ 280 \\
9.2.4 Analytic forms of Pad{\'e} approximations / 283
\\
9.3 Sequence transformations / 286 \\
9.3.1 The principles of sequence transformations / 286
\\
9.3.2 Examples of sequence transformations / 287 \\
9.3.3 The transformation of power series / 288 \\
9.3.4 Numerical examples / 288 \\
9.4 Best rational approximations / 290 \\
9.5 Numerical solution of ordinary differential
equations: Taylor expansion method / 291 \\
9.5.1 Taylor-series method: Initial value problems /
292 \\
9.5.2 Taylor-series method: Boundary value problem /
293 \\
9.6 Other quadrature methods / 294 \\
9.6.1 Romberg quadrature / 294 \\
9.6.2 Fej{\'e}r and Clenshaw--Curtis quadratures / 296
\\
9.6.3 Other Gaussian quadratures / 298 \\
9.6.4 Oscillatory integrals / 301 \\
III Related Topics and Examples / 307 \\
10 Inversion of Cumulative Distribution Functions / 309
\\
10.1 Introduction / 309 \\
10.2 Asymptotic inversion of the complementary error
function / 309 \\
10.3 Asymptotic inversion of incomplete gamma functions
/ 312 \\
10.3.1 The asymptotic inversion method / 312 \\
10.3.2 Determination of the coefficients i / 314 \\
10.3.3 Expansions of the coefficients i / 316 \\
10.3.4 Numerical examples / 316 \\
10.4 Generalizations / 317 \\
10.5 Asymptotic inversion of the incomplete beta
function / 318 \\
10.5.1 The nearly symmetric case / 319 \\
10.5.2 The general error function case / 322 \\
10.5.3 The incomplete gamma function case / 324 \\
10.5.4 Numerical aspects / 326 \\
10.6 High order Newton-like methods / 327 \\
11 Further Examples / 331 \\
11.1 Introduction / 331 \\
11.2 The Euler summation formula / 331 \\
11.3 Approximations of Stirling numbers / 336 \\
11.3.1 Definitions / 337 \\
11.3.2 Asymptotics for Stirling numbers of the second
kind / 338 \\
11.3.3 Stirling numbers of the first kind / 343 \\
11.4 Symmetric elliptic integrals / 344 \\
11.4.1 The standard forms in terms of symmetric
integrals / 345 \\
11.4.2 An algorithm / 346 \\
11.4.3 Other elliptic integrals / 347 \\
11.5 Numerical inversion of Laplace transforms / 347
\\
11.5.1 Complex Gauss quadrature / 348 \\
11.5.2 Deforming the contour / 349 \\
11.5.3 Using Pad{\'e} approximations / 352 \\
IV Software / 353 \\
12 Associated Algorithms / 355 \\
12.1 Introduction / 355 \\
12.1.1 Errors and stability: Basic terminology / 356
\\
12.1.2 Design and testing of software for computing
functions: General philosophy / 357 \\
12.1.3 Scaling the functions / 358 \\
12.2 Airy and Scorer functions of complex arguments /
359 \\
12.2.1 Purpose / 359 \\
12.2.2 Algorithms / 359 \\
12.3 Associated Legendre functions of integer and
half-integer degrees / 363 \\
12.3.1 Purpose / 363 \\
12.3.2 Algorithms / 364 \\
12.4 Bessel functions / 369 \\
12.4.1 Modified Bessel functions of integer and
half-integer orders / 370 \\
12.4.2 Modified Bessel functions of purely imaginary
orders / 372 \\
12.5 Parabolic cylinder functions / 377 \\
12.5.1 Purpose / 377 \\
12.5.2 Algorithm / 378 \\
12.6 Zeros of Bessel functions / 385 \\
12.6.1 Purpose / 385 \\
12.6.2 Algorithm / 385 \\
List of Algorithms / 387 \\
Bibliography / 389 \\
Index / 405",
}
@Article{Gil:2007:NSS,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Numerically satisfactory solutions of hypergeometric
recursions",
journal = j-MATH-COMPUT,
volume = "76",
number = "259",
pages = "1449--1468",
month = jul,
year = "2007",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Jul 8 06:24:22 MDT 2008",
bibsource = "http://www.ams.org/mcom/2007-76-259;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib",
URL = "http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01918-7/home.html;
http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01918-7/S0025-5718-07-01918-7.dvi;
http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01918-7/S0025-5718-07-01918-7.pdf;
http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01918-7/S0025-5718-07-01918-7.ps",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Glaser:2007:FAC,
author = "Andreas Glaser and Xiangtao Liu and Vladimir Rokhlin",
title = "A Fast Algorithm for the Calculation of the Roots of
Special Functions",
journal = j-SIAM-J-SCI-COMP,
volume = "29",
number = "4",
pages = "1420--1438",
month = "????",
year = "2007",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/06067016X",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:43:53 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/29/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "We describe a procedure for the determination of the
roots of functions satisfying second-order ordinary
differential equations, including the classical special
functions. The scheme is based on a combination of the
Pr{\"u}fer transform with the classical Taylor series
method for the solution of ordinary differential
equations and requires $ O(1) $ operations for the
determination of each root. When the functions in
question are classical orthogonal polynomials
(Legendre, Hermite, etc.), the techniques presented
here also provide tools for the evaluation of the
weights for the associated Gaussian quadratures. The
performance of the scheme for several classical special
functions (prolate spheroidal wave functions, Bessel
functions, and Legendre, Hermite, and Laguerre
polynomials) is illustrated with numerical examples.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Book{Gradshteyn:2007:TIS,
author = "I. S. Gradshteyn and I. M. Ryzhik and Alan Jeffrey and
Daniel Zwillinger",
title = "Table of Integrals, Series and Products",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
edition = "Seventh",
pages = "xlv + 1171",
year = "2007",
ISBN = "0-12-373637-4 (hardcover)",
ISBN-13 = "978-0-12-373637-6 (hardcover)",
LCCN = "QA55 .G6613 2007",
bibdate = "Thu Feb 18 12:04:10 MST 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
prodorbis.library.yale.edu:7090/voyager",
acknowledgement = ack-nhfb,
remark = "Previous edition 2000. Includes CD-ROM.",
subject = "Mathematics; Tables",
tableofcontents = "0 Introduction \\
1 Elementary Functions \\
2 Indefinite Integrals of Elementary Functions \\
3 Definite Integrals of Elementary Functions \\
4.Combinations involving trigonometric and hyperbolic
functions and power \\
5 Indefinite Integrals of Special Functions \\
6 Definite Integrals of Special Functions \\
7.Associated Legendre Functions \\
8 Special Functions \\
9 Hypergeometric Functions \\
10 Vector Field Theory \\
11 Algebraic Inequalities \\
12 Integral Inequalities \\
13 Matrices and related results \\
14 Determinants \\
15 Norms \\
16 Ordinary differential equations \\
17 Fourier, Laplace, and Mellin Transforms \\
18 The z-transform",
xxauthor = "I. S. (Izrail Solomonovich) Gradshteyn and I. M.
(Iosif Moiseevich) Ryzhik and Alan Jeffrey and Daniel
Zwillinger",
}
@Article{Guseinov:2007:UTE,
author = "I. I. Guseinov and B. A. Mamedov",
title = "Unified treatment for the evaluation of generalized
complete and incomplete gamma functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "202",
number = "2",
pages = "435--439",
day = "15",
month = may,
year = "2007",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:13:14 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042706001506",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Hernandez:2007:MPO,
author = "M. A. Hern{\'a}ndez and N. Romero",
title = "Methods with prefixed order for approximating square
roots with global and general convergence",
journal = j-APPL-MATH-COMP,
volume = "194",
number = "2",
pages = "346--353",
day = "15",
month = dec,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:09 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Kalmykov:2007:AOEa,
author = "M. Y. Kalmykov and B. F. L. Ward and Y. Yost",
title = "All order $ \epsilon $-expansion of {Gauss}
hypergeometric functions with integer and half\slash
integer values of parameters",
journal = j-J-HIGH-ENERGY-PHYS,
volume = "2007",
number = "02",
pages = "040--??",
month = "????",
year = "2007",
CODEN = "JHEPAB",
ISSN = "1126-6708",
ISSN-L = "1029-8479",
MRclass = "33C05 (33B30)",
MRnumber = "MR2318011 (2009g:33004)",
bibdate = "Thu Dec 01 09:16:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "JHEP",
fjournal = "Journal of High Energy Physics",
pagecount = "21",
}
@Article{Kalmykov:2007:AOEb,
author = "M. Y. Kalmykov and B. F. L. Ward and Y. Yost",
title = "On the all-order $ \epsilon $-expansion of generalized
hypergeometric functions with integer values of
parameters",
journal = j-J-HIGH-ENERGY-PHYS,
volume = "2007",
number = "11",
pages = "009",
month = "????",
year = "2007",
CODEN = "JHEPAB",
ISSN = "1126-6708",
ISSN-L = "1029-8479",
MRclass = "33C20 (33B30 41A58)",
MRnumber = "MR2362140 (2008m:33016)",
bibdate = "Thu Dec 01 09:16:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "JHEP",
fjournal = "Journal of High Energy Physics",
pagecount = "13",
}
@Article{Karagiannidis:2007:IAG,
author = "George Karagiannidis and Athanasios Lioumpas",
title = "An Improved Approximation for the {Gaussian}
{$Q$}-Function",
journal = j-IEEE-COMMUN-LET,
volume = "11",
number = "8",
pages = "644--646",
month = aug,
year = "2007",
CODEN = "ICLEF6",
DOI = "https://doi.org/10.1109/lcomm.2007.070470",
ISSN = "1089-7798 (print), 1558-2558 (electronic)",
ISSN-L = "1089-7798",
bibdate = "Sat Dec 16 16:49:58 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See corrections and comments \cite{Dyer:2008:CCI}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Communications Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}
@Book{King:2007:DNC,
author = "Louis Vessot King",
title = "On the Direct Numerical Calculation of Elliptic
Functions and Integrals",
publisher = "Mellon Press",
address = "",
pages = "56",
year = "2007",
ISBN = "1-4067-4226-0",
ISBN-13 = "978-1-4067-4226-8",
LCCN = "",
bibdate = "Wed Feb 03 08:53:04 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
note = "Dedicated to the memory of James Harkness, Peter
Redpath Professor of Pure Mathematics, McGill
University 1903--1923.",
URL = "https://www.google.com/books/edition/On_the_Direct_Numerical_Calculation_of_E/CMM4AAAAMAAJ",
acknowledgement = ack-nhfb,
remark = "The AGM method for Jacobian elliptic functions was
discovered by this book's author at McGill University
in 1913, first published in \cite{King:1921:SNF}, and
then in a 1924 monograph, of which this is a reprint.",
tableofcontents = "Preface / v \\
Introduction / 1 \\
II. Historical Note on Landen's Transformation and the
Various Scales of Moduli and Amplitudes / 2 \\
III. On the Scale of Arithmetico-Geometrical Means / 6
\\
IV. Landen's Scale of Increasing Amplitudes:
$\tan(\phi_{n + 1} - \phi_n) = (b_n / a_n) \tan \phi_n$
/ 7 \\
(i) Calculation of $F(\phi, k)$, $E(\phi, k)$, $K$, and
$E$ / 7 \\
(ii) Calculation of $\sn(u,k)$, $\cn(u,k)$, $\dn(u,k)$
in terms of the argument $u$ / 9 \\
V. The Hyperbolic Scale of Increasing Amplitudes:
$\tanh(\phi_{n + 1} - \phi_n) = (b_n / a_n)
\tanh(\phi_n)$ / 10 \\
(i) Calculation of $F(\phi, k')$, $E(\phi, k')$, etc. /
10 \\
(ii) Calculation of $\sn(u,k')$, $\cn(u,k')$,
$\dn(u,k')$ / 11 \\
(iii) Calculation of $\sn(i u,k)$, $\cn(i u,k)$, $\dn(i
u,k)$ / 12 \\
VI: Gauss' Scale of Increasing Amplitudes \\
VII: Landen's Scale of Decreasing Amplitudes:
$\sin(2\psi_{n + 1} - \psi_n) = (b_n / a_n) \sin
\psi)n$ / 14 \\
(i) Calculation of $F(\psi, k')$, $E(\psi, k')$, etc. /
14 \\
(ii) Calculation of $\sn(u,k')$, $\cn(u,k')$,
$\dn(u,k')$ / 16 \\
VIII. The Hyperbolic Scale of Decreasing Amplitudes:
$\sinh(2\psi_{n + 1} - \psi_n) = (b_n / a_n) \sinh
\psi)n$ / 17 \\
(i) Calculation of $F(\psi, k)$, $E(\psi, k)$, etc. /
17 \\
(ii) Calculation of $\sn(u,k)$, $\cn(u,k)$, $\dn(u,k)$
/ 18 \\
IX. On the Numerical Computation of the Third Elliptic
Integral / 19 \\
Case I. $n$ negative, between $0$ and $-k^2$
(Hyperbolic case) / 19 \\
Case II. $n$ negative, between $-1$ and $-\infty$
(Hyperbolic case) / 20 \\
Case III. $n$ negative, between $-k^2$ and $-1$
(Circular case) / 21 \\
First Method. (i) Use of circular recurrence formulae /
22 \\
(ii) Use of hyperbolic recurrence formulae / 23 \\
Second Method. (i) Use of circular recurrence formulae
/ 25 \\
(ii) Use of hyperbolic recurrence formulae / 25 \\
Case IV. $n$ positive, between $0$ and $\infty$
(Circular case) / 26 \\
First Method. (i) Use of circular recurrence formulae /
26 \\
(ii) Use of hyperbolic recurrence formulae / 27 \\
Second Method. (i) Use of circular recurrence formulae
/ 28 \\
(ii) Use of hyperbolic recurrence formulae / 29 \\
X. Note on the Calculation of the Third Elliptic
Integral in Terms of the Complementary A.G.M. Scale /
30 \\
Summary of Formulae / 31 \\
Appendix, Examples 1--35 / 35",
}
@Article{Kodama:2007:RA,
author = "Masao Kodama",
title = "Remark on {Algorithm 644}",
journal = j-TOMS,
volume = "33",
number = "4",
pages = "28:1--28:3",
month = aug,
year = "2007",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1268776.1268783",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Dec 17 18:09:13 MST 2007",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See
\cite{Amos:1986:APP,Amos:1990:RPP,Amos:1995:RAP}.",
abstract = "This remark details correction for errors in the
functions which compute the modified Bessel function of
the second kind and the log of the gamma function. In
both cases these errors cause a loss of precision for a
small range of values of the $ \nu $ argument. These
routines are used in the calculation of a number of
other functions within the package whose accuracy is
thus similarly affected.",
acknowledgement = ack-nhfb,
articleno = "28",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Kuijlaars:2007:TIH,
author = "A. B. J. Kuijlaars and H. Stahl and W. {Van Assche}
and F. Wielonsky",
title = "{Type II} {Hermite--Pad{\'e}} approximation to the
exponential function",
journal = j-J-COMPUT-APPL-MATH,
volume = "207",
number = "2",
pages = "227--244",
day = "15",
month = oct,
year = "2007",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:13:18 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042706005978",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Kuliamin:2007:STI,
author = "V. V. Kuliamin",
title = "Standardization and testing of implementations of
mathematical functions in floating point numbers",
journal = j-PROG-COMP-SOFT,
volume = "33",
number = "3",
pages = "154--173",
year = "2007",
CODEN = "PCSODA",
DOI = "https://doi.org/10.1134/S036176880703005X",
ISSN = "0361-7688 (print), 1608-3261 (electronic)",
ISSN-L = "0361-7688",
bibdate = "Fri Aug 08 09:01:30 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Requirements definition and test suites development
for implementations of mathematical functions in
floating point arithmetic in the framework of the IEEE
754 standard are considered. A method based on this
standard is proposed for defining requirements for such
functions. This method can be used for the
standardization of implementations of such functions;
this kind of standardization extends IEEE 754. A method
for designing test suites for the verification of those
requirements is presented. The proposed methods are
based on specific properties of the representation of
floating point numbers and on some features of the
functions under examination.",
acknowledgement = ack-nhfb,
fjournal = "Programming and Computer Software; translation of
Programmirovaniye (Moscow, USSR) Plenum",
journal-URL = "http://link.springer.com/journal/11086",
keywords = "floating-point function testing and verification",
}
@TechReport{Lefevre:2007:SNP,
author = "Vincent Lef{\'e}vre and Jean-Michel Muller",
title = "Some notes on the possible under\slash overflow of the
most common elementary functions",
type = "Report",
institution = "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "Lyon, France",
pages = "7",
year = "2007",
bibdate = "Fri May 25 16:18:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://prunel.ccsd.cnrs.fr/ensl-00149414",
abstract = "The purpose of this short note is not to describe when
underflow or overflow must be signalled (it is quite
clear that the rules are the same as for the basic
arithmetic operations). We just want to show that for
some of the most common functions and floating-point
formats, in many cases, we can know in advance that the
results will always lie in the range of the numbers
that are representable by normal floating-point
numbers, so that in these cases there is no need to
worry about underflow or overflow. Note that when it is
not the case, an implementation is still possible using
a run-time test.",
acknowledgement = ack-nhfb,
keywords = "elementary functions; floating-point arithmetic;
overflow; underflow",
}
@Article{Neher:2007:CSF,
author = "Markus Neher",
title = "Complex standard functions and their implementation in
the {CoStLy} library",
journal = j-TOMS,
volume = "33",
number = "1",
pages = "2:1--2:27",
month = mar,
year = "2007",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1206040.1206042",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Apr 14 09:48:58 MDT 2007",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "The practical calculation of range bounds for some
complex standard functions is addressed in this
article. The functions under consideration are root and
power functions, the exponential, trigonometric and
hyperbolic functions, and their inverse functions. For
such a function $f$ and a given rectangular complex
interval $z$, some interval $w$ is computed that
contains all function values of $f$ in $z$. This is
done by expressing the real and the imaginary part of
$f$ as compositions of real standard functions and then
estimating the ranges of these compositions. In many
cases, the inclusions are optimal, such that $w$ is the
smallest rectangular interval containing the range of
$f$.
The algorithms presented in this article have been
implemented in a C++ class library called CoStLy
(Complex Standard Functions License), which is
distributed under the conditions of the GNU General
Public License.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Book{Press:2007:NRA,
author = "William H. Press and Saul A. Teukolsky and William T.
Vetterling and Brian P. Flannery",
title = "Numerical Recipes --- The Art of Scientific
Computing",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Third",
pages = "xxi + 1235",
year = "2007",
ISBN = "0-521-88068-8 (hardcover), 0-521-88407-1 (with source
code CD ROM), 0-521-70685-8 (source code CD ROM)",
ISBN-13 = "978-0-521-88068-8 (hardcover), 978-0-521-88407-5 (with
source code CD ROM), 978-0-521-70685-8 (source code CD
ROM)",
LCCN = "QA297 .N866 2007",
bibdate = "Wed Dec 15 10:40:52 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
URL = "http://www.cambridge.org/numericalrecipes",
acknowledgement = ack-nhfb,
subject = "numerical analysis; computer programs; science;
mathematics; C++ (computer program language)",
tableofcontents = "1. Preliminaries \\
2. Solution of linear algebraic equations \\
3. Interpolation and extrapolation \\
4. Integration of functions \\
5. Evaluation of functions \\
6. Special functions \\
7. Random numbers \\
8. Sorting and selection \\
9. Root finding and nonlinear sets of equations \\
10. Minimization or maximization of functions \\
11. Eigensystems \\
12. Fast Fourier Transform \\
13. Fourier and spectral applications \\
14. Statistical description of data \\
15. Modeling of data \\
16. Classification and inference \\
17. Integration of ordinary differential equations \\
18. Two-point boundary value problems \\
19. Integral equations and inverse theory \\
20. Partial differential equations \\
21. Computational geometry \\
22. Less-numerical algorithms",
}
@Article{Ren:2007:CFA,
author = "C. Ren and A. R. MacKenzie",
title = "Closed-form approximations to the error and
complementary error functions and their applications in
atmospheric science",
journal = j-ATMOS-SCI-LETT,
volume = "8",
number = "3",
pages = "70--73",
month = "????",
year = "2007",
DOI = "https://doi.org/10.1002/asl.154",
ISSN = "1530-261X",
ISSN-L = "1530-261X",
bibdate = "Sat Dec 16 17:25:42 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/asl.154/full",
acknowledgement = ack-nhfb,
fjournal = "Atmospheric Science Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/1530261X;
http://rmets.onlinelibrary.wiley.com/hub/journal/10.1002/(ISSN)1530-261X/",
}
@Article{Rokhlin:2007:AFC,
author = "Vladimir Rokhlin and Hong Xiao",
title = "Approximate formulae for certain prolate spheroidal
wave functions valid for large values of both order and
band-limit",
journal = j-APPL-COMPUT-HARMON-ANAL,
volume = "22",
number = "1",
pages = "105--123",
month = jan,
year = "2007",
DOI = "https://doi.org/10.1016/j.acha.2006.05.004",
ISSN = "1063-5203 (print), 1096-603x (electronic)",
ISSN-L = "1063-5203",
bibdate = "Sun Oct 31 10:00:51 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "We construct asymptotic formulae for the approximation
of certain prolate spheroidal wave functions and of the
corresponding eigenvalues. We investigate two regimes:
when the ratio $ c / m $ decays, and when both $c$ and
$m$ grow, but the ratio $ c / m $ stays bounded. Both
the regions of validity and the accuracies of the
obtained expansions are illustrated with numerical
examples.",
acknowledgement = ack-nhfb,
fjournal = "Applied and Computational Harmonic Analysis.
Time-Frequency and Time-Scale Analysis, Wavelets,
Numerical Algorithms, and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/10635203",
keywords = "approximation; asymptotic; band-limit; prolate
spheroidal wave functions",
}
@Article{Schmelzer:2007:CGF,
author = "Thomas Schmelzer and Lloyd N. Trefethen",
title = "Computing the Gamma Function Using Contour Integrals
and Rational Approximations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "45",
number = "2",
pages = "558--571",
month = "????",
year = "2007",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/050646342",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Mon Nov 24 18:03:07 MST 2008",
bibsource = "http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJNAAM&Volume=45&Issue=2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Book{Slavjanov:2007:SFU,
author = "Sergej J. Slavjanov and Wolfgang Lay",
title = "Special Functions: a Unified Theory Based on
Singularities",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 293",
year = "2007",
ISBN = "0-19-850573-6",
ISBN-13 = "978-0-19-850573-0",
LCCN = "????",
bibdate = "Tue Dec 5 11:27:46 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Oxford mathematical monographs; Oxford science
publications",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: Linear second-order ODEs with polynomial
coefficients \\
2: The hypergeometric class of equations \\
3: The Heun class of equations \\
4: Application to physical sciences \\
5: The Painlev{\'e} class of equations \\
Appendix A: The gamma function and related functions
\\
Appendix B: CTCPs Heun equations in general form \\
Appendix C: Multipole Matrix elements \\
Appendix D: SFTools \\
Database of the special functions",
subject = "Functions, Special; Fonctions sp{\'e}ciales;
Functions, Special",
tableofcontents = "1: Linear second-order ODEs with polynomial
coefficients \\
Regular singularities and Fuchsian equations \\
Regular and Fuchsian singularities \\
Fuchsian equations and their transformations \\
Characteristic exponents \\
Frobenius solutions \\
Irregular singularities and confluent equations \\
The $s$-rank of a singularity \\
Confluent and reduced confluent equations \\
The $s$-homotopic transformation \\
Asymptotic solutions at irregular singularities \\
Canonical forms \\
A generalization of Fuchs's theorem \\
Confluence and reduction processes \\
Strong and weak confluence. A confluence theorem \\
A confluence principle \\
Reduction of an equation \\
Classes and types of equations \\
Standard forms of equations \\
Invariants of $s$-homotopic transformations \\
Types of solutions \\
Eigenfunctions of singular Sturm--Liouville problems
\\
Central and lateral connection problems \\
Stokes lines at singularities. Stokes matrices \\
Generalized Riemann scheme \\
Applications \\
Central two-point connection problems (CTCPs) \\
Two regular singularities as relevant endpoints \\
One regular singularity and one irregular singularity
as the endpoints \\
A proof \\
Two irregular singularities \\
2: The hypergeometric class of equations \\
Classification scheme \\
General presentation \\
Hypergeometric equation \\
Confluent equations \\
Reduced confluent equations \\
Difference equations \\
General consideration \\
Difference equations for hypergeometric functions \\
Confluent hypergeometric functions \\
\ldots{}",
}
@Article{Srinivasan:2007:GFE,
author = "Gopala Krishna Srinivasan",
title = "The Gamma Function: An Eclectic Tour",
journal = j-AMER-MATH-MONTHLY,
volume = "114",
number = "4",
pages = "297--315",
month = apr,
year = "2007",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jan 30 12:00:28 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/i27642189;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/27642193",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Temme:2007:NAS,
author = "Nico M. Temme",
title = "Numerical aspects of special functions",
journal = j-ACTA-NUMERICA,
volume = "16",
pages = "379--478",
year = "2007",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492906330012",
ISBN = "0-521-87743-1",
ISBN-13 = "978-0-521-87743-5",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "33F05 (65D20)",
MRnumber = "2417932 (2009g:33027)",
MRreviewer = "Amparo Gil",
bibdate = "Sat Sep 24 11:37:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This paper describes methods that are important for
the numerical evaluation of certain functions that
frequently occur in applied mathematics, physics and
mathematical statistics. This includes what we consider
to be the basic methods, such as recurrence relations,
series expansions (both convergent and asymptotic), and
numerical quadrature. Several other methods are
available and some of these will be discussed in less
detail. Examples will be given on the use of special
functions in certain problems from mathematical physics
and mathematical statistics (integrals and series with
special functions).",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "24 April 2007",
}
@InCollection{Weniger:2007:AAT,
author = "Ernst Joachim Weniger",
title = "Asymptotic approximations to truncation errors of
series representations for special functions",
crossref = "Iske:2007:AAP",
pages = "331--348",
year = "2007",
MRclass = "33F05",
MRnumber = "MR2335174 (2008h:33051)",
bibdate = "Thu Dec 01 09:38:02 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "Bernoulli numbers; Euler--MacLaurin formula;
exponential integer $E_1(z)$; Gaussian hypergeometric
series $_2F_1(a / b / c / z)$; Riemann zeta function",
remark = "Available as math.CA/0511074.",
}
@Book{Agarwal:2008:OPD,
author = "Ravi P. Agarwal and Donal O'Regan",
title = "Ordinary and Partial Differential Equations: with
Special Functions, {Fourier} Series, and Boundary Value
Problems",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 410",
year = "2008",
ISBN = "0-387-79145-0 (paperback)",
ISBN-13 = "978-0-387-79145-6 (paperback)",
LCCN = "????",
bibdate = "Sat Oct 30 17:22:04 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Universitext",
acknowledgement = ack-nhfb,
subject = "differential equations; differential equations,
partial; Fourier analysis; boundary value problems",
tableofcontents = "Preface vii l. Solvable Differential Equations / 1
\\
2. Second-Order Differential Equations / 8 \\
3. Preliminaries to Series Solutions / 15 \\
4. Solution at an Ordinary Point / 23 \\
5. Solution at a Singular Point / 31 \\
6. Solution at a Singular Point (Cont'd.) / 37 \\
7. Legendre Polynomials and Functions / 47 \\
8. Chebyshev, Hermite and Laguerre Polynomials / 57 \\
9. Bessel Functions / 64 \\
10. Hypergeometrie Functions / 75 \\
11. Piecewise Continuous and Periodic Functions / 83
\\
12. Orthogonal Functions and Polynomials / 90 \\
13. Orthogonal Functions and Polynomials (Cont'd.) / 95
\\
14. Boundary Value Problems / 104 \\
15. Boundary Value Problems (Cont'd.) / 109 \\
16. Green's Functions / 119 \\
17. Regular Perturbations / 129 \\
18. Singular Perturbations / 138 \\
19. Sturm--Liouville Problems / 145 \\
20. Eigenfunction Expansions / 157 \\
21. Eigenfunction Expansions (Cont'd.) / 163 \\
22. Convergence of the Fourier Series / 171 \\
23. Convergence of the Fourier Series (Cont'd.) / 176
\\
24. Fourier Series Solutions of Ordinary Differential
Equations / 187 \\
25. Partial Differential Equations / 194 \\
26. First-Order Partial Differential Equations / 202
\\
27. Solvable Partial Differential Equations / 210 \\
28. The Canonical Forms / 219 \\
29. The Method of Separation of Variables / 227 \\
30. The One-Dimensional Heat Equation / 234 \\
31. The One-Dimensional Heat Equation (Cont'd.) / 241
\\
32. The One-Dimensional Wave Equation / 249 \\
33. The One-Dimensional Wave Equation (Cont'd.) / 256
\\
34. Laplace Equation in Two Dimensions / 266 \\
35. Laplace Equation in Polar Coordinates / 275 \\
36. Two-Dimensional Heat Equation / 284 \\
37. Two-Dimensional Wave Equation / 292 \\
38. Laplace Equation in Three Dimensions / 300 \\
39. Laplace Equation in Three Dimensions (Cont'd.) /
306 \\
40. Nonhomogeneous Equations / 316 \\
41. Fourier Integral and Transforms / 323 \\
42. Fourier Integral and Transforms (Cont'd.) / 330 \\
43. Fourier Transform Method for Partial DEs / 338 \\
44. Fourier Transform Method for Partial DEs (Cont'd.)
/ 344 \\
45. Laplace Transforms / 354 \\
46. Laplace Transforms (Cont'd.) / 361 \\
47. Laplace Transform Method for Ordinary DEs / 374 \\
48. Laplace Transform Method for Partial DEs / 384 \\
49. Well-Posed Problems / 394 \\
50. Verification of Solutions / 399 \\
References for Further Reading / 405 \\
Index / 407",
}
@Article{Alzer:2008:GFI,
author = "Horst Alzer",
title = "Gamma function inequalities",
journal = j-NUMER-ALGORITHMS,
volume = "49",
number = "1--4",
pages = "53--84",
month = dec,
year = "2008",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 14:08:26 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=53",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Ancarani:2008:DOC,
author = "L. U. Ancarani and G. Gasaneo",
title = "Derivatives of any order of the confluent
hypergeometric function {$_1 F_1 (a, b, z)$} with
respect to the parameter $a$ or $b$",
journal = j-J-MATH-PHYS,
volume = "49",
number = "6",
pages = "063508",
month = jun,
year = "2008",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.2939395",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Wed Oct 26 09:06:03 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys2005.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v49/i6/p063508_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "20 June 2008",
pagecount = "16",
}
@Article{Borwein:2008:EBF,
author = "David Borwein and Jonathan M. Borwein and O-Yeat
Chan",
title = "The evaluation of {Bessel} functions via exp--arc
integrals",
journal = j-J-MATH-ANAL-APPL,
volume = "341",
number = "1",
pages = "478--500",
month = may,
year = "2008",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/j.jmaa.2007.10.003",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "33C10 (33F05 65D20)",
MRnumber = "2394100",
MRreviewer = "Richard B. Paris",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://adsabs.harvard.edu/abs/2008JMAA..341..478B;
http://docserver.carma.newcastle.edu.au/1231/;
http://www.sciencedirect.com/science/article/pii/S0022247X07012346",
abstract = "A standard method for computing values of Bessel
functions has been to use the well-known ascending
series for small argument, and to use an asymptotic
series for large argument; with the choice of the
series changing at some appropriate argument magnitude,
depending on the number of digits required. In a recent
paper, D. Borwein, J. Borwein, and R. Crandall [D.
Borwein, J. M. Borwein, R. Crandall, Effective Laguerre
asymptotics, preprint at
http://locutus.cs.dal.ca:8088/archive/00000334/]
derived a series for an ``exp-arc'' integral which gave
rise to an absolutely convergent series for the J and I
Bessel functions with integral order. Such series can
be rapidly evaluated via recursion and elementary
operations, and provide a viable alternative to the
conventional ascending-asymptotic switching. In the
present work, we extend the method to deal with Bessel
functions of general (non-integral) order, as well as
to deal with the Y and K Bessel functions.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "Bessel function; Exponential-hyperbolic expansions;
Uniform series expansion",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2008:ELA,
author = "David Borwein and Jonathan M. Borwein and Richard E.
Crandall",
title = "Effective {Laguerre} asymptotics",
journal = j-SIAM-J-NUMER-ANAL,
volume = "46",
number = "6",
pages = "3285--3312",
year = "2008",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/07068031X",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "33C65 (30E20 34E05)",
MRnumber = "2448665",
MRreviewer = "Yu-Qiu Zhao",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://docserver.carma.newcastle.edu.au/334/",
abstract = "It is known that the generalized Laguerre polynomials
can enjoy subexponential growth for large primary
index. In particular, for certain fixed parameter pairs
(a, z) one has the large-n asymptotic behavior
L-n((-a)) (-z) similar to C(a, z)(n)(-a)/2-1/ (4)e(2)
root nz. We introduce a computationally motivated
contour integral that allows efficient numerical
Laguerre evaluations yet also leads to the complete
asymptotic series over the full parameter domain of
subexponential behavior. We present a fast algorithm
for symbolic generation of the rather formidable
expansion coefficients. Along the way we address the
difficult problem of establishing effective (i. e.,
rigorous and explicit) error bounds on the general
expansion. A primary tool for these developments is an
``exp-arc'' method giving a natural bridge between
converging series and effective asymptotics.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2008:ELA",
}
@InProceedings{Brisebarre:2008:EME,
author = "Nicolas Brisebarre and Sylvain Chevillard and
Milo{\v{s}} D. Ercegovac and Jean-Michel Muller and
Serge Torres",
title = "An Efficient Method for Evaluating Polynomial and
Rational Function Approximations",
crossref = "IEEE:2008:ICA",
pages = "233--238",
year = "2008",
DOI = "https://doi.org/10.1109/ASAP.2008.4580185",
bibdate = "Mon Feb 10 07:28:25 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Chatterjee:2008:CNT,
author = "S. Chatterjee and D. Roy",
title = "A class of new transforms tailored for the
hypergeometric series",
journal = j-COMP-PHYS-COMM,
volume = "179",
number = "8",
pages = "555--561",
day = "15",
month = oct,
year = "2008",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2008.05.001",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Dec 01 09:09:57 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
xxauthor = "S. Charterjee and D. Roy",
}
@Book{Cuyt:2008:HCF,
author = "Annie Cuyt and Vigdis B. Petersen and Brigitte Verdonk
and Haakon Waadeland and William B. Jones",
title = "Handbook of Continued Fractions for Special
Functions",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xx + 440",
year = "2008",
DOI = "https://doi.org/10.1007/978-1-4020-6949-9",
ISBN = "1-4020-6948-0",
ISBN-13 = "978-1-4020-6948-2",
LCCN = "QA295 .H275 2008",
bibdate = "Tue Jun 24 07:17:37 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "applying the limit process; associated continued
fraction; asymptotic series expansion; basic
hypergeometric functions; canonical contraction;
combination with property; complementary incomplete
gamma function; complex error function; confluent
hypergeometric series; continued fraction converges;
continued fraction representations; fraction
approximants; modified approximant; monic orthogonal
polynomial sequence; normed field; nth approximant; nth
denominator; nth numerator; nth tail; oval sequence
theorem; parabola theorem; partial numerators; strong
moment distribution function; successive approximants;
truncation error bounds",
shorttableofcontents = "General considerations \\
Part 1, Basic Theory \\
1. Basics \\
2. Continued fraction representation of functions \\
3. Convergence criteria \\
4. Pade approximants \\
5. Moment theory and orthogonal functions \\
Part 2, Numerics \\
6. Continued fraction construction \\
7. Truncation error bounds \\
8. Continued fraction evaluation \\
Part 3, Special Functions \\
9. On tables and graphs \\
10. Mathematical constants \\
11. Elementary functions \\
12. Gamma function and related functions \\
13. Error function and related integrals \\
14. Exponential integrals and related functions \\
15. Hypergeometric functions \\
16. Confluent hypergeometric functions, \\
17. Bessel functions \\
18. Probability functions \\
19. Basic hypergeometric functions",
tableofcontents = "Preface / xi \\
Notation / xiii \\
0 General considerations \\
/ 1 \\
0.1 Part one / 1 \\
0.2 Part two / 2 \\
0.3 Part three / 2 \\
\\
Part I: Basic Theory \\
\\
1 Basics / 9 \\
1.1 Symbols and notation \\
1.2 Definitions / 10 \\
1.3 Recurrence relations / 13 \\
1.4 Equivalence transformations / 15 \\
1.5 Contractions and extensions / 16 \\
1.6 Continued fractions with prescribed approximants /
18 \\
1.7 Connection between continued fractions and series /
19 \\
1.8 Periodic and limit periodic continued fractions /
21 \\
1.9 Tails of continued fractions / 23 \\
1.10 Continued fractions over normed fields / 26 \\
1.11 Generalisations of continued fractions / 28 \\
\\
2 Continued fraction representation of functions / 29
\\
2.1 Symbols and notation / 29 \\
2.2 Correspondence / 30 \\
2.3 Families of continued fractions / 35 \\
2.4 Correspondence of C-fractions / 39 \\
2.5 Correspondence of P-fractions / 40 \\
2.6 Correspondence of J-fractions and T-fractions / 41
\\
2.7 Correspondence and three-term recurrences / 42 \\
\\
3 Convergence criteria / 45 \\
3.1 Some classical theorems / 45 \\
3.2 Convergence sets and value sets / 47 \\
3.3 Parabola and oval theorems / 49 \\
3.4 Correspondence and uniform convergence / 52 \\
3.5 Periodic and limit periodic continued fractions /
53 \\
3.6 Convergence and minimal solutions / 56 \\
\\
4 Pad{\'e} approximants / 59 \\
4.1 Definition and notation / 59 \\
4.2 Fundamental properties / 60 \\
4.3 Connection with regular C-fractions / 64 \\
4.4 Connection with P-fractions / 65 \\
4.5 Extension of the Pad{\'e} table / 67 \\
4.6 Connection with M-fractions and the M-table / 68
\\
4.7 Convergence of Pad{\'e} approximants / 70 \\
4.8 Formal orthogonality property / 72 \\
\\
5 Moment theory and orthogonal functions / 77 \\
5.1 Moment theory / 77 \\
5.2 Stieltjes transforms / 85 \\
5.3 Construction of solutions / 90 \\
5.4 Orthogonal polynomials / 91 \\
5.5 Monic orthogonal polynomials on $\mathbb{R}$ and
J-fractions / 92 \\
5.6 Szeg{\H{o}} polynomials and PPC-fractions / 100 \\
5.7 Orthogonal Laurent polynomials and APT-fractions /
102 \\
\\
Part II: Numerics \\
\\
6 Continued fraction construction / 107 \\
6.1 Regular C-fractions / 107 \\
6.2 C-fractions / 113 \\
6.3 S-fractions / 114 \\
6.4 P-fractions / 114 \\
6.5 J-fractions / 120 \\
6.6 M-fractions / 122 \\
6.7 Positive T-fractions / 124 \\
6.8 Thiele fractions / 125 \\
\\
7 Truncation error bounds / 129 \\
7.1 Parabola theorems / 129 \\
7.2 The oval sequence theorem / 131 \\
7.3 The interval sequence theorem / 136 \\
7.4 Specific a priori bounds for S-fractions / 138 \\
7.5 A posteriori truncation error bounds / 140 \\
7.6 Tails and truncation error bounds / 143 \\
7.7 Choice of modification / 143 \\
\\
8 Continued fraction evaluation / 149 \\
8.1 The effect of finite precision arithmetic / 149 \\
8.2 Evaluation of approximants / 152 \\
8.3 The forward recurrence and minimal solutions / 154
\\
8.4 Round-off error in the backward recurrence / 156
\\
\\
Part III: Special Functions \\
\\
9 On tables and graphs / 163 \\
9.1 Introduction / 163 \\
9.2 Comparative tables / 163 \\
9.3 Reliable graphs / 168 \\
\\
10 Mathematical constants / 175 \\
10.1 Regular continued fractions / 175 \\
10.2 Archimedes' constant, symbol $\pi$ / 176 \\
10.3 Euler's number, base of the natural logarithm /
178 \\
10.4 Integer powers and roots of $\pi$ and $e$ / 180
\\
10.5 The natural logarithm, $\ln(2)$ / 181 \\
10.6 Pythagoras' constant, the square root of two / 183
\\
10.7 The cube root of two / 183 \\
10.8 Euler's constant, symbol $\gamma$ / 185 \\
10.9 Golden ratio, symbol $\phi$ / 185 \\
10.10 The rabbit constant, symbol $\rho$ / 186 \\
10.11 Ap{\'e}ry's constant, $\zeta(3)$ / 188 \\
10.12 Catalan's constant, symbol $C$ / 189 \\
10.13 Gompertz' constant, symbol $G$ / 190 \\
10.14 Khinchin's constant, symbol $K$ / 190 \\
\\
11 Elementary functions / 193 \\
11.1 The exponential function / 193 \\
11.2 The natural logarithm / 196 \\
11.3 Trigonometric functions / 200 \\
11.4 Inverse trigonometric functions / 204 \\
11.5 Hyperbolic functions / 210 \\
11.6 Inverse hyperbolic functions / 213 \\
11.7 The power function / 217 \\
\\
12 Gamma function and related functions / 221 \\
12.1 Gamma function / 221 \\
12.2 Binet function / 224 \\
12.3 Polygamma functions / 229 \\
12.4 Trigamma function / 232 \\
12.5 Tetragamma function / 235 \\
12.6 Incomplete gamma functions / 238 \\
\\
13 Error function and related integrals / 253 \\
13.1 Error function and Dawson's integral / 253 \\
13.2 Complementary and complex error function / 261 \\
13.3 Repeated integrals / 268 \\
13.4 Fresnel integrals / 269 \\
\\
14 Exponential integrals and related functions / 275
\\
14.7 Exponential integrals / 275 \\
14.2 Related functions / 285 \\
\\
15 Hypergeometric functions / 291 \\
15.1 Definition and basic properties / 291 \\
15.2 Stieltjes transform / 295 \\
15.3 Continued fraction representations / 295 \\
15.4 Pad{\'e} approximants / 309 \\
15.5 Monotonicity properties / 313 \\
15.6 Hypergeometric series $_pF_q$ / 315 \\
\\
16 Confluent hypergeometric functions / 319 \\
16.1 Kummer functions / 319 \\
16.2 Confluent hypergeometric series $_2F_0$ / 330 \\
16.3 Confluent hypergeometric limit function / 333 \\
16.4 Whittaker functions / 334 \\
16.5 Parabolic cylinder functions / 337 \\
\\
17 Bessel functions / 334 \\
17.7 Bessel functions / 334 \\
17.2 Modified Bessel functions / 356 \\
\\
18 Probability functions / 371 \\
18.1 Definitions and elementary properties / 371 \\
18.2 Normal and log-normal distributions / 373 \\
18.3 Repeated integrals / 377 \\
18.4 Gamma and chi-square distribution / 378 \\
18.5 Beta, $F$- and Student's $t$-distributions / 382
\\
\\
19 Basic hypergeometric functions / 391 \\
19.1 Definition and basic properties / 391 \\
19.2 Continued fraction representations / 395 \\
19.3 Higher order basic hypergeometric functions / 399
\\
\\
Bibliography / 401 \\
\\
Index / 421",
}
@Article{Dyer:2008:CCI,
author = "J. S. Dyer and S. A. Dyer",
title = "Corrections to, and comments on, {``An improved
approximation for the Gaussian $Q$-Function''}",
journal = j-IEEE-COMMUN-LET,
volume = "12",
number = "4",
pages = "231--231",
month = apr,
year = "2008",
CODEN = "ICLEF6",
DOI = "https://doi.org/10.1109/lcomm.2008.080009",
ISSN = "1089-7798 (print), 1558-2558 (electronic)",
ISSN-L = "1089-7798",
bibdate = "Sat Dec 16 18:08:34 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Karagiannidis:2007:IAG}.",
URL = "http://ieeexplore.ieee.org/document/4489650/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Communications Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}
@Article{Elbert:2008:ZCE,
author = "{\'A}rp{\'a}d Elbert and Andrea Laforgia",
title = "The zeros of the complementary error function",
journal = j-NUMER-ALGORITHMS,
volume = "49",
number = "1--4",
pages = "153--157",
month = dec,
year = "2008",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 14:08:26 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=153",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Gabutti:2008:EQG,
author = "Bruno Gabutti and Giampietro Allasia",
title = "Evaluation of $q$-gamma function and $q$-analogues by
iterative algorithms",
journal = j-NUMER-ALGORITHMS,
volume = "49",
number = "1--4",
pages = "159--168",
month = dec,
year = "2008",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 15:07:19 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=159",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Gautschi:2008:LGW,
author = "Walter Gautschi and Carla Giordano",
title = "{Luigi Gatteschi}'s work on asymptotics of special
functions and their zeros",
journal = j-NUMER-ALGORITHMS,
volume = "49",
number = "1--4",
pages = "11--31",
month = dec,
year = "2008",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 14:08:26 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=11",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Harris:2008:IBG,
author = "Frank E. Harris",
title = "Incomplete {Bessel}, generalized incomplete gamma, or
leaky aquifer functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "215",
number = "1",
pages = "260--269",
year = "2008",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2007.04.008",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "33B10 (33C10 41A58); 33B20",
MRnumber = "2400632 (2009d:33003)",
MRreviewer = "Necdet Batir",
bibdate = "Wed Dec 4 07:03:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042707002014",
ZMnumber = "Zbl 1135.33002",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Isukapalli:2008:ATA,
author = "Yogananda Isukapalli and Bhaskar D. Rao",
title = "An Analytically Tractable Approximation for the
{Gaussian} {$Q$}-Function",
journal = j-IEEE-COMMUN-LET,
volume = "12",
number = "9",
pages = "669--671",
month = sep,
year = "2008",
CODEN = "ICLEF6",
DOI = "https://doi.org/10.1109/lcomm.2008.080815",
ISSN = "1089-7798 (print), 1558-2558 (electronic)",
ISSN-L = "1089-7798",
bibdate = "Sat Dec 16 16:44:42 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Communications Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}
@Book{Jeffrey:2008:HMF,
author = "Alan Jeffrey and Hui-Hui Dai",
title = "Handbook of Mathematical Formulas and Integrals",
publisher = pub-ELSEVIER-ACADEMIC,
address = pub-ELSEVIER-ACADEMIC:adr,
edition = "Fourth",
pages = "xlv + 541",
year = "2008",
ISBN = "0-12-374288-9 (paperback), 0-08-055684-1 (e-book)",
ISBN-13 = "978-0-12-374288-9 (paperback), 978-0-08-055684-0
(e-book)",
LCCN = "QA47 .J38 2008",
bibdate = "Thu May 8 16:02:52 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
melvyl.cdlib.org:210/CDL90",
URL = "https://shop.elsevier.com/books/handbook-of-mathematical-formulas-and-integrals/jeffrey/978-0-12-374288-9",
acknowledgement = ack-nhfb,
subject = "mathematics; tables; formulae",
tableofcontents = "Preface \\
Preface to the Fourth Edition \\
Notes for Handbook Users \\
Index of Special Functions and Notations \\
0. Quick Reference List of Frequently Used Data \\
1. Numerical, Algebraic, and Analytical Results for
Series and Calculus \\
2. Functions and Identities \\
3. Derivatives of Elementary Functions \\
4. Indefinite Integrals of Algebraic Functions \\
5. Indefinite Integrals of Exponential Functions \\
6. Indefinite Integrals of Logarithmic Functions \\
7. Indefinite Integrals of Hyperbolic Functions \\
8. Indefinite Integrals Involving Inverse Hyperbolic
Functions \\
9. Indefinite Integrals of Trigonometric Functions \\
10. Indefinite Integrals of Inverse Trigonometric
Functions \\
11. The Gamma, Beta, Pi, and Psi Functions, and the
Incomplete Gamma Functions \\
12. Elliptic Integrals and Functions \\
13. Probability Distributions and Integrals, and the
Error Function \\
14. Fresnel Integrals, Sine and Cosine Integrals \\
15. Definite Integrals \\
16. Different Forms of Fourier Series \\
17. Bessel Functions \\
18. Orthogonal Polynomials \\
19. Laplace Transformation \\
20. Fourier Transforms \\
21. Numerical Integration \\
22. Solutions of Standard Ordinary Differential
Equations \\
23. Vector Analysis \\
24. Systems of Orthogonal Coordinates \\
25. Partial Differential Equations and Special
Functions \\
26. Qualitative Properties of the Heat and Laplace
Equation \\
27. Solutions of Elliptic, Parabolic, and Hyperbolic
Equations \\
28. The z-Transform \\
29. Numerical Approximation \\
30. Conformal Mapping and Boundary Value Problems \\
Short Classified Reference List \\
Index",
}
@Article{Kiani:2008:AND,
author = "M. Kiani and J. Panaretos and S. Psarakis and M.
Saleem",
title = "Approximations to the normal distribution function and
an extended table for the mean range of the normal
variables",
journal = "J. Iran. Stat. Soc.",
volume = "7",
number = "1",
pages = "57--72",
month = "????",
year = "2008",
DOI = "",
bibdate = "Sat Dec 16 16:56:03 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "",
acknowledgement = ack-nhfb,
}
@Article{Kodama:2008:ASP,
author = "Masao Kodama",
title = "{Algorithm 877}: a Subroutine Package for Cylindrical
Functions of Complex Order and Nonnegative Argument",
journal = j-TOMS,
volume = "34",
number = "4",
pages = "22:1--22:21",
month = jul,
year = "2008",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1377596.1377602",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Jul 16 11:30:01 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "The algorithm presented provides a package of
subroutines for calculating the cylindrical functions $
J_\nu (x) $, $ N_\nu (x) $, $ H_\nu^1 (x) $, $ H_\nu^2
(x) $ where the order $ \nu $ is complex and the real
argument $x$ is nonnegative. The algorithm is written
in Fortran 95 and calculates the functions using
single, double, or quadruple precision according to the
value of a parameter defined in the algorithm. The
methods of calculating the functions are based on a
series expansion, Debye's asymptotic expansions,
Olver's asymptotic expansions, and recurrence methods
(Miller's algorithms). The relative errors of the
functional values computed by this algorithm using
double precision are less than $ 2.4 \times 10^{-13} $
in the region $ 0 \leq \mbox {Re}(\nu) \leq 64 $, $ 0
\leq \mbox {Im}(\nu) \leq 63 $, $ 0.024 \leq x \leq 97
$.",
acknowledgement = ack-nhfb,
articleno = "22",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Bessel functions; complex order; Cylindrical
functions; Debye's asymptotic expansions; Hankel
functions; Miller's algorithms; Neumann functions;
nonnegative argument; numerical calculation; Olver's
asymptotic expansions",
}
@Article{Lefevre:2008:WCE,
author = "Vincent Lef{\`e}vre and Damien Stehl{\'e} and Paul
Zimmermann",
title = "Worst Cases for the Exponential Function in the {IEEE
754r decimal64} Format",
journal = j-LECT-NOTES-COMP-SCI,
volume = "5045",
pages = "114--126",
year = "2008",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-540-85521-7_7",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Thu Oct 1 11:29:36 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2008a.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-85521-7_7.pdf",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-540-85521-7",
book-URL = "http://www.springerlink.com/content/978-3-540-85521-7",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
remark = "From the abstract: ``the worst case for $ |x| \geq 3
\times 10^{-11} $ is exp(9.407822313572878e-2) =
1.09864568206633850000000000000000278.''",
}
@Article{Lorch:2008:MSR,
author = "Lee Lorch and Martin E. Muldoon",
title = "Monotonic sequences related to zeros of {Bessel}
functions",
journal = j-NUMER-ALGORITHMS,
volume = "49",
number = "1--4",
pages = "221--233",
month = dec,
year = "2008",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 15:07:19 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=221",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Book{Mathai:2008:SFA,
author = "A. M. Mathai and H. J. Haubold",
title = "Special Functions for Applied Scientists",
publisher = "Springer Science+Business Media",
address = "New York, NY, USA",
pages = "xxv + 464",
year = "2008",
DOI = "https://doi.org/10.1007/978-0-387-75894-7",
ISBN = "0-387-75893-3",
ISBN-13 = "978-0-387-75893-0",
LCCN = "QA351 .M37X 2008",
bibdate = "Sat Oct 30 17:02:02 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
acknowledgement = ack-nhfb,
shorttableofcontents = "Basic ideas of special functions and
statistical distributions \\
Mittag-Leffler functions and fractional calculus \\
An introduction to q-series \\
Ramanujan's theories of theta and elliptic functions
\\
Lie group and special functions \\
Applications to stochastic process and time series \\
Applications to density estimation \\
Applications to order statistics \\
Applications to astrophysics problems \\
An introduction to wavelet analysis \\
Jacobians of matrix formations \\
Special functions of matrix argument",
subject = "Functions, Special; Fractional calculus; Wavelets
(Mathematics)",
tableofcontents = "1 Basic Ideas of Special Functions and Statistical
Distributions / 1 \\
1.0 Introduction / 1 \\
1.1 Gamma Function / 3 \\
1.1.1 Some basic properties of gamma functions / 4 \\
1.1.2 Wedge product and Jacobians of transformations /
6 \\
1.1.3 Multiplication formula for gamma functions / 8
\\
1.1.4 Asymptotic formula for a gamma function / 9 \\
1.1.5 Bernoulli polynomials / 9 \\
1.1.6 Some basic properties of generalized Bernoulli
polynomials / 9 \\
1.1.7 The first three generalized Bernoulli polynomials
/ 10 \\
Exercises 1.1 / 11 \\
1.2 The Psi and Zeta Functions / 12 \\
1.2.1 Generalized zeta function / 12 \\
Exercises 1.2 / 13 \\
1.3 Integral Transforms / 14 \\
1.3.1 Mellin transform / 14 \\
1.3.2 Laplace transform / 17 \\
Exercises 1.3 / 18 \\
1.4 Some Statistical Preliminaries / 19 \\
Exercises 1.4 / 26 \\
1.5 Some Properties of Random Variables / 28 \\
1.5.1 Multivariate analogues / 30 \\
1.5.2 Marginal and conditional densities / 31 \\
Exercises 1.5 / 33 \\
1.6 Beta and Related Functions / 34 \\
1.6.1 Dirichlet integrals and Dirichlet densities / 37
\\
Exercises 1.6 / 42 \\
1.7 Hypergeometric Series / 42 \\
1.7.1 Evaluation of some contour integrals / 45 \\
1.7.2 Residues when several gammas are involved / 46
\\
Exercises 1.7 / 48 \\
1.8 Meijer's $G$-function / 49 \\
Exercises 1.8 / 54 \\
1.9 The $H$-function / 54 \\
Exercises 1.9 / 57 \\
1.10 Lauricella Functions and Appell's Functions / 58
\\
1.10.1 Some properties of $f_A$ / 59 \\
1.10.2 Some properties of $f_B$ / 60 \\
1.10.3 Some properties of $f_C$ / 60 \\
1.10.4 Some properties of $f_D$ / 61 \\
Exercises 1.10 / 64 \\
1.11 Special Functions as Solutions of Differential
Equations and Applications / 64 \\
1.11.0 Introduction / 64 \\
1.11.1 Sine, cosine and exponential functions / 64 \\
Exercises 1.11 / 66 \\
1.11.2 Linear second order differential equations / 66
\\
1.11.3 Hypergeometric function / 67 \\
Exercises 1.11 / 69 \\
1.11.4 Confluent hypergeometric function / 70 \\
Exercises 1.11 / 71 \\
1.11.5 Hermite polynomials / 71 \\
Exercises 1.11 / 72 \\
1.11.6 Bessel functions / 72 \\
Exercises 1.11 / 73 \\
1.11.7 Laguerre polynomial / 74 \\
1.11.8 Legendre polynomial / 74 \\
Exercises 1.11 / 74 \\
1.11.9 Generalized hypergeometric function / 75 \\
1.11.10 $G$-function / 76 \\
Exercises 1.11 / 77 \\
References / 77 \\
2 Mittag-Leffler Functions and Fractional Calculus / 79
\\
2.0 Introduction / 79 \\
2.1 Mittag-Leffler Function / 79 \\
Revision Exercises 2.1 / 81 \\
2.2 Basic Properties of Mittag-Leffler Function / 82
\\
2.2.1 Mittag-Leffler functions of rational order / 84
\\
2.2.2 Euler transform of Mittag-Leffler function / 84
\\
2.2.3 Laplace transform of Mittag-Leffler function / 85
\\
2.2.4 Application of Laplace transform / 87 \\
2.2.5 Mittag-Leffler functions and the $H$-function /
88 \\
Exercises 2.2 / 90 \\
2.3 Generalized Mittag-Leffler Function / 91 \\
2.3.1 Special cases of $E_{\beta, \gamma}^\delta (z)$ /
92 \\
2.3.2 Mellin--Barnes integral representation / 92 \\
2.3.3 Relations with the H-function and Wright function
/ 92 \\
2.3.4 Cases of reducibility / 93 \\
2.3.5 Differentiation of generalized Mittag-Leffler
function / 94 \\
2.3.6 Integral property of generalized Mittag-Leffler
function / 94 \\
2.3.7 Integral transform of $E_{\beta, \gamma}^\delta
(z)$ / 95 \\
Exercises 2.3 / 96 \\
2.4 Fractional Integrals / 97 \\
2.4.1 Riemann--Liouville fractional integrals of
arbitrary order / 98 \\
2.4.2 Riemann--Liouville fractional integrals of order
$\alpha$ / 99 \\
2.4.3 Basic properties of fractional integrals / 100
\\
2.4.4 A useful integral / 101 \\
2.4.5 The Weyl integral / 103 \\
2.4.6 Basic properties of Weyl integral / 104 \\
Exercises 2.4 / 105 \\
2.4.7 Laplace transform of the fractional integral /
107 \\
2.4.8 Laplace transform of the fractional derivative /
107 \\
2.4.9 Laplace transform of Caputo derivative / 108 \\
Exercises 2.4 / 109 \\
2.5 Mellin Transform of the Fractional Integrals and
the Fractional Derivatives / 109 \\
2.5.1 Mellin transform / 109 \\
2.5.2 Mellin transform of the fractional integral / 110
\\
2.5.3 Mellin transform of the fractional derivative /
111 \\
Exercises 2.5 / 111 \\
2.6 Kober Operators / 111 \\
Exercises 2.6 / 113 \\
2.7 Generalized Kober Operators / 114 \\
Exercises 2.7 / 118 \\
2.8 Compositions of Riemann--Liouville Fractional
Calculus Operators and Generalized Mittag-Leffler
Functions / 121 \\
2.8.1 Composition relations between R-L operators and
$E_{\beta, \gamma}^\delta (z)$ / 121 \\
Exercises 2.8 / 126 \\
2.9 Fractional Differential Equations / 126 \\
2.9.1 Fractional relaxation / 127 \\
Exercises 2.9 / 130 \\
2.9.2 Fractional diffusion / 131 \\
Exercises 2.9 / 132 \\
References / 133 \\
3 An Introduction to $q$-Series / 135 \\
3.0 Introduction / 135 \\
3.1 Hypergeometric Series / 135 \\
Exercises 3.1 / 136 \\
3.2 Basic Hypergeometric Series ($q$-Series) / 138 \\
Exercises 3.2 / 140 \\
3.2.1 The $q$-binomial theorem / 142 \\
Exercises 3.2 / 146 \\
3.2.2 The $q$-binomial coefficients / 146 \\
Exercises 3.2 / 148 \\
3.3 $q$-Calculus / 149 \\
Exercises 3.3 / 151 \\
3.4 The $q$-Gamma and $q$-Beta Functions / 151 \\
3.5 Transformation and Summation Formulas for
$q$-Series / 152 \\
Exercises 3.5 / 154 \\
3.6 Jacobi's Triple Product and Rogers--Ramanujan
Identities / 154 \\
References / 157 \\
4 Ramanujan's Theories of Theta and Elliptic Functions
/ 159 \\
4.0 Introduction / 159 \\
4.1 Ramanujan's Theory of Classical Theta Functions /
159 \\
4.1.1 Series definition and additive results / 159 \\
4.2 Ramanujan's $_1\Psi_1$ Summation Formula and
Multiplicative Results for Theta Functions / 163 \\
4.3 Modular Equations / 170 \\
4.4 Inversion Formulas and Evaluations / 172 \\
4.5 Modular Identities (Classical Theory) / 175 \\
4.6 Ramanujan's Theory of Cubic Theta Functions / 177
\\
4.6.1 The cubic theta functions / 177 \\
4.6.2 Inversion formulas and evaluations (cubic theory)
/ 179 \\
4.6.3 Triplication and trimediation formulas / 182 \\
4.6.4 Further evaluations / 183 \\
4.6.5 Evaluations of Ramanujan--Eisenstein series ($L$,
$M$, $N$ or $P$, $Q$, $R$) / 185 \\
4.6.6 The cubic analogue of the Jacobian elliptic
functions / 186 \\
Test on Ramanujan's work / 187 \\
4.7 The One-variable Cubic Theta Functions / 188 \\
4.7.1 Cubic theta functions and some properties / 189
\\
4.7.2 Product representations for $b(q)$ and $c(q)$ /
190 \\
4.7.3 The cubic analogue of Jacobi's quartic modular
equations / 191 \\
4.8 The Two-variable Cubic Theta Functions / 193 \\
4.8.1 Series definitions and some properties / 193 \\
4.8.2 Product representations for $b(q,z)$ and $c(q,z)$
/ 195 \\
4.8.3 A two-variable cubic counterpart of Jacobi's
quartic modular equation / 200 \\
4.9 The Three-variable Cubic Theta Functions / 200 \\
4.9.1 Unification of one and two-variable cubic theta
functions / 200 \\
Exercises 4.9 / 200 \\
4.9.2 Generalization of Hirschhorn--Garvan--Borwein
identity / 202 \\
4.9.3 Laurent's expansions for two-parameter cubic
theta functions / 205 \\
References / 209 \\
5 Lie Group and Special Functions / 211 \\
5.1 General Introduction to Group Theory / 211 \\
5.1.1 Isomorphisms / 213 \\
5.1.2 Symmetry groups / 213 \\
5.1.3 Isometries of the Euclidean plane / 214 \\
5.1.4 Finite groups of motion / 215 \\
5.1.5 Discrete groups of motions / 216 \\
5.2 Lie Group and Special Functions / 217 \\
5.2.1 Subspace of a vector space / 218 \\
5.3 Lie Algebra / 219 \\
5.4 Representations of Lie Algebra / 222 \\
Exercises 5.4 / 225 \\
5.5 Special Functions / 226 \\
5.5.1 Gauss hypergeometric function / 226 \\
5.5.2 Differential equation satisfied by $_2F_1$ / 228
\\
5.5.3 Integral representation of
$_F_q(\alpha_1,\alpha_2, \ldots{}, \alpha_p \beta_1,
\beta_2, \ldots{}, \beta_p; z)$ / 230 \\
5.6 Laguerre Polynomial $L^{(\alpha)}_n(x)$ / 231 \\
5.6.1 Laguerre polynomial and Lie algebra / 232 \\
Exercises 5.6 / 232 \\
5.7 Helmholtz Equation / 234 \\
5.7.1 Helmholtz equation in three variables / 238 \\
5.8 Lie Group / 241 \\
5.8.1 Basis of the Lie algebra of the Lie group SL(2) /
242 \\
Exercises 5.8 / 243 \\
Test on Lie Theory and Special Functions / 244 \\
6 Applications to Stochastic Process and Time Series /
247 \\
6.0 Introduction / 247 \\
6.1 Stochastic Processes / 247 \\
6.1.1 Classical types of stochastic processes / 252 \\
6.1.2 Processes with stationary independent increments
/ 252 \\
6.1.3 Stationary processes / 253 \\
6.1.4 Gaussian processes and stationarity / 253 \\
6.1.5 Brownian processes / 257 \\
6.1.6 Markov chains / 258 \\
Exercises 6.1 / 261 \\
6.2 Modern Concepts in Distribution Theory / 262 \\
6.2.1 Introduction / 262 \\
6.2.2 Geometric infinite divisibility / 263 \\
6.2.3 Bernstein functions / 264 \\
6.2.4 Self-decomposability / 265 \\
6.2.5 Stable distributions / 265 \\
6.2.6 Geometrically strictly stable distributions / 266
\\
6.2.7 Mittag-Leffler distribution / 266 \\
6.2.8 $\alpha$-Laplace distribution / 267 \\
6.2.9 Semi-Pareto distribution / 268 \\
Exercises 6.2 / 268 \\
6.3 Stationary Time Series Models / 269 \\
6.3.1 Introduction / 269 \\
6.3.2 Autoregressive models / 270 \\
6.3.3 A general solution / 270 \\
6.3.4 Extension to a $k$-th order autoregressive model
/ 272 \\
6.3.5 Mittag-Leffler autoregressive structure / 273 \\
Exercises 6.3 / 274 \\
6.4 A Structural Relationship and New Processes / 275
\\
6.4.1 The TMLAR(1) process / 276 \\
6.4.2 The NEAR(1) model / 277 \\
6.4.3 New Mittag-Leffler autoregressive models / 278
\\
6.4.4 The NSMLAR(1) process / 280 \\
Exercises 6.4 / 281 \\
6.5 Tailed Processes / 281 \\
6.5.1 The exponential tailed autoregressive process
[ETAR(1)] / 282 \\
6.5.2 The Mittag-Leffler tailed autoregressive process
[MLTAR(1)] / 283 \\
Exercises 6.5 / 286 \\
6.6 Marshall--Olkin Weibull Time Series Models / 286
\\
6.6.1 Introduction / 286 \\
6.6.2 Marshall--Olkin semi-Weibull distribution / 287
\\
6.6.3 An AR(1) model with MOSW marginal distribution /
289 \\
6.6.4 Marshall--Olkin generalized Weibull distribution
/ 291 \\
6.6.5 An AR(1) model with MOGW marginal distribution /
292 \\
6.6.6 Case study / 293 \\
Exercises 6.6 / 293 \\
References / 294 \\
7 Applications to Density Estimation / 297 \\
7.0 Density Estimation and Orthogonal Polynomials / 297
\\
7.1 Introduction / 297 \\
7.2 Approximants Based on Legendre Polynomials / 299
\\
7.3 Approximants Based on Laguerre Polynomials / 301
\\
7.4 A Unified Methodology / 304 \\
7.5 Approximants Expressed in Terms of Orthogonal
Polynomials / 305 \\
7.5.1 Approximants expressed in terms of Laguerre
polynomials / 306 \\
7.5.2 Approximants expressed in terms of Legendre
polynomials / 306 \\
7.5.3 Approximants expressed in terms of Jacobi
polynomials / 307 \\
7.5.4 Approximants expressed in terms of Hermite
polynomials / 307 \\
References / 308 \\
8 Applications to Order Statistics / 311 \\
8.0 Introduction / 311 \\
8.1 Distribution Function / 311 \\
8.1.1 Density of the $r$-th order statistic / 313 \\
8.1.2 Joint distribution function of two order
statistics / 314 \\
8.1.3 Joint density of two order statistics / 314 \\
8.1.4 Moments of order statistics / 315 \\
8.1.5 Recurrence relations for moments / 317 \\
8.1.6 Recurrence relations on the product moments / 318
\\
8.1.7 Order statistics from symmetric distributions /
319 \\
8.2 Discrete Order Statistics / 319 \\
8.2.1 Probability function of discrete order statistics
/ 320 \\
8.2.2 Joint probability function of two order
statistics / 321 \\
8.2.3 Bernoulli order statistics / 321 \\
8.3 Independent Random Variables / 322 \\
8.3.1 Distribution of a single order statistic / 322
\\
8.3.2 Joint distribution of two order statistics / 324
\\
Test on Order Statistics / 325 \\
8.4 On Concomitants of Order Statistics / 326 \\
8.4.1 Application of concomitants of order statistics /
326 \\
8.4.2 Application in estimation / 328 \\
8.4.3 Concomitants of record values and estimation
problems / 333 \\
References / 339 \\
9 Applications to Astrophysics Problems / 341 \\
9.0 Introduction / 341 \\
9.1 Entropy: Boltzmann, Planck, and Einstein on W / 342
\\
9.1.1 Entropic functional / 342 \\
9.1.2 Entropy and probability / 342 \\
9.1.3 Boltzmann--Gibbs / 343 \\
9.2 Gravitationally Stabilized Fusion Reactor: The Sun
/ 345 \\
9.2.1 Internal solar structure / 345 \\
9.2.2 Solar fusion plasma / 349 \\
9.2.3 Estimation of central temperature in the Sun /
349 \\
9.3 Crucial Astrophysical Experiments: Data Analysis /
351 \\
9.3.1 The experiments / 351 \\
9.3.2 Analysis of the time series / 352 \\
9.4 Fundamental Equations for Nonequilibrium Processes
/ 355 \\
9.4.1 Chapman--Kolmogorov equation / 355 \\
9.4.2 Master equation / 355 \\
9.4.3 Fokker--Planck equation / 356 \\
9.4.4 Langevin equation / 357 \\
9.4.5 Reaction-diffusion equation / 357 \\
9.5 Fractional Calculus / 360 \\
9.6 Nonextensive Statistical Mechanics / 362 \\
9.7 Standard and Fractional Reaction / 363 \\
9.7.1 Boltzmann--Gibbs statistical mechanics / 363 \\
9.7.2 Generalized Boltzmann--Gibbs statistical
mechanics / 366 \\
9.7.3 Fractional reaction / 369 \\
9.7.4 Thermonuclear reaction coefficient / 371 \\
9.8 Standard and Fractional Diffusion / 380 \\
9.8.1 Fick's first law of diffusion / 380 \\
9.8.2 Einstein's approach to diffusion / 381 \\
9.8.3 Fractional diffusion / 381 \\
9.8.4 Spatio-temporal pattern formation / 383 \\
References / 384 \\
10 An Introduction to Wavelet Analysis / 389 \\
10.0 Introduction / 389 \\
10.1 Fourier Analysis to Wavelet Analysis / 390 \\
10.2 Construction of Orthonormal Wavelets / 393 \\
10.3 Classification of Wavelets and Multiresolution
Analysis / 400 \\
10.4 Spline Wavelets / 405 \\
10.5 A Variant of Construction of Orthonormal Wavelets
/ 407 \\
Exercises 10.5 / 408 \\
References / 408 \\
11 Jacobians of Matrix Transformations / 409 \\
11.0 Introduction / 409 \\
11.1 Jacobians of Linear Matrix Transformations / 410
\\
Exercises 11.1 / 415 \\
11.2 Jacobians in Some Nonlinear Transformations / 417
\\
Exercises 11.2 / 421 \\
11.3 Transformations Involving Orthonormal Matrices /
423 \\
Exercises 11.3 / 426 \\
References / 428 \\
12 Special Functions of Matrix Argument / 429 \\
12.0 Introduction / 429 \\
12.1 Real Matrix-Variate Scalar Functions / 429 \\
12.1.1 Real matrix-variate gamma / 430 \\
12.1.2 Real matrix-variate gamma density / 430 \\
Exercises 12.1 / 434 \\
12.2 The Laplace Transform in the Matrix Case / 435 \\
12.2.1 A convolution property for Laplace transforms /
436 \\
Exercises 12.2 / 439 \\
12.3 Hypergeometric Functions with Matrix Argument /
439 \\
12.3.1 Hypergeometric function through Laplace
transform / 440 \\
12.3.2 Hypergeometric function through zonal
polynomials / 441 \\
12.3.3 Hypergeometric functions through $M$-transforms
/ 443 \\
12.3.4 A convolution theorem for $M$-transforms / 445
\\
Exercises 12.3 / 446 \\
12.4 A Pathway Model / 448 \\
12.4.1 The pathway density / 448 \\
12.4.2 A general density / 451 \\
12.4.3 Arbitrary moments / 451 \\
12.4.4 Quadratic forms / 452 \\
12.4.5 Generalized quadratic form / 452 \\
12.4.6 Applications to random volumes / 453 \\
Exercises 12.4 / 453 \\
References / 454 \\
Author Index / 457 \\
Subject Index / 461",
}
@Article{Nam:2008:PAE,
author = "Byeong-Gyu Nam and Hyejung Kim and Hoi-Jun Yoo",
title = "Power and Area-Efficient Unified Computation of Vector
and Elementary Functions for Handheld {$3$D} Graphics
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "4",
pages = "490--504",
month = apr,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.12",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4432232",
abstract = "A unified computation method of vector and elementary
functions is proposed for handheld 3D graphics systems.
It unifies vector operations like vector multiply,
multiply-and-add, divide, divide-by-square-root, and
dot product and elementary functions like
trigonometric, inverse trigonometric, hyperbolic,
inverse hyperbolic, power ($ x^y $ with two variables),
and logarithm to an arbitrary base into a single
four-way arithmetic platform. A number system called
the fixed-point hybrid number system (FXP-HNS), which
combines the fixed-point number system (FXP) and the
logarithmic number system (LNS), is proposed for the
power and area-efficient unification. Power and
area-efficient logarithmic and antilogarithmic
conversion schemes are also proposed for the data
conversions between fixed-point and logarithmic numbers
in the FXP-HNS and achieve 0.41 percent and 0.08
percent maximum conversion errors, respectively. The
unified arithmetic unit based on the proposed schemes
is presented with less than 6.3 percent operation
error. Its fully pipelined architecture achieves
single-cycle throughput with maximum four-cycle latency
for all of the supported operations. Comparison results
show that the proposed arithmetic unit achieves 30
percent power and 10.9 percent area reductions and runs
two times faster than the previous approach.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Paszkowski:2008:CAO,
author = "Stefan Paszkowski",
title = "Convergence acceleration of orthogonal series",
journal = j-NUMER-ALGORITHMS,
volume = "47",
number = "1",
pages = "35--62",
month = jan,
year = "2008",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-007-9146-7",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "subject classification (2000); 33C45; 42A32; 42C10;
42C20; 65B10",
bibdate = "Tue Jul 8 19:14:30 MDT 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=47&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=47&issue=1&spage=35",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Convergence acceleration; convergence acceleration;
Orthogonal polynomials; Orthogonal series;
Trigonometric series",
}
@Article{Pinchon:2008:NEL,
author = "Didier Pinchon and Philip E. Hoggan and Frank E.
Harris",
title = "A new expansion of the leaky aquifer function",
journal = j-IJQC,
volume = "108",
number = "15",
pages = "3042--3046",
month = "????",
year = "2008",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/qua.21448;
https://doi.org/10.1002/qua.21835",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
MRclass = "86A05 80A20 33C10 82B80",
bibdate = "Sat Oct 1 14:02:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ijqc2000.bib",
ZMnumber = "Zbl 1189.86005",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Quantum Chem.",
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
onlinedate = "4 Aug 2008",
}
@Article{Pineiro:2008:RDD,
author = "J.-A. Pineiro and J. D. Bruguera and F. Lamberti and
P. Montuschi",
title = "A Radix-2 Digit-by-Digit Architecture for Cube Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "4",
pages = "562--566",
month = apr,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70848",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4407683",
abstract = "A radix-2 digit-recurrence algorithm and architecture
for the computation of the cube root are presented in
this paper. The original recurrence based on the
concept of completing the cube is modified to allow an
efficient implementation of the algorithm and the cycle
time and area cost of the resulting architecture are
estimated as 7.5 times the delay of a full adder and
around 9,000 nand2 cells, respectively, for
double-precision computations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Piso:2008:NRA,
author = "D. Piso and J. D. Bruguera",
editor = "Luca Fanucci",
booktitle = "Proceedings: {11th Euromicro Symposium on Digital
Systems Design: Architectures, Methods and Tools (DSD
2008), Parma, Italy, September 3--5, 2008}",
title = "A New Rounding Algorithm for Variable Latency Division
and Square Root Implementations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "760--767",
year = "2008",
DOI = "https://doi.org/10.1109/DSD.2008.28.",
ISBN = "0-7695-3277-2",
ISBN-13 = "978-0-7695-3277-6",
bibdate = "Sun Dec 10 13:55:38 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The aim of this work is to present a method for
rounding quadratically converging algorithms that
improves their performance. This method is able to
reduce significantly the number of cases where the
remainder calculation is necessary. It is based on
previous methods and incorporates additional bits of
the result approximation to be checked. This work
includes the result of exhaustive simulations that
permit us to measure exactly how many calculations are
avoided. Using these simulations, it is concluded that
the presented method is able to reduce by half the
number of remainder calculations. Using adequate result
approximations the remainder calculation is necessary
in only 5\% of the total cases",
acknowledgement = ack-nhfb,
}
@Article{Rodriguez-Henriquez:2008:LCB,
author = "F. Rodriguez-Henriquez and G. Morales-Luna and J.
Lopez",
title = "Low-Complexity Bit-Parallel Square Root Computation
over {$ \mathrm {GF}(2^m) $} for All Trinomials",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "4",
pages = "472--480",
month = apr,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70822",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358282",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Sablonniere:2008:BSH,
author = "Paul Sablonni{\`e}re",
title = "{B}-splines and {Hermite--Pad{\'e}} approximants to
the exponential function",
journal = j-J-COMPUT-APPL-MATH,
volume = "219",
number = "2",
pages = "509--517",
day = "1",
month = oct,
year = "2008",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:13:26 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270700252X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Schreier:2008:OIR,
author = "Franz Schreier and Dieter Kohlert",
title = "Optimized implementations of rational approximations
--- a case study on the {Voigt} and complex error
function",
journal = j-COMP-PHYS-COMM,
volume = "179",
number = "7",
pages = "457--465",
day = "1",
month = oct,
year = "2008",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2008.04.012",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 23:42:36 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465508001495",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Segura:2008:IZC,
author = "Javier Segura",
title = "Interlacing of the zeros of contiguous hypergeometric
functions",
journal = j-NUMER-ALGORITHMS,
volume = "49",
number = "1--4",
pages = "387--407",
month = dec,
year = "2008",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 15:07:19 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=387",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Misc{Steele:2008:FPSb,
author = "Guy L. {Steele Jr.}",
title = "Floating point square root provider with embedded
status information",
howpublished = "US Patent 7430576",
day = "30",
month = sep,
year = "2008",
bibdate = "Tue Dec 23 15:06:43 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7430576/fulltext.html",
abstract = "A system for providing a floating point square root
comprises an analyzer circuit configured to determine a
first status of a first floating point operand based
upon data within the first floating point operand. In
addition, the system comprises a results circuit
coupled to the analyzer circuit. The results circuit is
configured to assert a resulting floating point operand
containing the square root of the first floating point
operand and a resulting status embedded within the
resulting floating point operand.",
acknowledgement = ack-nhfb,
}
@Article{Vepstas:2008:EAA,
author = "Linas Vepstas",
title = "An efficient algorithm for accelerating the
convergence of oscillatory series, useful for computing
the polylogarithm and {Hurwitz} zeta functions",
journal = j-NUMER-ALGORITHMS,
volume = "47",
number = "3",
pages = "211--252",
month = mar,
year = "2008",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-007-9153-8",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 15:49:34 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=47&issue=3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=47&issue=3&spage=211",
abstract = "This paper sketches a technique for improving the rate
of convergence of a general oscillatory sequence, and
then applies this series acceleration algorithm to the
polylogarithm and the Hurwitz zeta function. As such,
it may be taken as an extension of the techniques given
by Borwein's ``An efficient algorithm for computing the
Riemann zeta function'' by Borwein for computing the
Riemann zeta function, to more general series. The
algorithm provides a rapid means of evaluating $
\operatorname {Li}_s(z) $ for general values of complex
$s$ and a kidney-shaped region of complex $z$ values
given by $ |z^2 / (z - 1)| < 4 $. By using the
duplication formula and the inversion formula, the
range of convergence for the polylogarithm may be
extended to the entire complex $z$-plane, and so the
algorithms described here allow for the evaluation of
the polylogarithm for all complex $s$ and $z$ values.
Alternatively, the Hurwitz zeta can be very rapidly
evaluated by means of an Euler Maclaurin series. The
polylogarithm and the Hurwitz zeta are related, in that
two evaluations of the one can be used to obtain a
value of the other; thus, either algorithm can be used
to evaluate either function. The Euler Maclaurin series
is a clear performance winner for the Hurwitz zeta,
while the Borwein algorithm is superior for evaluating
the polylogarithm in the kidney-shaped region. Both
algorithms are superior to the simple Taylor's series
or direct summation. The primary, concrete result of
this paper is an algorithm allows the exploration of
the Hurwitz zeta in the critical strip, where fast
algorithms are otherwise unavailable. A discussion of
the monodromy group of the polylogarithm is included.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "convergence acceleration",
}
@Book{Ware:2008:RIE,
author = "Willis H. Ware",
title = "{RAND} and the information evolution: a history in
essays and vignettes",
publisher = "Rand Corporation",
address = "Santa Monica, CA",
pages = "xxvi + 201",
year = "2008",
DOI = "https://doi.org/10.7249/cp537rc",
ISBN = "0-8330-4513-X, 0-8330-4816-3, 1-282-45123-5",
ISBN-13 = "978-0-8330-4513-3, 978-0-8330-4816-5,
978-1-282-45123-0",
LCCN = "QA76.27",
bibdate = "Tue Jun 2 19:14:18 MDT 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
URL = "http://www.jstor.org/stable/10.7249/cp537rc;
https://www.rand.org/content/dam/rand/pubs/corporate_pubs/2008/RAND_CP537.pdf",
abstract = "This professional memoir describes RAND's
contributions to the evolution of computer science,
particularly during the first decades following World
War II, when digital computers succeeded slide rules,
mechanical desk calculators, electric accounting
machines, and analog computers. The memoir includes
photographs and vignettes that reveal the collegial,
creative, and often playful spirit in which the
groundbreaking research was conducted at RAND.",
acknowledgement = ack-nhfb,
keywords = "JOHNNIAC; JOSS; JOSS-1; JOSS-2; RAND tablet",
remark-1 = "Page 13 has a photograph of the JOHNNIAC, and on the
wall of its room, a photograph of John von Neumann.",
remark-2 = "From page 15: ``\ldots{} the JOHNNIAC, which
nonetheless was the basis of a continuing series of
engineering advances, each making important
contributions to the art of the time. Among them were
the first commercially produced magnetic core memory,
which, for a while, was the largest in existence [4096
40-bit words]; a transistor-based adder and logic which
caused the JOHNNIAC to become a hybrid
transistor-vacuum tube device; the first high-speed
impact printer 140 columns wide (manufactured by
Anderson--Nichols, an engineering contracting firm);
and the first machine with extensive trouble-diagnostic
capability from the operating console.''",
remark-3 = "From page 53: ``the only bright spot was the Princeton
development at IAS, and thus it was that a working
alliance between RAND and IAS came into being. RAND
would build a machine patterned in the likeness of the
Princeton one. So JOHNNIAC came from an illustrious
ancestor --- the so-called von Neumann machine
developed at Princeton's IAS.''",
remark-4 = "Page 57 has a photograph of the JOHNNIAC's 256-word
Selectron high-speed memory. Page 59, a picture of its
140-column drum printer. Page 61 has an inside view of
the JOHNNIAC. Page 73 shows a step in the installation
of the JOHNNIAC. Page 162 has a photograph of the
JOHNNIAC console.",
remark-5 = "From page 66: ``RAND purchased the first commercially
available license for UNIX.''",
remark-6 = "Page 84 has a photo of a young Cecil Hastings, an
early pioneer of function approximation on digital
computers, and a few paragraphs about his work and its
influence.",
remark-7 = "Pages 87--90 discuss the preparation of RAND's famous
book of one million random digits, computed in Spring
1947, tested for two years after that before
publication in 1955. About 7000 copies of the book were
sold over three printings and fifteen years, and the
book was reprinted in 1966 and 2001.",
remark-8 = "From page 138: ``In the 1950s, RAND was involved in
designing and building one of the first stored-program
digital computers, the JOHNNIAC (named after John von
Neumann, a RAND consultant in the late 1940s and early
1950s). It was in operation from 1953 to 1966,
\ldots{}.''",
shorttableofcontents = "Introduction \\
The department \\
RAND's first computer people \\
RAND's early computers \\
A building for people with computers \\
Project essays \\
Lore, snippets, and snapshots \\
Epilogue",
tableofcontents = "Dedication / v \\
Preface / vii \\
Figures / xiii \\
Photographs / xv \\
Tables / xvii \\
Acknowledgments / xix \\
Abbreviations / xxiii \\
CHAPTER ONE \\
Introduction / 1 \\
Purpose and Scope / 1 \\
Organization of the Document / 3 \\
CHAPTER TWO \\
The Department / 5 \\
The Genesis of RAND / 5 \\
The Need for a New Kind of Organization / 6 \\
The Douglas Years / 7 \\
An Independent, Private Nonprofit Organization / 8 \\
The Nature of RAND's Contributions / 9 \\
RAND Contributions to the Development of Computing / 10
\\
In the Beginning / 10 \\
An Early Computing Success / 11 \\
The Move to Electronic Machines / 11 \\
The Middle Years / 14 \\
The JOHNNIAC Open-Shop System / 15 \\
The Tablet / 16 \\
Videographic System / 16 \\
The Later Years / 17 \\
RAND and the USAF Computing Evolution / 18 \\
The Bottom Line / 19 \\
CHAPTER THREE \\
RAND's First Computer People / 21 \\
The Legacy of Wartime Collaboration / 21 \\
Early RAND Leaders / 22 \\
Early Technical Staff / 24 \\
The Douglas Thread / 24 \\
The Wartime Thread / 26 \\
The University Thread / 28 \\
The Recruiting Thread / 30 \\
Departmental Growth / 36 \\
CHAPTER FOUR \\
RAND's Early Computers / 45 \\
Mid-20th Century Computation / 45 \\
Reeves Electronic Analog Computer / 47 \\
Plug-Board Interconnections / 50 \\
Chopper-Stabilized Amplifiers / 50 \\
Arbitrary Function Input / 51 \\
The JOHNNIAC Digital Computer / 53 \\
JOHNNIAC's ``Obituary'' / 63 \\
IBM Mainframes / 64 \\
Other Machinery. / 66 \\
CHAPTER FIVE \\
A Building for People with Computers / 67 \\
A New Building and Campus. / 68 \\
The Machine Room. / 72 \\
Two-Story Installation / 72 \\
REAC Installation. / 73 \\
Raised-Floor Installation / 73 \\
Air Conditioning. / 74 \\
Configurations of the Machine Room / 75 \\
Open House. / 75 \\
Later Enhancements / 79 \\
The Camera / 79 \\
Kevershan's Trough / 80 \\
Programmer-Alert Lights / 80 \\
CHAPTER SIX \\
Project Essays / 83 \\
Approximations / 83 \\
Random Digits and Normal Deviates / 87 \\
The Bombing Simulator (aka Pinball Machine) / 90 \\
The Air-Combat Room / 94 \\
System Research Laboratory / 94 \\
The RAND Tablet, Videographics, and Related Projects /
98 \\
The RAND Tablet / 98 \\
Handwriting Recognition / 99 \\
Chinese-Character Lookup / 100 \\
Map Annotation / 100 \\
Videographic System / 103 \\
GRAIL / 105 \\
BIOMOD / 105 \\
CLINFO / 107 \\
Time-Shared Computing: JOSS / 109 \\
JOSS-1 / 110 \\
JOSS-2 / 113 \\
Networked Computing: Packet Switching and Distributed
Communications / 115 \\
The Beginnings of Packet Switching: Some Underlying
Concepts / 116 \\
Text Editors (NED and e) / 122 \\
Word Processing / 126 \\
The Mail Handler / 128 \\
The Original MH-Proposal Memorandum / 129 \\
Implementation / 132 \\
Another Perspective / 134 \\
A User's Perspective / 135 \\
The Developers' Present Views / 137 \\
Artificial-Intelligence Research / 138 \\
The Beginnings of Artificial Intelligence / 138 \\
Newell, Shaw, and Simon: The Development of
List-Processing Languages / 138 \\
Expert Systems / 140 \\
Knowledge-Based Simulation / 142 \\
Computational Linguistics / 143 \\
The Perfect Buddy / 144 \\
Department of Defense Computer Institute / 147 \\
Officer Career Paths / 149 \\
Software / 150 \\
Security and Privacy / 152 \\
Security / 152 \\
Privacy / 154 \\
Fair Information Practices / 155 \\
CHAPTER SEVEN \\
Lore, Snippets, and Snapshots / 159 \\
The Great Machine Fire / 159 \\
The Gavel Caper / 159 \\
Department-Head-Office Decor / 161 \\
Oliver Alfred Gross and JOSS-1 / 162 \\
The Soviet ``Threat'' / 163 \\
Social Events / 164 \\
The One-Way Wire / 166 \\
Soviet Cybernetics / 166 \\
Inter/Exhume / 167 \\
The RAND Computer Symposia / 168 \\
Professional Societies / 169 \\
Microvignettes / 170 \\
The Marchant March / 170 \\
Getting Out the Documents / 171 \\
Hero of the Week / 171 \\
The Chiquita Banana War / 171 \\
The Mengel Joint / 171 \\
John Williams' Jaguar / 172 \\
Programmer Sweepstakes / 173 \\
CHAPTER EIGHT \\
Epilogue / 175 \\
Bibliography / 177 \\
Index / 191",
}
@Article{Zhu:2008:SNR,
author = "Ling Zhu and Jinju Sun",
title = "Six new {Redheffer}-type inequalities for circular and
hyperbolic functions",
journal = j-COMPUT-MATH-APPL,
volume = "56",
number = "2",
pages = "522--529",
month = jul,
year = "2008",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:15 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122108000813",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Anand:2009:OCS,
author = "C. K. Anand and W. Kahl",
title = "An Optimized {Cell BE} Special Function Library
Generated by {Coconut}",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "8",
pages = "1126--1138",
month = aug,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.223",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4731241",
abstract = "Coconut, a tool for developing high-assurance,
high-performance kernels for scientific computing,
contains an extensible domain-specific language (DSL)
embedded in Haskell. The DSL supports interactive
prototyping and unit testing, simplifying the process
of designing efficient implementations of common
patterns. Unscheduled C and scheduled assembly language
output are supported. Using the patterns, even
nonexpert users can write efficient function
implementations, leveraging special hardware features.
A production-quality library of elementary functions
for the cell BE SPU compute engines has been developed.
Coconut-generated and -scheduled vector functions were
more than four times faster than commercially
distributed functions written in C with intrinsics (a
nicer syntax for in-line assembly), wrapped in loops
and scheduled by {\tt spuxlc}. All Coconut functions
were faster, but the difference was larger for
hard-to-approximate functions for which register-level
SIMD lookups made a bigger difference. Other helpful
features in the language include facilities for
translating interval and polynomial descriptions
between GHCi, a Haskell interpreter used to prototype
in the DSL, and Maple, used for exploration and minimax
polynomial generation. This makes it easier to match
mathematical properties of the functions with efficient
calculational patterns in the SPU ISA. By using single,
literate source files, the resulting functions are
remarkably readable.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Backeljauw:2009:ACF,
author = "Franky Backeljauw and Annie Cuyt",
title = "{Algorithm 895}: a continued fractions package for
special functions",
journal = j-TOMS,
volume = "36",
number = "3",
pages = "15:1--15:20",
month = jul,
year = "2009",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1527286.1527289",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 21 14:09:07 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "The continued fractions for special functions package
(in the sequel abbreviated as CFSF package) complements
a systematic study of continued fraction
representations for special functions. It provides all
the functionality to create continued fractions, in
particular $k$-periodic or limit $k$-periodic
fractions, to compute approximants, make use of
continued fraction tails, perform equivalence
transformations and contractions, and much more. The
package, developed in Maple, includes a library of more
than 200 representations of special functions, of which
only 10\% can be found in the 1964 NBS {\em Handbook of
Mathematical Functions with Formulas, Graphs and
Mathematical Tables\/} by M. Abramowitz and I.
Stegun.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "CAS software; continued fractions; Maple; special
functions",
}
@Article{Blomquist:2009:MSC,
author = "Frithjof Blomquist and Werner Hofschuster and Walter
Kr{\"a}mer",
title = "A Modified Staggered Correction Arithmetic with
Enhanced Accuracy and Very Wide Exponent Range",
journal = j-LECT-NOTES-COMP-SCI,
volume = "5492",
pages = "41--67",
year = "2009",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-01591-5_4",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 10 08:32:19 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/content/k038294004403504/",
acknowledgement = ack-nhfb,
author-dates = "1952--2014 (WK)",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "C-XSC; complex interval functions; interval
computation; multiple precision; reliable numerical
computations; staggered correction; wide exponent
range",
remark = "Conference on Numerical Validation in Current Hardware
Architectures",
remark-2 = "Includes algorithms for division, $\exp(x)$, $(1 +
x)^n$, $\log(x)$, $\log(1 + x)$, and $\sqrt{x}$.
Staggered arithmetic represents numbers with tuples
$(e, x_1, x_2, \ldots{}, x_n)$ where $e$ is either
integer or a floating-point whole number, the $x_k$ are
floating-point, and a number has the value $2^e \sum_{k
= 1}^n x_k$. For interval arithmetic, the last element
is a pair of lower and upper bounds.",
}
@Article{Boldo:2009:FVA,
author = "S. Boldo and M. Daumas and Ren-Cang Li",
title = "Formally Verified Argument Reduction with a Fused
Multiply-Add",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "8",
pages = "1139--1145",
month = aug,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4711042",
abstract = "The Cody and Waite argument reduction technique works
perfectly for reasonably large arguments, but as the
input grows, there are no bits left to approximate the
constant with enough accuracy. Under mild assumptions,
we show that the result computed with a fused
multiply-add provides a fully accurate result for many
possible values of the input with a constant almost
accurate to the full working precision. We also present
an algorithm for a fully accurate second reduction step
to reach full double accuracy (all the significand bits
of two numbers are accurate) even in the worst cases of
argument reduction. Our work recalls the common
algorithms and presents proofs of correctness. All the
proofs are formally verified using the Coq automatic
proof checker.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bowling:2009:LAC,
author = "Shannon R. Bowling and Mohammad T. Khasawneh and
Sittichai Kaewkuekool and Byung Rae Cho",
title = "A logistic approximation to the cumulative normal
distribution",
journal = "Journal of Industrial Engineering and Management",
volume = "2",
number = "1",
pages = "114--127",
month = "",
year = "2009",
DOI = "https://doi.org/10.3926/jiem..v2n1.p114-127",
bibdate = "Sat Dec 16 15:22:05 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jiem.org/index.php/jiem/article/view/60",
acknowledgement = ack-nhfb,
ajournal = "J. Ind. Eng. Manage.",
fjournal = "Journal of Industrial Engineering and Management",
journal-URL = "http://www.jiem.org/index.php/jiem/",
}
@Article{Boyd:2009:AAC,
author = "John P. Boyd",
title = "Acceleration of algebraically-converging {Fourier}
series when the coefficients have series in powers of $
1 / n $",
journal = j-J-COMPUT-PHYS,
volume = "228",
number = "5",
pages = "1404--1411",
day = "20",
month = mar,
year = "2009",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2008.10.039",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Thu Dec 01 10:35:35 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
keywords = "Bernoulli polynomials; Clausen functions; convergence
acceleration; Lanczos--Krylov (LK) functions",
}
@Article{Bunck:2009:FAE,
author = "Benjamin F. Bunck",
title = "A fast algorithm for evaluation of normalized
{Hermite} functions",
journal = j-BIT-NUM-MATH,
volume = "49",
number = "2",
pages = "281--295",
month = jun,
year = "2009",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon May 24 15:36:43 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=49&issue=2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=49&issue=2&spage=281",
abstract = "An algorithm for computing the normalized Hermite
Functions, $ h_n(x) $, in floating point arithmetic is
presented. The algorithm is based on an efficient
numerical evaluation of certain closed contour
integrals in the complex plane. For large degree $n$,
the algorithm is significantly faster than the $ O(n) $
complexity of the well known three-term recurrence
relation. Comparable accuracy is achieved in no more $
O(\sqrt {n}) $ than operations, and for arguments
bounded away from $ \pm \sqrt {2n} $, only $ O(\sqrt
{\log n}) $ operations.",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "fast algorithm; Hermite functions; numerical
integration; recursion",
}
@Article{Chen:2009:SPA,
author = "Yunfei Chen and Norman C. Beaulieu",
title = "A simple polynomial approximation to the {Gaussian}
{$Q$}-function and its application",
journal = j-IEEE-COMMUN-LET,
volume = "13",
number = "2",
pages = "124--126",
month = feb,
year = "2009",
CODEN = "ICLEF6",
DOI = "https://doi.org/10.1109/lcomm.2009.081754",
ISSN = "1089-7798 (print), 1558-2558 (electronic)",
ISSN-L = "1089-7798",
bibdate = "Sat Dec 16 15:46:17 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/4783779/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Communications Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}
@InProceedings{Chevillard:2009:CFC,
author = "Sylvain Chevillard and Mioara Joldes and Christoph
Lauter",
title = "Certified and Fast Computation of Supremum Norms of
Approximation Errors",
crossref = "Bruguera:2009:PIS",
pages = "169--176",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In many numerical programs there is a need for a
high-quality floating-point approximation of useful
functions $f$, such as such as $ \exp $, $ \sin $, $
\erf $. In the actual implementation, the function is
replaced by a polynomial $p$, which leads to an
approximation error (absolute or relative) $ \epsilon =
p - f $ or $ \epsilon = p / f - 1 $. The tight yet
certain bounding of this error is an important step
towards safe implementations. The problem is difficult
mainly because that approximation error is very small
and the difference $ p - f $ is subject to high
cancellation. Previous approaches for computing the
supremum norm in this degenerate case, have proven to
be unsafe, not sufficiently tight or too tedious in
manual work. We present a safe and fast algorithm that
computes a tight lower and upper bound for the supremum
norms of approximation errors. The algorithm is based
on a combination of several techniques, including
enhanced interval arithmetic, automatic differentiation
and isolation of the roots of a polynomial. We have
implemented our algorithm and give timings on several
examples.",
acknowledgement = ack-nhfb,
keywords = "approximation error; ARITH-19; automatic/algorithmic
differentiation; certified computation; elementary
function; interval arithmetic; roots isolation
technique.; supremum/infinity norm",
}
@TechReport{Chevillard:2009:FEE,
author = "S. Chevillard",
title = "The functions {ERF} and {ERFC} computed with arbitrary
precision",
type = "Report",
number = "RRLIP2009-04",
institution = "HAL",
address = "????",
pages = "32",
year = "2009",
bibdate = "Mon Jun 12 16:09:53 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Daumas:2009:VRN,
author = "M. Daumas and D. Lester and C. Muoz",
title = "Verified Real Number Calculations: a Library for
Interval Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "226--237",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.213",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 12 08:51:00 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Real number calculations on elementary functions are
remarkably difficult to handle in mechanical proofs. In
this paper, we show how these calculations can be
performed within a theorem prover or proof assistant in
a convenient and highly automated as well as
interactive way. First, we formally establish upper and
lower bounds for elementary functions. Then, based on
these bounds, we develop a rational interval arithmetic
where real number calculations take place in an
algebraic setting. In order to reduce the dependency
effect of interval arithmetic, we integrate two
techniques: interval splitting and Taylor series
expansions. This pragmatic approach has been developed,
and formally verified, in a theorem prover. The formal
development also includes a set of customizable
strategies to automate proofs involving explicit
calculations over real numbers. Our ultimate goal is to
provide guaranteed proofs of numerical properties with
minimal human theorem-prover interaction.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "interval arithmetic; proof checking; real number
calculations; theorem proving",
remark = "Extended version of ARITH-18 article
\cite{Daumas:2009:VRN}.",
}
@Article{Deano:2009:MAS,
author = "Alfredo Dea{\~n}o and Nico M. Temme",
title = "On modified asymptotic series involving confluent
hypergeometric functions",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "35",
pages = "88--103",
year = "2009",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:30 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://etna.mcs.kent.edu/vol.35.2009/pp88-103.dir/pp88-103.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{FreitasDeAbreu:2009:JCU,
author = "Giuseppe Thadeu {Freitas De Abreu}",
title = "{Jensen--Cotes} upper and lower bounds on the
{Gaussian} {$Q$}-function and related functions",
journal = j-IEEE-TRANS-COMM,
volume = "57",
number = "11",
pages = "3328--3338",
month = nov,
year = "2009",
CODEN = "IECMBT",
DOI = "https://doi.org/10.1109/tcomm.2009.11.080479",
ISSN = "0090-6778 (print), 1558-0857 (electronic)",
ISSN-L = "0090-6778",
bibdate = "Sat Dec 16 15:12:46 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Communications",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=26",
}
@Article{Fukushima:2009:FCC,
author = "Toshio Fukushima",
title = "Fast computation of complete elliptic integrals and
{Jacobian} elliptic functions",
journal = j-CELEST-MECH-DYN-ASTR,
volume = "105",
number = "4",
pages = "305--328",
month = dec,
year = "2009",
CODEN = "CLMCAV",
DOI = "https://doi.org/10.1007/s10569-009-9228-z",
ISSN = "0923-2958 (print), 1572-9478 (electronic)",
ISSN-L = "0923-2958",
MRclass = "33E05 (33F05 65E05)",
MRnumber = "2559416",
MRreviewer = "Mehdi Hassani",
bibdate = "Wed Oct 20 21:29:31 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/0923-2958/",
abstract = "As a preparation step to compute Jacobian elliptic
functions efficiently, we created a fast method to
calculate the complete elliptic integral of the first
and second kinds, $ K(m) $ and $ E(m) $, for the
standard domain of the elliptic parameter, $ 0 < m < 1
$. For the case $ 0 < m < 0.9 $, the method utilizes $
10 $ pairs of approximate polynomials of the order of
$9$--$ 19 $ obtained by truncating Taylor series
expansions of the integrals. Otherwise, the associate
integrals, $ K(1 - m) $ and $ E(1 - m) $, are first
computed by a pair of the approximate polynomials and
then transformed to $ K(m) $ and $ E(m) $ by means of
Jacobi's nome, $q$, and Legendre's identity relation.
In average, the new method runs more-than-twice faster
than the existing methods including Cody's Chebyshev
polynomial approximation of Hastings type and Innes'
formulation based on $q$-series expansions. Next, we
invented a fast procedure to compute simultaneously
three Jacobian elliptic functions, {\tt sn(u|m)}, {\tt
cn(u|m)}, and {\tt dn(u|m)}, by repeated usage of the
double argument formulae starting from the Maclaurin
series expansions with respect to the elliptic
argument, $u$, after its domain is reduced to the
standard range, $ 0 \leq u < K(m) / 4 $, with the help
of the new method to compute K(m). The new procedure is
25--70\% faster than the methods based on the Gauss
transformation such as Bulirsch's algorithm, sncndn,
quoted in the Numerical Recipes even if the
acceleration of computation of $ K(m) $ is not taken
into account.",
acknowledgement = ack-nhfb,
fjournal = "Celestial Mechanics \& Dynamical Astronomy. An
International Journal of Space Dynamics",
keywords = "complete elliptic integrals; Encke's method; Innes'
method; Jacobian elliptic functions; nome expansion;
numerical methods",
}
@Article{Fukushima:2009:FCJ,
author = "Toshio Fukushima",
title = "Fast computation of {Jacobian} elliptic functions and
incomplete elliptic integrals for constant values of
elliptic parameter and elliptic characteristic",
journal = j-CELEST-MECH-DYN-ASTR,
volume = "105",
number = "1--3",
pages = "245--260",
year = "2009",
CODEN = "CLMCAV",
DOI = "https://doi.org/10.1007/s10569-008-9177-y",
ISSN = "0923-2958 (print), 1572-9478 (electronic)",
ISSN-L = "0923-2958",
MRclass = "33E05 (33F05 65D20 70M20)",
MRnumber = "2551836",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/0923-2958/",
abstract = "In order to accelerate the numerical evaluation of
torque-free rotation of triaxial rigid bodies, we
present a fast method to compute various kinds of
elliptic functions for a series of the elliptic
argument when the elliptic parameter and the elliptic
characteristic are fixed. The functions we evaluate are
the Jacobian elliptic functions and the incomplete
elliptic integral of the second and third kinds
regarded as a function of that of the first kind. The
key technique is the utilization of the Maclaurin
series expansion and the addition theorems with respect
to the elliptic argument. The new method is around 25
times faster than the method using the incomplete
elliptic integral of general kind and around 70 times
faster than the method using mathematical libraries
given in the latest version of Numerical Recipes.",
acknowledgement = ack-nhfb,
fjournal = "Celestial Mechanics \& Dynamical Astronomy. An
International Journal of Space Dynamics",
keywords = "elliptic integrals; extended body dynamics; Jacobian
elliptic functions; numerical method; rotation",
}
@Article{Guo:2009:CLC,
author = "Senlin Guo and Feng Qi",
title = "A class of logarithmically completely monotonic
functions associated with the gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "224",
number = "1",
pages = "127--132",
day = "1",
month = feb,
year = "2009",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:13:29 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042708001829",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Guralnik:2009:ISV,
author = "Elena Guralnik and Ariel J. Birnbaum and Anatoly
Koyfman and Avi Kaplan",
title = "Implementation Specific Verification of Divide and
Square Root Instructions",
crossref = "Bruguera:2009:PIS",
pages = "114--121",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point operations such as divide and square
root are typically implemented in microcode rather than
dedicated logic. Bugs in these operations missed by
generic black-box verification tools, were analyzed.
This led to the conclusion that the corner cases, in
addition to being implementation dependent, could not
be characterized in terms of special input or output
values in a straightforward manner.\par
However, many of those cases can be easily generalized
for many known implementations. The typical
implementation uses a known iterative approximation
algorithm, such as the Newton--Raphson method, to
calculate the desired result; thus, it is sufficient to
produce the corner cases associated with the specific
algorithm.\par
We investigated the following problem: given an
iterative algorithm to compute a binary floating point
operation, the iteration number, and an interval, find
random inputs for the operation that, after the
requested iteration, yield a relative error within the
specified interval. This paper describes a method to
solve this problem. This method was implemented in a
floating-point test generator and is currently being
used to verify the floating-point units of several
processors.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Han:2009:ICS,
author = "Dong-Guk Han and Dooho Choi and Howon Kim",
title = "Improved Computation of Square Roots in Specific
Finite Fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "188--196",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.201",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663058",
abstract = "In this paper, we study exponentiation in the specific
finite fields $ F_q $ with very special exponents such
as those that occur in algorithms for computing square
roots. Here, $q$ is a prime power, $ q = p^k $, where $
k > 1 $, and $k$ is odd. Our algorithmic approach
improves the corresponding exponentiation resulted from
the better rewritten exponent. To the best of our
knowledge, it is the first major improvement to the
Tonelli--Shanks algorithm, for example, the number of
multiplications can be reduced to at least 60 percent
on the average when $ p \equiv 1 \pmod 16 $. Several
numerical examples are given that show the speedup of
the proposed methods.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "cryptography; efficient computation; finite fields;
square roots",
}
@Article{Harris:2009:MIB,
author = "Frank E. Harris and J. G. Fripiat",
title = "Methods for incomplete {Bessel} function evaluation",
journal = j-IJQC,
volume = "109",
number = "8",
pages = "1728--1740",
month = feb,
year = "2009",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/qua.21972",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Fri Mar 27 07:41:18 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Presented here are detailed methods for evaluating the
incomplete Bessel functions arising when Gaussian-type
orbitals are used for systems periodic in one spatial
dimension. The scheme is designed to yield these
incomplete Bessel functions with an absolute accuracy
of $ \pm 1 \times 10^{-10} $, for the range of integer
orders $ 0 \leq n \leq 12 $ [a range sufficient for a
basis whose members have angular momenta of up to three
units ($s$, $p$, $d$, or $f$ atomic functions)]. To
reach this accuracy level within acceptable computation
times, new rational approximations were developed to
compute the special functions involved, namely, the
exponential integral $ E_1 (x) $ and the modified
Bessel functions $ K_0 (x) $ and $ K_1 (x) $, to
absolute accuracy $ \pm 1 \times 10^{-15} $.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
keywords = "E1(x); exponential integral; incomplete Bessel
function; K0(x); K1(x); leaky aquifer function;
modified Bessel function; numerical methods",
}
@InProceedings{Harrison:2009:DTB,
author = "John Harrison",
title = "Decimal Transcendentals via Binary",
crossref = "Bruguera:2009:PIS",
pages = "187--194",
year = "2009",
DOI = "https://doi.org/10.1109/ARITH.2009.32",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "We describe the design and implementation of a
comprehensive library of transcendental functions for
the new IEEE decimal floating-point formats. In
principle, such functions are very much analogous to
their binary counterparts, though with a few additional
subtleties connected with `scale' (preferred exponent).
But our approach has been not to employ direct
techniques, but rather to re-use existing binary
functions as much as possible, both for greater
efficiency and ease of implementation. For some
functions the most straightforward approach (convert
from decimal to binary, perform binary operation,
convert back) works well. In many cases, however, these
are insufficiently accurate, and subtler approaches
must be used.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@InProceedings{Harrison:2009:FAB,
author = "John Harrison",
title = "Fast and Accurate {Bessel} Function Computation",
crossref = "Bruguera:2009:PIS",
pages = "104--113",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The Bessel functions are considered relatively
difficult to compute. Although they have a simple power
series expansion that is everywhere convergent, they
exhibit approximately periodic behavior which makes the
direct use of the power series impractically slow and
numerically unstable. We describe an alternative method
based on systematic expansion around the zeros,
refining existing techniques based on Hankel
expansions, which mostly avoids the use of
multiprecision arithmetic while yielding accurate
results.",
acknowledgement = ack-nhfb,
keywords = "$J0(x), J1(1), Y0(x), Y1(1)$; ARITH-19; ordinary
Bessel functions of the first and second kinds",
}
@Book{Henner:2009:MMP,
author = "Victor Henner and Tatyana Belozerova and Kyle
Forinash",
title = "Mathematical Methods in Physics: Partial Differential
Equations, {Fourier} Series, and Special Functions",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
pages = "xviii + 841",
year = "2009",
DOI = "https://doi.org/10.1201/b10695",
ISBN = "1-56881-335-X",
ISBN-13 = "978-1-56881-335-6",
LCCN = "QC20 .H487 2009",
bibdate = "Sat Oct 30 17:39:29 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Mathematical physics; Textbooks",
tableofcontents = "1: Fourier Series \\
2: Sturm--Liouville Theory \\
3: One-Dimensional Hyperbolic Equations \\
4: Two-Dimensional Hyperbolic Equations \\
5: One-Dimensional Parabolic Equations \\
6: Parabolic Equations for Higher-Dimensional Problems
\\
7: Elliptic Equations \\
8: Bessel Functions \\
9: Legendre Functions \\
A: Eigenvalues and Eigen functions of the
Sturm--Liouville Problem \\
B: Auxiliary Functions for Different Types of Boundary
Conditions \\
C: The Sturm--Liouville Problem and the Laplace
Equation \\
D: Vector Calculus \\
E: How to Use the Software Associated with this Book",
}
@Article{Lauter:2009:ERB,
author = "C. Q. Lauter and V. Lefevre",
title = "An Efficient Rounding Boundary Test for {\tt pow(x,
y)} in Double Precision",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "197--207",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.202",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 12 08:51:00 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The correct rounding of the function $ \textrm {pow} :
(x, y) \rightarrow x^y $ is currently based on Ziv's
iterative approximation process. In order to ensure its
termination, cases when $ x^y $ falls on a
rounding-boundary must be filtered out. Such
rounding-boundaries are floating-point numbers and
midpoints between two consecutive floating-point
numbers. Detecting rounding-boundaries for pow is a
difficult problem. Previous approaches use repeated
square root extraction followed by repeated square and
multiply. This paper presents a new rounding-boundary
test for pow in double precision, which reduces this to
a few comparisons with precomputed constants. These
constants are deduced from worst cases for the Table
Maker's Dilemma, searched over a small subset of the
input domain. This is a novel use of such worst-case
bounds. The resulting algorithm has been designed for a
fast-on-average correctly rounded implementation of
pow, considering the scarcity of rounding-boundary
cases. It does not stall average computations for
rounding-boundary detection. This paper includes its
correctness proof and experimental results.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "correct rounding; floating-point arithmetic; power
function.",
}
@Article{Linhart:2009:ACL,
author = "Jean Marie Linhart",
title = "{Algorithm 885}: Computing the Logarithm of the Normal
Distribution",
journal = j-TOMS,
volume = "35",
number = "3",
pages = "20:1--20:10",
month = oct,
year = "2009",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1391989.1391993",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 1 19:57:00 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We present and compare three C functions to compute
the logarithm of the cumulative standard normal
distribution. The first is a new algorithm derived from
Algorithm 304's calculation of the standard normal
distribution via a series or continued fraction
approximation, and it is good to the accuracy of the
machine. The second is based on Algorithm 715's
calculation of the standard normal distribution via
rational Chebyshev approximation. This is related to,
and an improvement on, the algorithm for the logarithm
of the normal distribution available in the software
package R. The third is a new and simple algorithm that
uses the compiler's implementation of the error
function, and complement of the error function, to
compute the log of the normal distribution.",
acknowledgement = ack-nhfb,
articleno = "20",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "error function; logarithm of the standard normal
distribution; Normal distribution; normal integral",
}
@Article{Loskot:2009:PPA,
author = "P. Loskot and N. C. Beaulieu",
title = "{Prony} and Polynomial Approximations for Evaluation
of the Average Probability of Error Over Slow-Fading
Channels",
journal = j-IEEE-TRANS-VEH-TECHNOL,
volume = "58",
number = "3",
pages = "1269--1280",
month = mar,
year = "2009",
CODEN = "ITUTAB",
DOI = "https://doi.org/10.1109/tvt.2008.926072",
ISSN = "0018-9545 (print), 1939-9359 (electronic)",
ISSN-L = "0018-9545",
bibdate = "Sat Dec 16 18:08:41 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/4529094/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Vehicular Technology",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
}
@Article{Nagayama:2009:CGB,
author = "S. Nagayama and T. Sasao",
title = "Complexities of Graph-Based Representations for
Elementary Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "1",
pages = "106--119",
month = jan,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.134",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4599569",
abstract = "This paper analyzes complexities of decision diagrams
for elementary functions such as polynomial,
trigonometric, logarithmic, square root, and reciprocal
functions. These real functions are converted into
integer-valued functions by using fixed-point
representation. This paper presents the numbers of
nodes in decision diagrams representing the
integer-valued functions. First, complexities of
decision diagrams for polynomial functions are
analyzed, since elementary functions can be
approximated by polynomial functions. A theoretical
analysis shows that binary moment diagrams (BMDs) have
low complexity for polynomial functions. Second, this
paper analyzes complexity of edge-valued binary
decision diagrams (EVBDDs) for monotone functions,
since many common elementary functions are monotone. It
introduces a new class of integer functions,
Mp-monotone increasing function, and derives an upper
bound on the number of nodes in an EVBDD for the
Mp-monotone increasing function. A theoretical analysis
shows that EVBDDs have low complexity for Mp-monotone
increasing functions. This paper also presents the
exact number of nodes in the smallest EVBDD for the
n-bit multiplier function, and a variable order for the
smallest EVBDD.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "binary moment diagram; decision diagrams; edge-valued
binary decision diagram; elementary function;
elementary function approximation; fixed-point
representation; general representations; graph-based
representation; integer-valued function; monotone
function; polynomial function; trees",
}
@Book{Oldham:2009:AF,
editor = "Keith B. Oldham and Jan Myland and Jerome Spanier",
title = "An Atlas of Functions: With Equator, the Atlas
Function Calculator",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xi + 748",
year = "2009",
DOI = "https://doi.org/10.1007/978-0-387-48807-3",
ISBN = "0-387-48807-3 (softcover), 0-387-48806-5 (hardcover)",
ISBN-13 = "978-0-387-48807-3 (softcover), 978-0-387-48806-6
(hardcover)",
LCCN = "QA331 .S685 2009",
bibdate = "Fri Aug 31 16:20:13 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/canjstat.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$129.95",
acknowledgement = ack-nhfb,
subject = "Functions",
tableofcontents = "Front Matter / i--xi \\
General Considerations / 1--11 \\
The Constant Function $c$ / 13--19 \\
The Factorial Function $n!$ / 21--27 \\
The Zeta Numbers and Related Functions / 29--38 \\
The Bernoulli Numbers $B_n$ / 39--44 \\
The Euler Numbers $E_n$ / 45--48 \\
The Binomial Coefficients $\binom{\nu}{m}$ / 49--56 \\
The Linear Function $b x + c$ and Its Reciprocal /
57--65 \\
Modifying Functions / 67--74 \\
The Heaviside $u(x - a)$ And Dirac $\delta(x - a)$
Functions / 75--80 \\
The Integer Powers $x^n$ and $(b x + c)^n$ / 81--93 \\
The Square-Root Function $\sqrt{b x + c}$ and Its
Reciprocal / 95--102 \\
The Noninteger Powers $x^\nu$ / 103--112 \\
The Semielliptic Function $(b / a)\sqrt{a^2 - x^2}$ and
Its Reciprocal / 113--120 \\
The Semihyperbolic Functions $(b / a) \sqrt{x^2 \pm
a^2}$ and Their Reciprocals / 121--130 \\
The Quadratic Function $a x^2 + b x + c$ and Its
Reciprocal / 131--138 \\
The Cubic Function $x^3 + a x^2 + b x + c$ / 139--146
\\
Polynomial Functions / 147--158 \\
The Pochhammer Polynomials $(x)_n$ / 159--174 \\
The Bernoulli Polynomials $B_n(x)$ / 175--180 \\
The Euler Polynomials $E_n(x)$ / 181--186 \\
The Legendre Polynomials $P_n(x)$ / 187--196 \\
The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
197--208 \\
The Laguerre Polynomials $L_n(x)$ / 209--216 \\
The Hermite Polynomials $H_n(x)$ / 217--227 \\
The Logarithmic Function $\ln(x)$ / 229--239 \\
The Exponential Function $\exp(\pm x)$ / 241--253 \\
Exponentials of Powers $\exp(\pm x^\nu)$ / 255--267 \\
The Hyperbolic Cosine $\cosh(x)$ and Sine $\sinh(x)$
Functions / 269--279 \\
The Hyperbolic Secant $\sech(x)$ and Cosecant
$\csch(x)$ Functions / 281--288 \\
The Hyperbolic Tangent $\tanh(x)$ and Cotangent
$\coth(x)$ Functions / 289--296 \\
The Inverse Hyperbolic Functions / 297--307 \\
The Cosine $\cos(x)$ and Sine $\sin(x)$ Functions /
309--328 \\
The Secant $\sec(x)$ and Cosecant $\csc(x)$ Functions /
329--338 \\
The Tangent $\tan(x)$ and Cotangent $\cot(x)$ Functions
/ 339--350 \\
The Inverse Circular Functions / 351--366 \\
Periodic Functions / 367--374 \\
The Exponential Integrals $\Ei(x)$ and $\Ein(x)$ /
375--383 \\
Sine and Cosine Integrals / 385--394 \\
The Fresnel Integrals $C(x)$ and $S(x)$ / 395--404 \\
The Error Function $\erf(x)$ and Its Complement
$\erfc(x)$ / 405--415 \\
The $\exp(x)\erfc(\sqrt{x})$ and Related Functions /
417--426 \\
Dawson's Integral $\daw(x)$ / 427--433 \\
The Gamma Function $\Gamma(\nu)$ / 435--448 \\
The Digamma Function $\psi(\nu)$ / 449--460 \\
The Incomplete Gamma Functions / 461--470 \\
The Parabolic Cylinder Function $D_\nu(x)$ / 471--484
\\
The Kummer Function $M(a, c, x)$ / 485--496 \\
The Tricomi Function $U(a, c, x)$ / 497--506 \\
The Modified Bessel Functions $I_n(x)$ of Integer Order
/ 507--517 \\
The Modified Bessel Function $I_\nu(x)$ of Arbitrary
Order / 519--526 \\
The Macdonald Function $K_\nu(x)$ / 527--536 \\
The Bessel Functions $J_n(x)$ of Integer Order /
537--552 \\
The Bessel Function $J_\nu(x)$ of Arbitrary Order /
553--565 \\
The Neumann Function $Y_\nu(x)$ / 567--576 \\
The Kelvin Functions / 577--584 \\
The Airy Functions $\Ai(x)$ and $\Bi(x)$ / 585--592 \\
The Struve Function $h_\nu(x)$ / 593--601 \\
The Incomplete Beta Function $B(\nu, \mu, x)$ /
603--609 \\
The Legendre Functions $P_\nu(x)$ and $Q_\nu(x)$ /
611--626 \\
The Gauss Hypergeometric Function $F(a, b, c, x)$ /
627--636 \\
The Complete Elliptic Integrals $K(k)$ and $E(k)$ /
637--651 \\
The Incomplete Elliptic Integrals $F(k, \phi)$ and
$E(k, \phi)$ / 653--669 \\
The Jacobian Elliptic Functions / 671--684 \\
The Hurwitz Function $\zeta(\nu, u)$ / 685--695 \\
Back Matter / 697--748",
}
@Article{Opps:2009:RFA,
author = "Sheldon B. Opps and Nasser Saad and H. M. Srivastava",
title = "Recursion formulas for {Appell}'s hypergeometric
function {$ F_2 $} with some applications to radiation
field problems",
journal = j-APPL-MATH-COMP,
volume = "207",
number = "2",
pages = "545--558",
day = "15",
month = jan,
year = "2009",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Sep 3 10:53:24 MDT 2010",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Paris:2009:HPE,
author = "R. B. Paris",
title = "High-precision evaluation of the {Bessel} functions
via {Hadamard} series",
journal = j-J-COMPUT-APPL-MATH,
volume = "224",
number = "1",
pages = "84--100",
day = "1",
month = feb,
year = "2009",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:13:29 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042708001799",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@MastersThesis{Pearson:2009:CHF,
author = "J. Pearson",
title = "Computation of hypergeometric functions",
type = "{Master}'s thesis",
school = "Oxford University",
address = "Oxford, UK",
year = "2009",
bibdate = "Thu Dec 01 09:05:26 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Talman:2009:NSC,
author = "J. D. Talman",
title = "{NumSBT}: a subroutine for calculating spherical
{Bessel} transforms numerically",
journal = j-COMP-PHYS-COMM,
volume = "180",
number = "2",
pages = "332--338",
month = feb,
year = "2009",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2008.10.003",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 23:42:39 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465508003329",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Temme:2009:AER,
author = "Nico M. Temme and Vladimir Varlamov",
title = "Asymptotic expansions for {Riesz} fractional
derivatives of {Airy} functions and applications",
journal = j-J-COMPUT-APPL-MATH,
volume = "232",
number = "2",
pages = "201--215",
day = "15",
month = oct,
year = "2009",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:24:17 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042709003410",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Vazquez:2009:CDT,
author = "{\'A}lvaro V{\'a}zquez and Julio Villalba and Elisardo
Antelo",
title = "Computation of Decimal Transcendental Functions Using
the {CORDIC} Algorithm",
crossref = "Bruguera:2009:PIS",
pages = "179--186",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In this work we propose new decimal floating-point
CORDIC algorithms for transcendental function
evaluation. We show how these algorithms are mapped to
a state of the art Decimal Floating-Point Unit (DFPU),
both considering the use of a carry-propagate adder or
a carry-save redundant adder. We compared with previous
decimal CORDIC proposals and with table-driven
algorithms, and we concluded that our approach have
significant potential advantages for transcendental
function evaluation in state of the art DFPUs with
minor modifications of the hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Weniger:2009:SHF,
author = "Ernst Joachim Weniger",
title = "The strange history of {$B$} functions or how
theoretical chemists and mathematicians do (not)
interact",
journal = j-IJQC,
volume = "109",
number = "8",
pages = "1728--1740",
month = feb,
year = "2009",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/qua.22014",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Fri Mar 27 07:47:31 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "$B$ functions are a class of relatively complicated
exponentially decaying basis functions. Because the
molecular multicenter integrals of the much simpler
Slater-type functions are notoriously difficult, it is
not at all obvious why $B$ functions should offer any
advantages. However, $B$ functions have Fourier
transforms of exceptional simplicity, which greatly
simplifies many of their molecular multicenter
integrals. This article discusses the historical
development of $B$ functions from the perspective of
the interaction between mathematics and theoretical
chemistry, which traditionally has not been very good.
Nevertheless, future progress in theoretical chemistry
depends very much on a fertile interaction with
neighboring disciplines.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
keywords = "B functions; electronic structure theory;
exponentially decaying basis functions;
interdisciplinary collaboration; multicenter
integrals",
}
@Article{Wozny:2009:MSS,
author = "Pawe{\l} Wo{\'z}ny and Rafa{\l} Nowak",
title = "Method of summation of some slowly convergent series",
journal = j-APPL-MATH-COMP,
volume = "215",
number = "4",
pages = "1622--1645",
month = "????",
year = "2009",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "65B10",
MRnumber = "MR2571650",
bibdate = "Thu Dec 01 09:25:02 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "convergence acceleration",
}
@Article{Yun:2009:ACN,
author = "Beong In Yun",
title = "Approximation to the cumulative normal distribution
using hyperbolic tangent based functions",
journal = "Journal of the Korean Mathematical Society",
volume = "46",
number = "6",
pages = "1267--1276",
year = "2009",
DOI = "https://doi.org/10.4134/JKMS.2009.46.6.1267",
ISSN = "0304-9914",
MRclass = "62E17 (65C60)",
MRnumber = "2572515",
bibdate = "Sat Dec 16 18:04:41 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Korean Math. Soc.",
fjournal = "Journal of the Korean Mathematical Society",
}
@Article{Ahmadi:2010:LCC,
author = "O. Ahmadi and F. R. Henr{\'\i}quez",
title = "Low Complexity Cubing and Cube Root Computation over
{$ F_3^m $} in Polynomial Basis",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "10",
pages = "1297--1308",
month = oct,
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.183",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:32 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5374372",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Akbarpour:2010:VSI,
author = "Behzad Akbarpour and Amr T. Abdel-Hamid and
Sofi{\`e}ne Tahar and John Harrison",
title = "Verifying a Synthesized Implementation of {IEEE-754}
Floating-Point Exponential Function using {HOL}",
journal = j-COMP-J,
volume = "53",
number = "4",
pages = "465--488",
month = may,
year = "2010",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxp023",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Apr 28 14:33:36 MDT 2010",
bibsource = "http://comjnl.oxfordjournals.org/content/vol53/issue4/index.dtl;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://comjnl.oxfordjournals.org/cgi/content/abstract/53/4/465;
http://comjnl.oxfordjournals.org/cgi/reprint/53/4/465",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Alimohammad:2010:UAA,
author = "A. Alimohammad and S. F. Fard and B. F. Cockburn",
title = "A Unified Architecture for the Accurate and
High-Throughput Implementation of Six Key Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "4",
pages = "449--456",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.169",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5313801",
abstract = "This paper presents a unified architecture for the
compact implementation of several key elementary
functions, including reciprocal, square root, and
logarithm, in single-precision floating-point
arithmetic. The proposed high-throughput design is
based on uniform domain segmentation and curve fitting
techniques. Numerically accurate least-squares
regression is utilized to calculate the polynomial
coefficients. The architecture is optimized by
analyzing the trade-off between the size of the
required memory and the precision of intermediate
variables to achieve the minimum 23-bit accuracy
required for single-precision floating-point
representation. The efficiency of the proposed unified
data path is demonstrated on a common
field-programmable gate array.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Alzer:2010:EFI,
author = "Horst Alzer",
title = "Error function inequalities",
journal = j-ADV-COMPUT-MATH,
volume = "33",
number = "3",
pages = "349--379",
month = oct,
year = "2010",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/s10444-009-9139-2",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
MRclass = "33B20 (26D07 26D15)",
MRnumber = "2718103",
MRreviewer = "Feng Qi",
bibdate = "Sat Feb 3 18:22:50 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/s10444-009-9139-2",
acknowledgement = ack-nhfb,
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
}
@Article{Anand:2010:UTE,
author = "Christopher Kumar Anand and Anuroop Sharma",
title = "Unified Tables for Exponential and Logarithm
Families",
journal = j-TOMS,
volume = "37",
number = "3",
pages = "28:1--28:23",
month = sep,
year = "2010",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1824801.1824806",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 27 10:15:50 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Accurate table methods allow for very accurate and
efficient evaluation of elementary functions. We
present new single-table approaches to logarithm and
exponential evaluation, by which we mean that a single
table of values works for both $ \log (x) $ and $ l o
g(1 + x) $, and a single table for $ e^x $ and $ e^x -
1 $. This approach eliminates special cases normally
required to evaluate $ \log (1 + x) $ and $ e^x - 1 $
accurately near zero, which will significantly improve
performance on architectures which use SIMD
parallelism, or on which data-dependent branching is
expensive.\par
We have implemented it on the Cell/B.E. SPU (SIMD
compute engine) and found the resulting functions to be
up to twice as fast as the conventional implementations
distributed in the IBM Mathematical Acceleration
Subsystem (MASS). We include the literate code used to
generate all the variants of exponential and log
functions in the article, and discuss relevant language
and hardware features.",
acknowledgement = ack-nhfb,
articleno = "28",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Accurate tables method; Cell/B.E; IEEE arithmetic;
SIMD; vector library",
}
@Book{Baricz:2010:GBF,
author = "{\'A}rp{\'a}d Baricz",
title = "Generalized {Bessel} Functions of the First Kind",
volume = "1994",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 206",
year = "2010",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/978-3-642-12230-9",
ISBN = "3-642-12229-9 (print), 3-642-12230-2 (e-book)",
ISBN-13 = "978-3-642-12229-3 (print), 978-3-642-12230-9
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L28 no. 1994",
MRclass = "33C10 (33-02 33C05 33C75)",
MRnumber = "2656410 (2011f:33007)",
MRreviewer = "Matti Vuorinen",
bibdate = "Tue May 6 14:56:34 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lnm2010.bib",
series = ser-LECT-NOTES-MATH,
URL = "http://link.springer.com/book/10.1007/978-3-642-12230-9;
http://www.springerlink.com/content/978-3-642-12230-9",
acknowledgement = ack-nhfb,
series-URL = "http://link.springer.com/bookseries/304",
tableofcontents = "1 Introduction and Preliminary Results / 1 \\
1.1 Overview / 1 \\
1.2 Generalized Bessel Functions of the First Kind / 7
\\
1.3 Classical Inequalities / 21 \\
2 Geometric Properties of Generalized Bessel Functions
/ 23 \\
2.1 Univalence of Generalized Bessel Functions / 23 \\
2.1.1 Sufficient Conditions Involving Jack's Lemma / 26
\\
2.1.2 Sufficient Conditions Involving the Admissible
Function Method / 28 \\
2.1.3 Sufficient Conditions Involving the Alexander
Transform / 31 \\
2.1.4 Sufficient Conditions Involving Results of L.
Fej{\'e}r / 36 \\
2.2 Starlikeness and Convexity Properties of
Generalized Bessel Functions / 39 \\
2.2.1 Sufficient Conditions Involving Jack's Lemma / 39
\\
2.2.2 Sufficient Conditions Involving the Admissible
Function Method / 41 \\
2.2.3 Sufficient Conditions Involving Results of H.
Silverman / 50 \\
2.2.4 Close-to-Convexity with Respect to Certain
Functions / 55 \\
2.3 Applications Involving Bessel Functions Associated
with Hardy Space of Analytic Functions / 57 \\
2.3.1 Bessel Transforms and Hardy Space of Generalized
Bessel Functions / 58 \\
2.3.2 A Monotonicity Property of Generalized Bessel
Functions / 62 \\
3 Inequalities Involving Bessel and Hypergeometric
Functions / 71 \\
3.1 Functional Inequalities Involving Quotients of Some
Special Functions / 73 \\
3.1.1 Preliminary Results / 77 \\
3.1.2 Inequalities Involving Ratios of Generalized
Bessel Functions / 80 \\
3.1.3 Inequalities Involving Ratios of Hypergeometric
Functions / 82 \\
3.1.4 Inequalities Involving Ratios of General Power
Series / 83 \\
3.2 Functional Inequalities Involving Special Functions
/ 85 \\
3.2.1 Inequalities Involving Gaussian Hypergeometric
Functions / 85 \\
3.2.2 Inequalities Involving Generalized Bessel
Functions / 91 \\
3.2.3 Inequalities Involving Confluent Hypergeometric
Functions / 93 \\
3.2.4 Inequalities Involving General Power Series and
Concluding Remarks / 94 \\
3.3 Landen-Type Inequality for Bessel Functions / 99
\\
3.3.1 Landen-Type Inequality for Generalized Bessel
Functions / 100 \\
3.3.2 Landen-Type Inequality for General Power Series /
102 \\
3.4 Convexity of Hypergeometric Functions with Respect
to H{\"o}lder Means / 103 \\
3.4.1 Introduction and Preliminaries / 103 \\
3.4.2 Convexity of Hypergeometric Functions with
Respect to H{\"o}lder Means / 104 \\
3.4.3 Convexity of General Power Series with Respect to
H{\"o}lder Means / 108 \\
3.4.4 Concluding Remarks / 110 \\
3.5 Askey's and Gr{\"u}nbaum's Inequality for
Generalized Bessel Functions / 112 \\
3.5.1 Askey's and Gr{\"u}nbaum's Inequality for
Generalized Bessel Functions / 113 \\
3.5.2 Lower and Upper Bounds for Generalized Bessel
Functions / 115 \\
3.6 Inequalities Involving Modified Bessel Functions /
118 \\
3.7 Miscellaneous Inequalities Involving the
Generalized Bessel Functions / 128 \\
3.7.1 Mitrinovic's Inequality and Mahajan's Inequality
/ 129 \\
3.7.2 Redheffer's Inequality / 132 \\
3.7.3 Cusa's Inequality and Related Inequalities / 135
\\
3.7.4 Extensions of Jordan's Inequality / 139 \\
3.7.5 Sharp Jordan Type Inequalities for Bessel
Functions / 144 \\
3.7.6 The Sine and Hyperbolic Sine Integral / 159 \\
3.8 Redheffer Type Inequalities for Bessel Functions /
161 \\
3.8.1 An Extension of Redheffer's Inequality and Its
Hyperbolic Analogue / 162 \\
3.8.2 Sharp Exponential Redheffer-Type Inequalities for
Bessel Functions / 165 \\
3.8.3 A Lower Bound for the Gamma Function / 183 \\
Appendix A / 187 \\
A. 1 Conjectures / 187 \\
A.2 Open Problems / 187 \\
A.3 Matlab Programs for Graphs / 188 \\
References / 193 \\
Index / 203",
}
@Article{Baricz:2010:GPG,
author = "{\'A}rp{\'a}d Baricz",
title = "Geometric Properties of Generalized {Bessel}
Functions",
journal = j-LECT-NOTES-MATH,
volume = "1994",
pages = "23--69",
year = "2010",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/978-3-642-12230-9_2",
ISBN = "3-642-12229-9 (print), 3-642-12230-2 (e-book)",
ISBN-13 = "978-3-642-12229-3 (print), 978-3-642-12230-9
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Fri May 9 19:06:58 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lnm2010.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-12230-9_2.pdf",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-12230-9",
book-URL = "http://www.springerlink.com/content/978-3-642-12230-9",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Book{Beals:2010:SFG,
author = "Richard Beals and R. (Roderick) Wong",
title = "Special functions: a graduate text",
volume = "126",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "ix + 456",
year = "2010",
ISBN = "0-521-19797-X",
ISBN-13 = "978-0-521-19797-7",
LCCN = "QA351 .B34 2010; QA351 BEA 2010",
bibdate = "Sat Oct 30 16:43:46 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Cambridge studies in advanced mathematics",
URL = "http://assets.cambridge.org/97805211/97977/cover/9780521197977.jpg;
http://www.loc.gov/catdir/enhancements/fy1009/2010017815-b.html;
http://www.loc.gov/catdir/enhancements/fy1009/2010017815-d.html;
http://www.loc.gov/catdir/enhancements/fy1009/2010017815-t.html",
abstract = "From the Publisher: The subject of special functions
is often presented as a collection of disparate
results, which are rarely organised in a coherent way.
This book answers the need for a different approach to
the subject. The authors' main goals are to emphasise
general unifying principles coherently and to provide
clear motivation, efficient proofs, and original
references for all of the principal results. The book
covers standard material, but also much more, including
chapters on discrete orthogonal polynomials and
elliptic functions. The authors show how a very large
part of the subject traces back to two equations ---
the hypergeometric equation and the confluent
hypergeometric equation --- and describe the various
ways in which these equations are canonical and
special. Providing ready access to theory and formulas,
this book serves as an ideal graduate-level textbook as
well as a convenient reference.",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Textbooks",
tableofcontents = "Preface; 1. Orientation\\
2. Gamma, beta, zeta\\
3. Second order differential equations\\
4. Orthogonal polynomials\\
5. Discrete orthogonal polynomials\\
6. Confluent hypergeometric functions\\
7. Cylinder functions\\
8. Hypergeometric functions\\
9. Spherical functions\\
10. Asymptotics\\
11. Elliptic functions\\
References\\
Index",
}
@InProceedings{Benoit:2010:DDM,
author = "Alexandre Benoit and Fr{\'e}d{\'e}ric Chyzak and
Alexis Darrasse and Stefan Gerhold and Marc Mezzarobba
and Bruno Salvy",
title = "The Dynamic Dictionary of Mathematical Functions
{(DDMF)}",
crossref = "Fukuda:2010:MSI",
pages = "35--41",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_7",
bibdate = "Sat Sep 23 06:20:46 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Borghi:2010:AFE,
author = "Riccardo Borghi",
title = "Asymptotic and factorial expansions of {Euler} series
truncation errors via exponential polynomials",
journal = j-APPL-NUM-MATH,
volume = "60",
number = "12",
pages = "1242--1250",
month = dec,
year = "2010",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65B10 (33F05 40A25)",
MRnumber = "MR2735157",
bibdate = "Thu Dec 01 09:47:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
}
@Article{Brent:2010:UAE,
author = "Richard P. Brent",
title = "Unrestricted algorithms for elementary and special
functions",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "1--13",
month = apr,
year = "2010",
bibdate = "Sat Feb 25 10:56:45 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://arxiv.org/abs/1004.3621",
abstract = "We describe some ``unrestricted'' algorithms which are
useful for the computation of elementary and special
functions when the precision required is not known in
advance. Several general classes of algorithms are
identified and illustrated by examples. The topics
include: power series methods, use of halving
identities, asymptotic expansions, continued fractions,
recurrence relations, Newton's method, numerical
contour integration, and the arithmetic-geometric mean.
Most of the algorithms discussed are implemented in the
MP package.",
acknowledgement = ack-nhfb,
}
@Article{Celledoni:2010:AFF,
author = "Elena Celledoni and Antonella Zanna",
title = "{Algorithm 903}: {FRB} --- {Fortran} routines for the
exact computation of free rigid body motions",
journal = j-TOMS,
volume = "37",
number = "2",
pages = "23:1--23:24",
month = apr,
year = "2010",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1731022.1731033",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Apr 21 11:39:57 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We present two algorithms and their corresponding
Fortran routines for the exact computation of free
rigid body motions. The methods use the same
description of the angular momentum part $m$ by Jacobi
elliptic functions, and suitably chosen frames for the
attitude matrix\slash quaternion $ Q / q $,
respectively. The frame transformation requires the
computation of elliptic integrals of the third kind.
Implementation and usage of the routines are described,
and some examples of drivers are included. Accuracy and
performance are also tested to provide reliable
numerical results.",
acknowledgement = ack-nhfb,
articleno = "23",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "attitude rotation; Jacobi elliptic integrals;
numerical methods; Rigid body; splitting methods",
}
@InProceedings{Chevillard:2010:SED,
author = "Sylvain Chevillard and Mioara Jolde and Christoph
Lauter",
title = "{Sollya}: An Environment for the Development of
Numerical Codes",
crossref = "Fukuda:2010:MSI",
pages = "28--31",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_5",
bibdate = "Tue Sep 24 14:50:44 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Cuyt:2010:VSF,
author = "Annie Cuyt and Franky Backeljauw and Stefan Becuwe and
Joris {Van Deun}",
title = "Validated Special Functions Software",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6327",
pages = "32--34",
year = "2010",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_6",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Aug 9 15:34:11 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_6.pdf",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-15582-6",
book-URL = "http://www.springerlink.com/content/978-3-642-15582-6",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{deDinechin:2010:FPE,
author = "Florent de Dinechin and Bogdan Pasca",
editor = "Jinian Bian and Qiang Zhou and Kang Zhao",
booktitle = "{Proceedings 2010 International Conference on
Field-Programmable Technology, 8--10 December 2010,
Beijing, China}",
title = "Floating-point exponential functions for {DSP}-enabled
{FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "110--117",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1109/FPT.2010.5681764",
bibdate = "Sat Feb 08 09:35:06 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Dumbgen:2010:BSG,
author = "L. D{\"u}mbgen",
title = "Bounding standard {Gaussian} tail probabilities",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "9",
month = dec,
year = "2010",
bibdate = "Sat Dec 16 16:24:48 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://arxiv.org/abs/1012.2063",
acknowledgement = ack-nhfb,
}
@InProceedings{Erocal:2010:SPU,
author = "Bur{\c{c}}in Er{\"o}cal and William Stein",
title = "The {Sage Project}: Unifying Free Mathematical
Software to Create a Viable Alternative to {Magma},
{Maple}, {Mathematica} and {MATLAB}",
crossref = "Fukuda:2010:MSI",
pages = "12--27",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_4",
bibdate = "Sat Sep 23 06:20:46 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
acknowledgement = ack-nhfb,
}
@Article{Fukushima:2010:FCI,
author = "Toshio Fukushima",
title = "Fast computation of incomplete elliptic integral of
first kind by half argument transformation",
journal = j-NUM-MATH,
volume = "116",
number = "4",
pages = "687--719",
month = oct,
year = "2010",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-010-0321-8",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Oct 16 16:02:41 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=116&issue=4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=116&issue=4&spage=687",
abstract = "We developed a new method to calculate the incomplete
elliptic integral of the first kind, $ F(\varphi |m) $,
by using the half argument formulas of Jacobian
elliptic functions. The method reduces the magnitude of
$ \varphi $ by repeated usage of the formulas while
fixing $m$. The method is sufficiently precise in the
sense that the maximum relative error is $3$--$5$
machine epsilons at most. Thanks to the simplicity of
the half argument formulas, the new procedure is
significantly faster than the existing procedures. For
example, it runs 20--60\% faster than Bulirsch's
function, {\tt el1}, and 1.9--2.2 times faster than the
method using Carlson's function, $ R_F $.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{ISO:2010:IIIa,
author = "{ISO}",
title = "{ISO\slash IEC 29124:2010}: Information technology ---
Programming languages, their environments and system
software interfaces --- Extensions to the {C++ Library}
to support mathematical special functions",
publisher = pub-ISO,
address = pub-ISO:adr,
year = "2010",
LCCN = "????",
bibdate = "Thu Nov 25 08:56:44 2010",
bibsource = "http://www.iso.org/iso/search.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/isostd.bib",
series = "Technical report",
URL = "http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=50511",
acknowledgement = ack-nhfb,
subject = "programming languages (electronic computers)",
}
@Article{Li:2010:NRB,
author = "Rong Li and Pooi Yuen Kam and Hua Fu",
title = "New representations and bounds for the generalized
{Marcum} {$Q$}-function via a geometric approach, and
an application",
journal = j-IEEE-TRANS-COMM,
volume = "58",
number = "1",
pages = "157--169",
month = jan,
year = "2010",
CODEN = "IECMBT",
DOI = "https://doi.org/10.1109/tcomm.2010.01.070426",
ISSN = "0090-6778 (print), 1558-0857 (electronic)",
ISSN-L = "0090-6778",
bibdate = "Sat Dec 16 16:52:49 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/5397910/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Communications",
}
@Article{Nandagopal:2010:NEF,
author = "Mohankumar Nandagopal and Soubhadra Sen and Ajay
Rawat",
title = "A Note on the Error Function",
journal = j-COMPUT-SCI-ENG,
volume = "12",
number = "4",
pages = "84--88",
month = jul # "\slash " # aug,
year = "2010",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCSE.2010.79",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Tue Jul 27 16:37:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See improvements \cite{Iacono:2021:BEF}.",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}
@Article{Paszkowski:2010:UMC,
author = "Stefan Paszkowski",
title = "Untypical methods of convergence acceleration",
journal = j-NUMER-ALGORITHMS,
volume = "54",
number = "??",
pages = "??--??",
month = "????",
year = "2010",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-010-9381-1",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 14:24:01 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=0&issue=0;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=0&issue=0&spage=??",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "convergence acceleration",
remark = "Article in press, not yet assigned to an issue.",
}
@Article{Prevost:2010:RVZ,
author = "Marc Pr{\'e}vost",
title = "Recurrence for values of the zeta function",
journal = j-APPL-NUM-MATH,
volume = "60",
number = "12",
pages = "1382--1394",
month = dec,
year = "2010",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2010.05.011",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Sat Oct 16 16:17:49 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Using the Pad{\'e} approximation of the exponential
function, we obtain a general recurrence relation for
values of the zeta function which contains, as
particular cases, many relations already proved.
Applications to Bernoulli polynomials are given.
Finally, we derive some new recurrence relations with
gap of length 4 for zeta numbers.",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "Pad{\'e} approximants; zeta function",
}
@Article{Qi:2010:CMS,
author = "Feng Qi and Senlin Guo and Bai-Ni Guo",
title = "Complete monotonicity of some functions involving
polygamma functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "233",
number = "9",
pages = "2149--2160",
day = "1",
month = mar,
year = "2010",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:24:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042709006682",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Safouhi:2010:BSC,
author = "Hassan Safouhi",
title = "{Bessel}, sine and cosine functions and extrapolation
methods for computing molecular multi-center
integrals",
journal = j-NUMER-ALGORITHMS,
volume = "54",
number = "1",
pages = "141--167",
month = may,
year = "2010",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon May 17 14:08:57 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=54&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=54&issue=1&spage=141",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Slevinsky:2010:RAT,
author = "Richard M. Slevinsky and Hassan Safouhi",
title = "A recursive algorithm for the {$G$} transformation and
accurate computation of incomplete {Bessel} functions",
journal = j-APPL-NUM-MATH,
volume = "60",
number = "12",
pages = "1411--1417",
month = dec,
year = "2010",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2010.04.005",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Sat Oct 16 16:17:49 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "In the present contribution, we develop an efficient
algorithm for the recursive computation of the $
G_n^{(1)} $ source transformation for the approximation
of infinite-range integrals. Previous to this
contribution, the theoretically powerful $ G_n^{(1)} $
transformation was handicapped by the lack of an
algorithmic implementation. Our proposed algorithm
removes this handicap by introducing a recursive
computation of the successive $ G_n^{(1)} $
transformations with respect to the order $n$. This
recursion, however, introduces the $ (x^2 d / d x) $
source operator applied to the integrand. Consequently,
we employ the Slevinsky--Safouhi formula I for the
analytical and numerical developments of these required
successive derivatives.\par
Incomplete Bessel functions, which pose as a numerical
challenge, are computed to high pre-determined
accuracies using the developed algorithm. The numerical
results obtained show the high efficiency of the new
method, which does not resort to any numerical
integration in the computation.",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "Extrapolation methods; Incomplete Bessel functions;
Nonlinear transformations; Slevinsky--Safouhi
formulae",
}
@InProceedings{Sofotasios:2010:NEM,
author = "Paschalis C. Sofotasios and Steven Freear",
booktitle = "2010 7th International Symposium on Wireless
Communication Systems",
title = "Novel expressions for the {Marcum} and one dimensional
{$Q$}-functions",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "",
month = sep,
year = "2010",
DOI = "https://doi.org/10.1109/iswcs.2010.5624374",
ISBN = "1-4244-6315-7 (print), 1-4244-6317-3 (e-book),
1-4244-6316-5 (CD-ROM)",
ISBN-13 = "978-1-4244-6315-2 (print), 978-1-4244-6317-6 (e-book),
978-1-4244-6316-9 (CD-ROM)",
ISSN = "2154-0217 (print), 2154-0225 (electronic)",
ISSN-L = "2154-0225",
bibdate = "Sat Dec 16 17:36:08 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/5624374/",
acknowledgement = ack-nhfb,
}
@Book{Vallee:2010:AFA,
author = "Olivier Vall{\'e}e and Manuel Soares",
title = "{Airy} Functions and Applications to Physics",
publisher = "Imperial College Press",
address = "London WC26 9HE, UK",
edition = "Second",
pages = "x + 202",
year = "2010",
ISBN = "1-84816-548-X, 1-84816-550-1",
ISBN-13 = "978-1-84816-548-9, 978-1-84816-550-2",
LCCN = "QA351",
bibdate = "Tue Dec 5 10:05:10 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Addressed mainly to physicist and chemical physicist,
this textbook is the result of a broad compilation of
current knowledge on analytical properties of Airy
functions. In particular, the calculus implying the
Airy functions is developed with care. In the latter
chapters, examples are given to succinctly illustrate
the use of Airy functions in classical and quantum
physics. The physicist, for instance in fluid
mechanics, can find what he is looking for, in the
references for works of molecular physics or in physics
of surfaces, and vice versa. The knowledge on Airy
functions is frequently reviewed. The reason may be
found in the need to express a physical phenomenon in
terms of an effective and comprehensive analytical form
for the whole scientific community.",
acknowledgement = ack-nhfb,
remark = "See also first edition \cite{Vallee:2004:AFA}",
subject = "Airy functions; Airy-Funktion; Mathematische Physik",
tableofcontents = "Preface / x \\
1: A Historical Introduction: Sir George Biddell Airy /
1 \\
2: Definitions and Properties / 5 \\
2.1: Homogeneous Airy functions \\
2.1.1: The Airy equation \\
2.1.2: Elementary properties \\
2.1.3: Integral representations \\
2.1.4: Ascending and asymptotic series \\
2.2: Properties of Airy functions \\
2.2.1: Zeros of Airy functions \\
2.2.2: The spectral zeta function \\
2.2.3: Inequalities \\
2.2.4: Connection with Bessel functions \\
2.2.5: Modulus and phase of Airy functions \\
2.3: Inhomogeneous Airy functions \\
2.3.1: Definitions \\
2.3.2: Properties of inhomogeneous Airy functions \\
2.3.3: Ascending series and asymptotic expansion \\
2.3.4: Zeros of the Scorer functions \\
2.4: Squares and products of Airy functions \\
2.4.1: Differential equation and integral
representation \\
2.4.2: A remarkable identity \\
2.4.3: The product $\Ai(x) \Ai(-x)$: Airy wavelets \\
3: Primitives and Integrals of Airy Functions / 37 \\
3.1: Primitives containing one Airy function \\
3.1.1: In terms of Airy functions \\
3.1.2: Ascending series \\
3.1.3: Asymptotic expansions \\
3.1.4: Primitives of Scorer functions \\
3.1.5: Repeated primitives \\
3.2: Product of Airy functions \\
3.2.1: The method of Albright \\
3.2.2: Some primitives \\
3.3: Other primitives \\
3.4: Miscellaneous \\
3.5: Elementary integrals \\
3.5.1: Particular integrals \\
3.5.2: Integrals containing a single Airy function \\
3.5.3: Integrals of products of two Airy functions \\
3.6: Other integrals \\
3.6.1: Integrals involving the Volterra $\mu$-function
\\
3.6.2: Canonisation of cubic forms \\
3.6.3: Integrals with three Airy functions \\
3.6.4: Integrals with four Airy functions \\
3.6.5: Double integrals \\
4: Transformations of Airy functions / 69 \\
4.1: Causal properties of Airy functions \\
4.1.1: Causal relations \\
4.1.2: Green's function of the Airy equation \\
4.1.3: Fractional derivatives of Airy functions \\
4.2: The Airy transform \\
4.2.1: Definitions and elementary properties \\
4.2.2: Some examples \\
4.2.3: Airy polynomials \\
4.2.4: A particular case: correlation Airy transform
\\
4.3: Other kinds of transformations \\
4.3.1: Laplace transform of Airy functions \\
4.3.2: Mellin transform of Airy functions \\
4.3.3: Fourier transform of Airy functions \\
4.3.4: Hankel transform and the Airy kernel \\
4.4: Expansion into Fourier--Airy series \\
5: The Uniform Approximation / 101 \\
5.1: Oscillating integrals \\
5.1.1: The method of stationary phase \\
5.1.2: The uniform approximation of oscillating
integrals \\
5.1.3: The Airy uniform approximation \\
5.2: Differential equations of the second order \\
5.2.1: The JWKB method \\
5.2.2: The Langer generalisation \\
5.3: Inhomogeneous differential equations \\
6: Generalisation of Airy Functions / 111 \\
6.1: Generalisation of the Airy integral \\
6.1.1: The generalisation of Watson \\
6.1.2: Oscillating integrals and catastrophes \\
6.2: Third order differential equations \\
6.2.1: The linear third order differential equation \\
6.2.2: Asymptotic solutions \\
6.2.3: The comparison equation \\
6.3: A differential equation of the fourth order \\
7: Applications to Classical Physics / 127 \\
7.1: Optics and electromagnetism \\
7.2: Fluid mechanics \\
7.2.1: The Tricomi equation \\
7.2.2: The Orr--Sommerfeld equation \\
7.3: Elasticity \\
7.4: The heat equation \\
7.5: Nonlinear physics \\
7.5.1: Korteweg--de Vries equation \\
7.5.2: The Second Painlev{\'e} equation \\
8: Applications to Quantum Physics / 147 \\
8.1: The Schr{\"o}dinger equation \\
8.1.1: Particle in a Uniform field \\
8.1.2: The 8.1.3: Uniform approximation of the
Schr{\"o}dinger equation \\
8.2: Evaluation of the Franck--Condon factors \\
8.2.1: The Franck--Condon principle \\
8.2.2: The JWKB approximation \\
8.2.3: The uniform approximation \\
8.3: The semiclassical Wigner distribution \\
8.3.1: The Weyl--Wigner formalism \\
8.3.2: The one-dimensional Wigner distribution \\
8.3.3: The two-dimensional Wigner distribution \\
8.3.4: Configuration of the Wigner distribution \\
8.4: Airy transform of the Schr{\"o}dinger equation \\
Appendix A: Numerical Computation of the Airy Functions
/ 185 \\
A.1: Homogeneous functions \\
A.2: Inhomogeneous functions \\
Bibliography / 191 \\
Index / 201",
}
@Article{Weniger:2010:SDP,
author = "E. J. Weniger",
title = "Summation of divergent power series by means of
factorial series",
journal = j-APPL-NUM-MATH,
volume = "60",
number = "12",
pages = "1429--1441",
month = "????",
year = "2010",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Thu Dec 01 10:37:55 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Presented at Approximation and Extrapolation of
Convergent and Divergent Sequences and Series (CIRM,
Luminy --- France, 2009).",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
}
@Article{Wozny:2010:EAS,
author = "Pawe{\l} Wo{\'z}ny",
title = "Efficient algorithm for summation of some slowly
convergent series",
journal = j-APPL-NUM-MATH,
volume = "60",
number = "12",
pages = "1442--1453",
month = "????",
year = "2010",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Thu Dec 01 09:26:24 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Presented at Approximation and Extrapolation of
Convergent and Divergent Sequences and Series (CIRM,
Luminy - France, 2009).",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
keywords = "convergence acceleration",
}
@Article{Zhu:2010:JTI,
author = "Ling Zhu",
title = "{Jordan} type inequalities involving the {Bessel} and
modified {Bessel} functions",
journal = j-COMPUT-MATH-APPL,
volume = "59",
number = "2",
pages = "724--736",
month = jan,
year = "2010",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:34 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122109007196",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Ali:2011:NGJ,
author = "Ahmad T. Ali",
title = "New generalized {Jacobi} elliptic function rational
expansion method",
journal = j-J-COMPUT-APPL-MATH,
volume = "235",
number = "14",
pages = "4117--4127",
day = "15",
month = may,
year = "2011",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2011.03.002",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:24:28 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042711001257",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Borwein:2011:SVG,
author = "Jonathan M. Borwein and Armin Straub",
title = "Special values of generalized log-sine integrals",
crossref = "Schost:2011:IPI",
pages = "43--50",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993899",
bibdate = "Fri Mar 14 12:20:08 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/issac.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
abstract = "We study generalized log-sine integrals at special
values. At $ \pi $ and multiples thereof explicit
evaluations are obtained in terms of Nielsen
polylogarithms at $ \pm 1 $. For general arguments we
present algorithmic evaluations involving Nielsen
polylogarithms at related arguments. In particular, we
consider log-sine integrals at $ \pi / 3 $ which
evaluate in terms of polylogarithms at the sixth root
of unity. An implementation of our results for the
computer algebra systems Mathematica and SAGE is
provided.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brisebarre:2011:APS,
author = "Nicolas Brisebarre and Mioara Joldes and Peter
Kornerup and {\'E}rik Martin-Dorel and Jean-Michel
Muller",
title = "Augmented Precision Square Roots and {$2$-D} Norms,
and Discussion on Correctly Rounding $ \sqrt {x^2 +
y^2} $",
crossref = "Schwarz:2011:PIS",
pages = "23--30",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.13",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992105",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; hypotenuse",
}
@InProceedings{Butts:2011:RDR,
author = "J. Adam Butts and Ping Tak Peter Tang and Ron O. Dror
and David E. Shaw",
title = "Radix-8 Digit-by-Rounding: Achieving High-Performance
Reciprocals, Square Roots, and Reciprocal Square
Roots",
crossref = "Schwarz:2011:PIS",
pages = "149--158",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.28",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992120",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Cai:2011:CSB,
author = "Liang-Wu Cai",
title = "On the computation of spherical {Bessel} functions of
complex arguments",
journal = j-COMP-PHYS-COMM,
volume = "182",
number = "3",
pages = "663--668",
month = mar,
year = "2011",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2010.11.019",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 11 10:10:56 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465510004650",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Cardoso:2011:IFP,
author = "Jo{\~a}o Ribeiro Cardoso and Ana F. Loureiro",
title = "Iteration functions for $p$ th roots of complex
numbers",
journal = j-NUMER-ALGORITHMS,
volume = "57",
number = "3",
pages = "329--356",
month = jul,
year = "2011",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Fri Jul 22 09:48:58 MDT 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=57&issue=3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=57&issue=3&spage=329",
abstract = "A novel way of generating higher-order iteration
functions for the computation of pth roots of complex
numbers is the main contribution of the present work.
The behavior of some of these iteration functions will
be analyzed and the conditions on the starting values
that guarantee the convergence will be stated. The
illustration of the basins of attractions of the pth
roots will be carried out by some computer generated
plots. In order to compare the performance of the
iterations some numerical examples will be
considered.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Chang:2011:CTB,
author = "Seok-Ho Chang and Pamela C. Cosman and Laurence B.
Milstein",
title = "{Chernoff}-Type Bounds for the {Gaussian} Error
Function",
journal = j-IEEE-TRANS-COMM,
volume = "59",
number = "11",
pages = "2939--2944",
month = nov,
year = "2011",
CODEN = "IECMBT",
DOI = "https://doi.org/10.1109/tcomm.2011.072011.100049",
ISSN = "0090-6778 (print), 1558-0857 (electronic)",
ISSN-L = "0090-6778",
bibdate = "Fri Jul 22 09:48:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Communications",
}
@Article{Chen:2011:SPF,
author = "Chao-Ping Chen",
title = "Some properties of functions related to the gamma, psi
and tetragamma functions",
journal = j-COMPUT-MATH-APPL,
volume = "62",
number = "9",
pages = "3389--3395",
month = nov,
year = "2011",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:51:02 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122111007267",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Chen:2011:TSA,
author = "Jianxun Chen and Yongzhong Huang and Shaozhong Guo and
Shimiao Chen and Wei Wang",
booktitle = "{2011 Third International Conference on Measuring
Technology and Mechatronics Automation (ICMTMA)}",
title = "Test Standardization and Analyse Model of Mathematical
Functions for Precision",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "652--655",
year = "2011",
DOI = "https://doi.org/10.1109/ICMTMA.2011.734",
ISBN = "0-7695-4296-4",
ISBN-13 = "978-0-7695-4296-6",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5721571",
abstract = "This article describes problems of meet the
requirements to implementations of mathematical
functions working with floating-point numbers, and so
facilitate the comprehensive testing of mathematical
functions. Inconsistency and incompleteness of
available standards in the domain is demonstrated.
Correct rounding requirement is suggested to guarantee
preservation of all important properties of functions
and to support high level of interoperability between
different mathematical libraries and software using
them. The article also concerns precision analyse of
mathematical functions. Conformance test construction
method is proposed based on different sources of test
data.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5720445",
remark = "This paper contains unattributed plagiaristic copying
of material from
\url{https://www.math.utah.edu/~beebe/software/ieee/index.html}.",
}
@Article{Chlebus:2011:RSI,
author = "Edward Chlebus",
title = "A Recursive Scheme for Improving the Original Rate of
Convergence to the {Euler--Mascheroni} Constant",
journal = j-AMER-MATH-MONTHLY,
volume = "118",
number = "3",
pages = "268--274",
month = mar,
year = "2011",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.118.03.268",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jan 30 08:58:19 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/10.4169/amermathmont.118.issue-3;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.03.268.pdf",
abstract = "We have used Euler--Maclaurin summation to develop a
recursive scheme for modifying the original
approximation for the Euler--Mascheroni constant $
\gamma $. Convergence to $ \gamma $ resulting from
successively employing the proposed scheme has been
significantly accelerated while the form of the
approximation originally introduced by Euler is still
preserved.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
remark = "The author derives relations between $ \gamma $ and
the $n$-th partial sum of the harmonic series that have
an error $ O(n^{-2 k}) $ for increasing $k$. He also
references prior work from 2009 that computes $ \gamma
$ to 29,844,489,545 decimal digits.",
}
@Article{Choi:2011:AFT,
author = "Junesang Choi and H. M. Srivastava",
title = "Asymptotic formulas for the triple {Gamma} function {$
\Gamma_3 $} by means of its integral representation",
journal = j-APPL-MATH-COMP,
volume = "218",
number = "6",
pages = "2631--2640",
day = "15",
month = nov,
year = "2011",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2011.08.002",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Oct 25 09:03:08 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300311010289",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Colman:2011:VCC,
author = "Michel Colman and Annie Cuyt and Joris {Van Deun}",
title = "Validated computation of certain hypergeometric
functions",
journal = j-TOMS,
volume = "38",
number = "2",
pages = "11:1--11:20",
month = dec,
year = "2011",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2049673.2049675",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Dec 30 17:43:07 MST 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We present an efficient algorithm for the validated
high-precision computation of real continued fractions,
accurate to the last digit. The algorithm proceeds in
two stages. In the first stage, computations are done
in double precision. A forward error analysis and some
heuristics are used to obtain an a priori error
estimate. This estimate is used in the second stage to
compute the fraction to the requested accuracy in high
precision (adaptively incrementing the precision for
reasons of efficiency). A running error analysis and
techniques from interval arithmetic are used to
validate the result.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{deDinechin:2011:CFP,
author = "Florent de Dinechin and Christoph Lauter and Guillaume
Melquiond",
title = "Certifying the Floating-Point Implementation of an
Elementary Function Using {Gappa}",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "242--253",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.128",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "High confidence in floating-point programs requires
proving numerical properties of final and intermediate
values. One may need to guarantee that a value stays
within some range, or that the error relative to some
ideal value is well bounded. This certification may
require a time-consuming proof for each line of code,
and it is usually broken by the smallest change to the
code, e.g., for maintenance or optimization purpose.
Certifying floating-point programs by hand is,
therefore, very tedious and error-prone. The Gappa
proof assistant is designed to make this task both
easier and more secure, due to the following novel
features: It automates the evaluation and propagation
of rounding errors using interval arithmetic. Its input
format is very close to the actual code to validate. It
can be used incrementally to prove complex mathematical
properties pertaining to the code. It generates a
formal proof of the results, which can be checked
independently by a lower level proof assistant like
Coq. Yet it does not require any specific knowledge
about automatic theorem proving, and thus, is
accessible to a wide community. This paper demonstrates
the practical use of this tool for a widely used class
of floating-point programs: implementations of
elementary functions in a mathematical library.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Fu:2011:ETB,
author = "Hua Fu and Pooi-Yuen Kam",
booktitle = "2011 {IEEE} Global Telecommunications Conference ---
{GLOBECOM 2011}",
title = "Exponential-Type Bounds on the First-Order {Marcum}
Q-Function",
publisher = pub-IEEE,
address = pub-IEEE:adr,
month = dec,
year = "2011",
DOI = "https://doi.org/10.1109/glocom.2011.6133801",
bibdate = "Sat Dec 16 16:28:28 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/6133801/",
acknowledgement = ack-nhfb,
}
@Article{Fukushima:2011:PFC,
author = "Toshio Fukushima",
title = "Precise and fast computation of the general complete
elliptic integral of the second kind",
journal = j-MATH-COMPUT,
volume = "80",
number = "275",
pages = "1725--1743",
month = jul,
year = "2011",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Apr 18 06:32:30 MDT 2011",
bibsource = "http://www.ams.org/mcom/2011-80-275;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02455-5/home.html;
http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02455-5/S0025-5718-2011-02455-5.pdf",
abstract = "We developed an efficient procedure to evaluate two
auxiliary complete elliptic integrals of the second
kind $ B(m) $ and $ D(m) $ by using their Taylor series
expansions, the definition of Jacobi's nome, and
Legendre's relation. The developed procedure is more
precise than the existing ones in the sense that the
maximum relative errors are 1--3 machine epsilons, and
it runs drastically faster; around 5 times faster than
Bulirsch's cel2 and 16 times faster than Carlson's $
R_F $ and $ R_D $.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gautschi:2011:LWF,
author = "Walter Gautschi",
title = "The {Lambert} {$W$}-functions and some of their
integrals: a case study of high-precision computation",
journal = j-NUMER-ALGORITHMS,
volume = "57",
number = "1",
pages = "27--34",
month = may,
year = "2011",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-010-9409-6",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Apr 27 08:44:14 MDT 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=57&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=57&issue=1&spage=27",
abstract = "The real-valued Lambert W-functions considered here
are $ w_0 (y) $ and $ w_{-1}(y) $, solutions of $ w e^w
= y $, $ - 1 / e < y < 0 $, with values respectively in
$ ( - 1, 0) $ and $ ( - \infty, - 1) $. A study is made
of the numerical evaluation to high precision of these
functions and of the integrals, $ \alpha > 0 $, $ \beta
\in \mathbb {R} $, and $ \alpha > - 1 $, $ \beta < 1 $.
For the latter we use known integral representations
and their evaluation by nonstandard Gaussian
quadrature, if $ \alpha \neq \beta $, and explicit
formulae involving the trigamma function, if $ \alpha =
\beta $.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Integrals of Lambert W-functions; Lambert W-functions;
Nonstandard Gaussian quadrature; Variable-precision
computation",
}
@Article{Gil:2011:APC,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 914}: {Parabolic} cylinder function {$ W(a,
x) $} and its derivative",
journal = j-TOMS,
volume = "38",
number = "1",
pages = "6:1--6:5",
month = nov,
year = "2011",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2049662.2049668",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Dec 15 08:59:34 MST 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "A Fortran 90 program for the computation of the real
parabolic cylinder functions $ W(a, \pm x) $, $ x \geq
0 $ and their derivatives is presented. The code also
computes scaled functions for $ a > 50 $. The functions
$ W(a, \pm x) $ are a numerically satisfactory pair of
solutions of the parabolic cylinder equation $ y^\prime
+ (x^2 / 4 - a)y = 0 $, $ x \geq 0 $. Using Wronskian
tests, we claim a relative accuracy better than $ 5
\times 10^{-13} $ in the computable range of unscaled
functions, while for scaled functions the aimed
relative accuracy is better than $ 5 \times 10^{-14} $.
This code, together with the algorithm and related
software described in Gil et al.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gil:2011:FAC,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Fast and accurate computation of the {Weber} parabolic
cylinder function {$ W(a, x) $}",
journal = j-IMA-J-NUMER-ANAL,
volume = "31",
number = "3",
pages = "1194--1216",
month = jul,
year = "2011",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drq012",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Fri Jul 15 12:37:42 MDT 2011",
bibsource = "http://imanum.oxfordjournals.org/content/31/3.toc;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://imajna.oxfordjournals.org/content/31/3/1194.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
onlinedate = "July 7, 2010",
}
@Article{Jaime:2011:HSA,
author = "F. J. Jaime and M. A. S{\'a}nchez and J. Hormigo and
J. Villalba and E. L. Zapata",
title = "High-Speed Algorithms and Architectures for Range
Reduction Computation",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "19",
number = "3",
pages = "512--516",
month = "????",
year = "2011",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2009.2033932",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5308221",
abstract = "Range reduction is a crucial step for accuracy in
trigonometric functions evaluation. This paper shows
and compares a set of algorithms for additive range
reduction computation and their corresponding
application-specific integrated circuit implementations
(ensuring an accuracy of one unit in the last place). A
word-serial architecture implementation has been used
as a reference for clearer comparisons. Besides, a new
table-based pipelined architecture for range reduction
has also been proposed.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=92",
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
}
@Article{Jang:2011:CTS,
author = "Won Mee Jang",
title = "Corrections to {``A Simple Upper Bound of the Gaussian
$Q$-Function with Closed-form Error Bound''}",
journal = j-IEEE-COMMUN-LET,
volume = "15",
number = "12",
pages = "1274--1274",
month = dec,
year = "2011",
CODEN = "ICLEF6",
DOI = "https://doi.org/10.1109/lcomm.2011.101911.111996",
ISSN = "1089-7798 (print), 1558-2558 (electronic)",
ISSN-L = "1089-7798",
bibdate = "Sat Dec 16 16:46:05 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/6065242/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Communications Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}
@Article{Jang:2011:SUB,
author = "Won Mee Jang",
title = "A Simple Upper Bound of the {Gaussian} {$Q$}-Function
with Closed-Form Error Bound",
journal = j-IEEE-COMMUN-LET,
volume = "15",
number = "2",
pages = "157--159",
month = feb,
year = "2011",
CODEN = "ICLEF6",
DOI = "https://doi.org/10.1109/lcomm.2011.011011.102207",
ISSN = "1089-7798 (print), 1558-2558 (electronic)",
ISSN-L = "1089-7798",
bibdate = "Sat Dec 16 16:47:28 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/5692888/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Communications Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}
@Article{Jeannerod:2011:CFP,
author = "Claude-Pierre Jeannerod and Herv{\'e} Knochel and
Christophe Monat and Guillaume Revy",
title = "Computing Floating-Point Square Roots via Bivariate
Polynomial Evaluation",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "214--227",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.152",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "In this paper, we show how to reduce the computation
of correctly rounded square roots of binary
floating-point data to the fixed-point evaluation of
some particular integer polynomials in two variables.
By designing parallel and accurate evaluation schemes
for such bivariate polynomials, we show further that
this approach allows for high instruction-level
parallelism (ILP) exposure, and thus, potentially
low-latency implementations. Then, as an illustration,
we detail a C implementation of our method in the case
of IEEE 754-2008 binary32 floating-point data (formerly
called single precision in the 1985 version of the IEEE
754 standard). This software implementation, which
assumes 32-bit unsigned integer arithmetic only, is
almost complete in the sense that it supports special
operands, subnormal numbers, and all rounding-direction
attributes, but not exception handling (that is, status
flags are not set). Finally, we have carried out
experiments with this implementation on the ST231, an
integer processor from the STMicroelectronics' ST200
family, using the ST200 family VLIW compiler. The
results obtained demonstrate the practical interest of
our approach in that context: for all
rounding-direction attributes, the generated assembly
code is optimally scheduled and has indeed low latency
(23 cycles).",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Johansson:2011:CRE,
author = "Bo G{\"o}ran Johansson",
title = "Cube root extraction in medieval mathematics",
journal = j-HIST-MATH,
volume = "38",
number = "3",
pages = "338--367",
month = aug,
year = "2011",
CODEN = "HIMADS",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Jun 26 06:21:13 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086010000546",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860",
}
@Article{Knessl:2011:EAF,
author = "Charles Knessl and Mark W. Coffey",
title = "An effective asymptotic formula for the {Stieltjes}
constants",
journal = j-MATH-COMPUT,
volume = "80",
number = "273",
pages = "379--386",
month = jan,
year = "2011",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-2010-02390-7",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Oct 13 16:46:42 MDT 2010",
bibsource = "http://www.ams.org/mcom/2011-80-273;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02390-7/home.html;
http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02390-7/S0025-5718-2010-02390-7.pdf",
abstract = "The Stieltjes constants $ \gamma_k $ appear in the
coefficients in the regular part of the Laurent
expansion of the Riemann zeta function $ \zeta (s) $
about its only pole at $ s = 1 $. We present an
asymptotic expression for $ \gamma_k $ for $ k \gg 1 $.
This form encapsulates both the leading rate of growth
and the oscillations with $k$. Furthermore, our result
is effective for computation, consistently in close
agreement (for both magnitude and sign) for even
moderate values of $k$. Comparison to some earlier work
is made.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kodama:2011:AMC,
author = "Masao Kodama",
title = "{Algorithm 912}: a Module for Calculating Cylindrical
Functions of Complex Order and Complex Argument",
journal = j-TOMS,
volume = "37",
number = "4",
pages = "47:1--47:25",
month = feb,
year = "2011",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1916461.1916471",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 1 16:05:18 MST 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "The present algorithm provides a module for
calculating the cylindrical functions $ J_\nu (z) $, $
Y_\nu (z) $, $ H_{\nu (1)}(z) $, and $ H_{\nu (2)}(z)
$, where the order $ \nu $ is complex and the complex
argument $z$ satisfies $ - \pi < \arg z \leq \pi $. The
algorithm is written in Fortran 90 and calculates the
functions using real and complex numbers of any
intrinsic data type whose kind type parameter the
user's Fortran system accepts. The methods of
calculating the functions are based on two kinds of
series expansions and numerical integration. Wronskian
tests examine the functional values computed by this
algorithm with double precision at 4,100,625
pseudorandom test points in the region $ | \Re \nu |
\leq 60 $, $ | \Im \nu | \leq 60 $, $ | \Re z| \leq 300
$, $ | \Im z| \leq 300 $.",
acknowledgement = ack-nhfb,
articleno = "47",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Kormanyos:2011:APC,
author = "Christopher Kormanyos",
title = "{Algorithm 910}: a Portable {C++} Multiple-Precision
System for Special-Function Calculations",
journal = j-TOMS,
volume = "37",
number = "4",
pages = "45:1--45:27",
month = feb,
year = "2011",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1916461.1916469",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 1 16:05:18 MST 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "This article presents a portable C++ system for
multiple precision calculations of special functions
called {\tt e\_float}. It has an extendable
architecture with a uniform C++ layer which can be used
with any suitably prepared MP type. The system
implements many high-precision special functions and
extends some of these to very large parameter ranges.
It supports calculations with 30 \ldots{} 300 decimal
digits of precision. Interoperabilities with
Microsoft's CLR, Python, and Mathematica{\reg} are
supported. The {\tt e\_float} system and its usage are
described in detail. Implementation notes, testing
results, and performance measurements are provided.",
acknowledgement = ack-nhfb,
articleno = "45",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Lopez-Benitez:2011:VAA,
author = "Miguel L{\"o}pez-Benitez and Fernando Casadevall",
title = "Versatile, Accurate, and Analytically Tractable
Approximation for the {Gaussian} {$Q$}-Function",
journal = j-IEEE-TRANS-COMM,
volume = "59",
number = "4",
pages = "917--922",
month = apr,
year = "2011",
CODEN = "IECMBT",
DOI = "https://doi.org/10.1109/tcomm.2011.012711.100105",
ISSN = "0090-6778 (print), 1558-0857 (electronic)",
ISSN-L = "0090-6778",
bibdate = "Sat Dec 16 17:01:00 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/5706433/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Communications",
}
@Article{Mortici:2011:IAF,
author = "Cristinel Mortici",
title = "Improved asymptotic formulas for the gamma function",
journal = j-COMPUT-MATH-APPL,
volume = "61",
number = "11",
pages = "3364--3369",
month = jun,
year = "2011",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/j.camwa.2011.04.036",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:47 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122111003373",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Nannarelli:2011:RCD,
author = "Alberto Nannarelli",
title = "Radix-16 Combined Division and Square Root Unit",
crossref = "Schwarz:2011:PIS",
pages = "169--176",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.30",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992122",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; sqrt(x); square root",
}
@Article{Paszkowski:2011:UMC,
author = "Stefan Paszkowski",
title = "Untypical methods of convergence acceleration",
journal = j-NUMER-ALGORITHMS,
volume = "56",
number = "2",
pages = "185--209",
month = "????",
year = "2011",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65B10 (33C20 33E05 41Axx)",
MRnumber = "MR2755669",
bibdate = "Thu Dec 01 09:27:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "convergence acceleration",
}
@Article{Pawellek:2011:GJE,
author = "Michael Pawellek",
title = "On a generalization of {Jacobi}'s elliptic functions
and the double {sine--Gordon} kink chain",
journal = j-J-MATH-PHYS,
volume = "52",
number = "11",
pages = "113701",
month = nov,
year = "2011",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.3656873",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Wed Jan 4 08:04:23 MST 2012",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v52/i11/p113701_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "4 November 2011",
pagecount = "18",
}
@Article{Pegoraro:2011:ECV,
author = "Vincent Pegoraro and Philipp Slusallek",
title = "On the Evaluation of the Complex-Valued Exponential
Integral",
journal = j-J-GRAPHICS-GPU-GAME-TOOLS,
volume = "15",
number = "3",
pages = "183--198",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1080/2151237X.2011.617177",
ISSN = "2151-237X",
bibdate = "Wed Dec 14 10:31:39 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jgraphtools.bib",
abstract = "Although its applications span a broad scope of
scientific fields ranging from applied physics to
computer graphics, the exponential integral is a
nonelementary special function available in specialized
software packages but not in standard libraries,
consequently requiring custom implementations on most
platforms. In this paper, we provide a concise and
comprehensive description of how to evaluate the
complex-valued exponential integral. We first introduce
some theoretical background on the main characteristics
of the function, and outline available third-party
proprietary implementations. We then provide an
analysis of the various known representations of the
function and present an effective algorithm allowing
the computation of results within a desired accuracy,
together with the corresponding pseudocode in order to
facilitate portability onto various systems. An
application to the calculation of the closed-form
solution to single light scattering in homogeneous
participating media illustrates the practical benefits
of the provided implementation with the hope that, in
the long term, the latter will contribute to
standardizing the availability of the complex-valued
exponential integral on graphics platforms.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/loi/ujgt20",
onlinedate = "21 Oct 2011",
}
@Article{Shi:2011:AEA,
author = "Qinghua Shi and Y. Karasawa",
title = "An Accurate and Efficient Approximation to the
{Gaussian} {$Q$}-Function and its Applications in
Performance Analysis in {Nakagami}-$m$ Fading",
journal = j-IEEE-COMMUN-LET,
volume = "15",
number = "5",
pages = "479--481",
month = may,
year = "2011",
CODEN = "ICLEF6",
DOI = "https://doi.org/10.1109/lcomm.2011.032111.102440",
ISSN = "1089-7798 (print), 1558-2558 (electronic)",
ISSN-L = "1089-7798",
bibdate = "Sat Dec 16 17:32:51 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/5740503/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Communications Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}
@Article{Smith:2011:AMP,
author = "David M. Smith",
title = "{Algorithm 911}: Multiple-Precision Exponential
Integral and Related Functions",
journal = j-TOMS,
volume = "37",
number = "4",
pages = "46:1--46:16",
month = feb,
year = "2011",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1916461.1916470",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 1 16:05:18 MST 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "This article describes a collection of Fortran-95
routines for evaluating the exponential integral
function, error function, sine and cosine integrals,
Fresnel integrals, Bessel functions, and related
mathematical special functions using the FM
multiple-precision arithmetic package.",
acknowledgement = ack-nhfb,
articleno = "46",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Srivastava:2011:ADZ,
author = "H. M. Srivastava and Jian-Rong Zhou and Zhi-Gang
Wang",
title = "Asymptotic distributions of the zeros of certain
classes of hypergeometric functions and polynomials",
journal = j-MATH-COMPUT,
volume = "80",
number = "275",
pages = "1769--1784",
month = jul,
year = "2011",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Apr 18 06:32:30 MDT 2011",
bibsource = "http://www.ams.org/mcom/2011-80-275;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02409-9/home.html;
http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02409-9/S0025-5718-2011-02409-9.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Strollo:2011:EFH,
author = "Antonio Giuseppe Maria Strollo and Davide {De Caro}
and Nicola Petra",
title = "Elementary Functions Hardware Implementation Using
Constrained Piecewise-Polynomial Approximations",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
pages = "418--432",
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.127",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:10:07 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A novel technique for designing piecewise-polynomial
interpolators for hardware implementation of elementary
functions is investigated in this paper. In the
proposed approach, the interval where the function is
approximated is subdivided in equal length segments and
two adjacent segments are grouped in a segment pair.
Suitable constraints are then imposed between the
coefficients of the two interpolating polynomials in
each segment pair. This allows reducing the total
number of stored coefficients. It is found that the
increase in the approximation error due to constraints
between polynomial coefficients can easily be overcome
by increasing the fractional bits of the coefficients.
Overall, compared with standard unconstrained
piecewise-polynomial approximation having the same
accuracy, the proposed method results in a considerable
advantage in terms of the size of the lookup table
needed to store polynomial coefficients. The calculus
of the coefficients of constrained polynomials and the
optimization of coefficients bit width is also
investigated in this paper. Results for several
elementary functions and target precision ranging from
12 to 42 bits are presented. The paper also presents
VLSI implementation results, targeting a 90 nm CMOS
technology, and using both direct and Horner
architectures for constrained degree-1, degree-2, and
degree-3 approximations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "computer arithmetic; elementary functions; min-max
approximation; polynomial approximation; VLSI
systems.",
}
@InProceedings{Tang:2011:TCT,
author = "Ping Tak Peter Tang and J. Adam Butts and Ron O. Dror
and David E. Shaw",
title = "Tight Certification Techniques for Digit-by-Rounding
Algorithms with Application to a New $ 1 / \sqrt {x} $
Design",
crossref = "Schwarz:2011:PIS",
pages = "159--168",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.29",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992121",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; reciprocal square root; rsqrt(x)",
}
@Article{Trudgian:2011:ITM,
author = "Timothy Trudgian",
title = "Improvements to {Turing}'s method",
journal = j-MATH-COMPUT,
volume = "80",
number = "276",
pages = "2259--2279",
month = oct,
year = "2011",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Oct 24 10:33:34 MDT 2011",
bibsource = "http://www.ams.org/mcom/2011-80-276;
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
note = "See \cite{Turing:1953:SCR,Lehman:1970:DZR}.",
URL = "http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02470-1/home.html;
http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02470-1/S0025-5718-2011-02470-1.pdf;
http://www.ams.org/mathscinet-getitem?mr=2813359",
abstract = "This article improves the estimate of the size of the
definite integral of {$ S(t) $}, the argument of the
Riemann zeta-function. The primary application of this
improvement is Turing's Method for the Riemann
zeta-function. Analogous improvements are given for the
arguments of Dirichlet {$L$}-functions and of Dedekind
zeta-functions.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{VanDeun:2011:RIC,
author = "Joris {Van Deun} and Lloyd N. Trefethen",
title = "A robust implementation of the
{Carath{\'e}odory-Fej{\'e}r} method for rational
approximation",
journal = j-BIT-NUM-MATH,
volume = "51",
number = "??",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-011-0331-7",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Thu Sep 29 07:17:26 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/ag2514840142707r/",
abstract = "Best rational approximations are notoriously difficult
to compute. However, the difference between the best
rational approximation to a function and its
Carath{\'e}odory-Fej{\'e}r (CF) approximation is often
so small as to be negligible in practice, while CF
approximations are far easier to compute. We present a
robust and fast implementation of this method in the
Chebfun software system and illustrate its use with
several examples. Our implementation handles both
polynomial and rational approximation and substantially
improves upon earlier published software.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Carath{\'e}odory-Fej{\'e}r approximation; Chebfun;
Near-best rational approximation",
onlinedate = "04 May 2011",
}
@Article{Veling:2011:GIG,
author = "E. J. M. Veling",
title = "The Generalized Incomplete Gamma Function as sum over
Modified {Bessel} Functions of the First Kind",
journal = j-J-COMPUT-APPL-MATH,
volume = "235",
number = "14",
pages = "4107--4116",
day = "15",
month = may,
year = "2011",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:24:28 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042711001245",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Wu:2011:NEL,
author = "Mingwei Wu and Xuzheng Lin and Pooi-Yuen Kam",
booktitle = "{2011 IEEE 73rd Vehicular Technology Conference (VTC
Spring)}",
title = "New Exponential Lower Bounds on the {Gaussian}
{$Q$}-Function via {Jensen}'s Inequality",
publisher = pub-IEEE,
address = pub-IEEE:adr,
month = may,
year = "2011",
DOI = "https://doi.org/10.1109/vetecs.2011.5956392",
bibdate = "Sat Dec 16 16:53:49 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/5956392/",
acknowledgement = ack-nhfb,
}
@Article{Yerukala:2011:ACS,
author = "R. Yerukala and N. K. Boiroju and M. K. Reddy",
title = "An Approximation to the {CDF} of Standard Normal
Distribution",
journal = "International Journal of Mathematical Archive",
volume = "2",
number = "7",
pages = "1077--1079",
month = "????",
year = "2011",
ISSN = "2229-5046",
ISSN-L = "2229-5046",
bibdate = "Sat Dec 16 18:03:12 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ijma.info/index.php/ijma/article/view/393",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Math. Arch.",
}
@Article{Zaghloul:2011:ACF,
author = "Mofreh R. Zaghloul and Ahmed N. Ali",
title = "{Algorithm 916}: Computing the {Faddeyeva} and {Voigt}
functions",
journal = j-TOMS,
volume = "38",
number = "2",
pages = "15:1--15:22",
month = dec,
year = "2011",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2049673.2049679",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Dec 30 17:43:07 MST 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See remark \cite{Zaghloul:2016:RAC}.",
abstract = "We present a MATLAB function for the numerical
evaluation of the Faddeyeva function $ w(z) $. The
function is based on a newly developed accurate
algorithm. In addition to its higher accuracy, the
software provides a flexible accuracy vs efficiency
trade-off through a controlling parameter that may be
used to reduce accuracy and computational time and vice
versa. Verification of the flexibility, reliability,
and superior accuracy of the algorithm is provided
through comparison with standard algorithms available
in other libraries and software packages.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Zhou:2011:ADZ,
author = "Jian-Rong Zhou and Yu-Qiu Zhao",
title = "Asymptotic distributions of the zeros of certain
classes of {Gauss} hypergeometric polynomials",
journal = j-APPL-MATH-COMP,
volume = "218",
number = "3",
pages = "1153--1159",
day = "1",
month = oct,
year = "2011",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2011.05.106",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Oct 25 09:02:50 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Special Issue in Honour of Hari M. Srivastava on his
70th birth anniversary.",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300311007892",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Adlaj:2012:EFP,
author = "Semjon Adlaj",
title = "An Eloquent Formula for the Perimeter of an Ellipse",
journal = j-NAMS,
volume = "59",
number = "8",
pages = "1094--1099",
month = sep,
year = "2012",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Wed Sep 05 09:12:25 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/notices/201208/rtx120801094p.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
keywords = "complete elliptic integral; pendulum; perimeter of
ellipse",
remark = "This paper introduces several arithmetic-geometric
mean (AGM) algorithms for fast and practical
computation of complete elliptic integrals.",
}
@Article{Al-Mohy:2012:MAB,
author = "Awad H. Al-Mohy",
title = "A more accurate {Briggs} method for the logarithm",
journal = j-NUMER-ALGORITHMS,
volume = "59",
number = "3",
pages = "393--402",
month = mar,
year = "2012",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-011-9496-z",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Fri Oct 26 08:07:24 MDT 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=59&issue=3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://www.springerlink.com/content/4110609h521kg66m/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=59&issue=3&spage=393",
abstract = "A new approach for computing an expression of the form
$ a^{1 / 2^k} - 1 $ is presented that avoids the danger
of subtractive cancellation in floating point
arithmetic, where $a$ is a complex number not belonging
to the closed negative real axis and $k$ is a
nonnegative integer. We also derive a condition number
for the problem. The algorithm therefore allows highly
accurate numerical calculation of $ \log (a) $ using
Briggs' method.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Briggs' method; Briggs' tables; Inverse scaling and
squaring method; Logarithm function",
}
@Misc{Anonymous:2012:FIS,
author = "Anonymous",
title = "Fast inverse square root",
howpublished = "Wikipedia article.",
day = "20",
month = mar,
year = "2012",
bibdate = "Mon Apr 02 17:03:18 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This article describes an algorithm for the inverse
square root. The only novel feature is use of two
IEEE-754 specific magic constants for 32-bit and 64-bit
binary arithmetic that allow obtaining fast starting
estimates for Newton--Raphson iterations by
manipulating the floating-point representations as
integers. The code fails to handle signed zero,
Infinity, and NaN arguments, uses too few iterations,
and does not adjust for rounding errors to obtain
correctly-rounded results. See \cite{Blinn:1997:JBC}.",
URL = "http://en.wikipedia.org/wiki/Fast_inverse_square_root",
acknowledgement = ack-nhfb,
}
@Article{Bailey:2012:AIS,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Ancient {Indian} Square Roots: An Exercise in Forensic
Paleo-Mathematics",
journal = j-AMER-MATH-MONTHLY,
volume = "119",
number = "8",
pages = "646--657",
month = oct,
year = "2012",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.119.08.646",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Thu Nov 8 07:34:21 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.119.08.646.pdf",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@InProceedings{Brisebarre:2012:MPK,
author = "Nicolas Brisebarre and Milo D. Ercegovac and
Jean-Michel Muller",
editor = "{IEEE}",
booktitle = "{2012 IEEE 23rd International Conference on
Application-Specific Systems, Architectures and
Processors, 9--11 July 2012. Delft, The Netherlands}",
title = "{$ (M, p, k) $}-Friendly Points: a Table-Based Method
for Trigonometric Function Evaluation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "46--52",
year = "2012",
DOI = "https://doi.org/10.1109/ASAP.2012.17",
ISBN = "0-7695-4768-0",
ISBN-13 = "978-0-7695-4768-8",
ISSN = "1063-6862",
ISSN-L = "1063-6862",
bibdate = "Fri Sep 29 10:49:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Chen:2012:SIM,
author = "Chao-Ping Chen and Necdet Batir",
title = "Some inequalities and monotonicity properties
associated with the gamma and psi functions",
journal = j-APPL-MATH-COMP,
volume = "218",
number = "17",
pages = "8217--8225",
day = "1",
month = may,
year = "2012",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2012.02.007",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu Apr 5 06:00:26 MDT 2012",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300312001257",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
remark = "New bounds on the gamma function in terms of the psi
function, and a new estimate for the error in
Stirling's formula, $ \Gamma (x + 1) \approx x^x e^{-x}
\sqrt {2 \pi x} $.",
}
@Article{Cohl:2012:TEF,
author = "Howard S. Cohl",
title = "Table Errata to {``Formulas and theorems for the
special functions of mathematical physics'' by W.
Magnus, F. Oberhettinger \& R. P. Soni (1966)}",
journal = j-MATH-COMPUT,
volume = "81",
number = "280",
pages = "2251--2251",
month = oct,
year = "2012",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Nov 6 09:52:53 MST 2012",
bibsource = "http://www.ams.org/mcom/2012-81-280;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
note = "See \cite{Magnus:1966:FTS}.",
URL = "http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02612-3;
http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02612-3/S0025-5718-2012-02612-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Report of sign error in a sum of two Gauss
hypergeometric functions for Ferrers function of the
second kind.",
}
@Article{Cote:2012:CTL,
author = "F. D. C{\^o}t{\'e} and I. N. Psaromiligkos and W. J.
Gross",
title = "A {Chernoff}-type lower bound for the {Gaussian}
{$Q$}-function",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "??--??",
year = "2012",
bibdate = "Sat Dec 16 16:04:00 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://arxiv.org/abs/1202.6483",
acknowledgement = ack-nhfb,
pagecount = "3",
}
@Book{Crandall:2012:ARS,
author = "Richard E. Crandall",
title = "Algorithmic Reflections: Selected Works",
publisher = "PSI Press",
address = "Portland, OR, USA",
edition = "First Perfectly Scientific Press paperback",
pages = "410",
year = "2012",
ISBN = "1-935638-19-X",
ISBN-13 = "978-1-935638-19-3",
LCCN = "QA958 .C736 2012",
bibdate = "Fri Jun 30 11:14:26 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "1947--2012",
subject = "Algorithms; Algorithmes",
tableofcontents = "Part I: Number theory \\
On the $ 3 x + 1$ problem \\
On a conjecture of Crandall concerning the $ q n + 1$
problem \\
A search for Wieferich and Wilson primes \\
Parallelization of Pollard-rho factorization \\
Three new factors of Fermat numbers \\
Random generators and normal numbers \\
The googol-th bit of the Erd{\H{o}}s--Borwein constant
\\
Part II: Analytical algorithms \\
Fast evaluation of multiple zeta sums \\
On the Khintchine Constant \\
On the dynamics of certain recurrence relations \\
Effective Laguerre asymptotics \\
Theory of ROOF walks \\
Unified algorithms for polylogarithm, $L$-series, and
zeta variants \\
Part III: Physics, biology, epidemics, and physiology
\\
The potential within a crystal lattice \\
The fractal character of space-time epidemics \\
Mathematical signatures as tools for visual dysfunction
\\
NLA system for medical-data classification \\
On the fractal distribution of brain synapses",
}
@Misc{Crandall:2012:UAP,
author = "R. E. Crandall",
title = "Unified algorithms for polylogarithm, {$L$}-series,
and zeta variants",
type = "Preprint",
pages = "53",
year = "2012",
bibdate = "Tue Sep 09 11:50:04 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Crandall:2012:ARS}.",
URL = "http://www.perfscipress.com/papers/universalTOC25.pdf;
https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/universalTOC25.pdf",
abstract = "We describe a general computational scheme for
evaluation of a wide class of number-theoretical
functions. We avoid asymptotic expansions in favor of
manifestly convergent series that lend themselves
naturally to rigorous error bounds. By employing three
fundamental series algorithms we achieve a unified
strategy to compute the various functions via parameter
selection. This work amounts to a compendium of methods
to establish extreme-precision results as typify modern
experimental mathematics. A fortuitous byproduct of
this unified approach is automatic analytic
continuation over complex parameters. Another byproduct
is a host of converging series for various fundamental
constants.",
acknowledgement = ack-nhfb,
remark-1 = "In memory of gentle colleague Jerry Keiper
(1953--1995).",
remark-2 = "Host in URL field no longer exists; cited in
\cite{Coffey:2014:SRR}.",
}
@Article{DeSchrijver:2012:DPRa,
author = "Steven K. {De Schrijver} and El-Houssaine Aghezzaf and
Hendrik Vanmaele",
title = "Double precision rational approximation algorithm for
the inverse standard normal first order loss function",
journal = j-APPL-MATH-COMP,
volume = "219",
number = "3",
pages = "1375--1382",
day = "15",
month = oct,
year = "2012",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2012.07.011",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu Oct 25 09:05:16 MDT 2012",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300312007114",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{DeSchrijver:2012:DPRb,
author = "Steven K. {De Schrijver} and El-Houssaine Aghezzaf and
Hendrik Vanmaele",
title = "Double precision rational approximation algorithms for
the standard normal first and second order loss
functions",
journal = j-APPL-MATH-COMP,
volume = "219",
number = "4",
pages = "2320--2330",
day = "1",
month = nov,
year = "2012",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2012.08.012",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu Oct 25 09:05:21 MDT 2012",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300312008041",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Develi:2012:NAB,
author = "I. Develi",
title = "A new approximation based on the differential
evolution algorithm for the {Gaussian} {$Q$}-function",
journal = "Int. J. Innov. Comput. Inf. Control",
volume = "8",
number = "10(B)",
pages = "7095--7102",
month = "????",
year = "2012",
bibdate = "Sat Dec 16 16:14:27 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/content/pdf/10.1007/s10957-012-0217-0.pdf;
http://www.ijicic.org/ijicic-11-08039.pdf",
acknowledgement = ack-nhfb,
}
@Article{Fukushima:2012:SES,
author = "Toshio Fukushima",
title = "Series expansions of symmetric elliptic integrals",
journal = j-MATH-COMPUT,
volume = "81",
number = "278",
pages = "957--990",
month = "",
year = "2012",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sat Feb 4 09:28:39 MST 2012",
bibsource = "http://www.ams.org/mcom/2012-81-278;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02531-7;
http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02531-7/S0025-5718-2011-02531-7.pdf",
abstract = "Based on general discussion of series expansions of
Carlson's symmetric elliptic integrals, we developed
fifteen kinds of them including eleven new ones by
utilizing the symmetric nature of the integrals. Thanks
to the special addition formulas of the integrals, we
also obtained their complementary series expansions. By
considering the balance between the speed of
convergence and the amount of computational labor, we
chose four of them as the best series expansions.
Practical evaluation of the integrals is conducted by
the most suitable one among these four series
expansions. Its selection rule was analytically
specified in terms of the numerical values of given
parameters. As a by-product, we obtained an efficient
asymptotic expansion of the integrals around their
logarithmic singularities. Numerical experiments
confirmed the effectiveness of these new series
expansions.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gaudreau:2012:CTP,
author = "Philippe Gaudreau and Richard M. Slevinsky and Hassan
Safouhi",
title = "Computation of Tail Probabilities via Extrapolation
Methods and Connection with Rational and {Pad{\'e}}
Approximants",
journal = j-SIAM-J-SCI-COMP,
volume = "34",
number = "1",
pages = "B65--B85",
month = jan,
year = "2012",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/100803778",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Sat Dec 16 16:33:00 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "http://epubs.siam.org/doi/abs/10.1137/100803778",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Gil:2012:CRZ,
author = "Amparo Gil and Javier Segura",
title = "Computing the real zeros of cylinder functions and the
roots of the equation {$ x C^\prime_\nu (x) + \gamma
C_\nu (x) = 0 $}",
journal = j-COMPUT-MATH-APPL,
volume = "64",
number = "1",
pages = "11--21",
month = jul,
year = "2012",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/j.camwa.2012.02.032",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:51:09 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122112001460",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From the abstract: ``Fast methods to compute the zeros
of general cylinder functions $ C_\nu (x) = \cos \alpha
J_\nu (x) - \sin \alpha Y_\nu (x) C_\nu (x) = \cos
\alpha J_\nu (x) - \sin \alpha Y_\nu (x) $ in real
intervals can be obtained from an approximate
integration of the second order ODE satisfied by these
functions, leading to fourth order methods with global
convergence.''",
}
@Article{Gil:2012:EAA,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Efficient and Accurate Algorithms for the Computation
and Inversion of the Incomplete Gamma Function Ratios",
journal = j-SIAM-J-SCI-COMP,
volume = "34",
number = "6",
pages = "A2965--A2981",
month = "????",
year = "2012",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/120872553",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Jul 19 07:43:33 MDT 2013",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/34/6;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2012",
}
@Article{Gil:2012:IAF,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "An improved algorithm and a {Fortran 90} module for
computing the conical function $ p^m_{1 / 2 + i \tau
}(x) $",
journal = j-COMP-PHYS-COMM,
volume = "183",
number = "3",
pages = "794--799",
month = mar,
year = "2012",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2011.11.025",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 11 10:11:02 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465511003936",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Jablonski:2012:EAC,
author = "A. Jablonski",
title = "An effective algorithm for calculating the
{Chandrasekhar} function",
journal = j-COMP-PHYS-COMM,
volume = "183",
number = "8",
pages = "1773--1782",
month = aug,
year = "2012",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2012.02.022",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Tue Apr 24 06:33:31 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465512000847",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InCollection{Jargstorff:2012:AEF,
author = "Frank Jargstorff",
title = "Approximating the {{\tt erfinv}} Function",
crossref = "Hwu:2012:GCG",
chapter = "10",
pages = "??--??",
year = "2012",
bibdate = "Sat Feb 08 19:05:23 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Jentschura:2012:NCB,
author = "U. D. Jentschura and E. L{\"o}tstedt",
title = "Numerical calculation of {Bessel}, {Hankel} and {Airy}
functions",
journal = j-COMP-PHYS-COMM,
volume = "183",
number = "3",
pages = "506--519",
month = mar,
year = "2012",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2011.11.010",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 11 10:11:02 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465511003729",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Misc{Johnson:2012:FPF,
author = "Steven G. Johnson",
title = "{Faddeeva} package, a free\slash open-source {C++}
Software to compute the various error functions of
arbitrary complex arguments",
howpublished = "Web site",
year = "2012",
bibdate = "Sat Feb 17 14:11:45 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ab-initio.mit.edu/wiki/index.php/Faddeeva_Package",
acknowledgement = ack-nhfb,
keywords = "$\erf(x) (the error function); $\erfc() (complementary
error function = $1 - \erf(z)$); $\erfcx() (scaled
complementary error function $e^{z^2} \erfc(z) = w(i
z)$); $\erfi(z) (imaginary error function = $-i \erf(i
z)$); Dawson ($((\sqrt \pi)/2) e^{-z^2} \erfi(z)$); w
(Faddeeva function $w(z) = e^{-z^2} \erfc(-i z)$)",
}
@InProceedings{Phong:2012:EAG,
author = "Dao Ngoc Phong and Nguyen Quang Uy and Nguyen Xuan
Hoai and R. I. (Bob) McKay",
editor = "????",
booktitle = "Proceedings of the 2012 {IEEE} Congress on
Evolutionary Computation, June 10--15, 2012 ---
Brisbane, {QLD}, Australia",
title = "Evolving approximations for the {Gaussian}
{$Q$}-function by genetic programming with semantic
based crossover",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2012",
DOI = "https://doi.org/10.1109/CEC.2012.6256588",
bibdate = "Sat Dec 16 16:08:39 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ieeexplore.ieee.org/document/6256588/",
acknowledgement = ack-nhfb,
}
@Article{Poelke:2012:DCC,
author = "Konstantin Poelke and Konrad Polthier",
title = "Domain Coloring of Complex Functions: An
Implementation-Oriented Introduction",
journal = j-IEEE-CGA,
volume = "32",
number = "5",
pages = "90--97",
month = sep # "\slash " # oct,
year = "2012",
CODEN = "ICGADZ",
DOI = "https://doi.org/10.1109/MCG.2012.100",
ISSN = "0272-1716 (print), 1558-1756 (electronic)",
ISSN-L = "0272-1716",
bibdate = "Mon Oct 22 06:56:23 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeecga.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Computer Graphics and Applications",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/cga",
}
@Article{Rzadkowski:2012:SEE,
author = "Grzegorz Rz{\k{a}}dkowski",
title = "On some expansions for the {Euler} Gamma function and
the {Riemann} Zeta function",
journal = j-J-COMPUT-APPL-MATH,
volume = "236",
number = "15",
pages = "3710--3719",
month = sep,
year = "2012",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:24:35 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042711004663",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Book{Srivastava:2012:ZZF,
author = "H. M. Srivastava and Choi Junesang",
title = "Zeta and $q$-Zeta functions and associated series and
integrals",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "xvi + 657",
year = "2012",
ISBN = "0-12-385218-8",
ISBN-13 = "978-0-12-385218-2",
LCCN = "QA351 .S745 2012",
bibdate = "Wed Jun 10 16:19:46 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Elsevier Insights",
URL = "http://www.sciencedirect.com/science/book/9780123852182",
acknowledgement = ack-nhfb,
remark = "Revised, enlarged, and updated version of
\cite{Srivastava:2001:SAZ}.",
subject = "Functions, Zeta",
tableofcontents = "1. Introduction and preliminaries \\
2. The zeta and related functions \\
3. Series involving zeta functions \\
4. Evaluations and series representations \\
5. Determinants of the laplacians \\
6. q-Extensions of some special functions and
polynomials \\
7. Miscellaneous results",
}
@Article{Vazquez-Leal:2012:HAS,
author = "Hector Vazquez-Leal and Roberto Castaneda-Sheissa and
Uriel Filobello-Nino and Arturo Sarmiento-Reyes and
Jesus Sanchez Orea",
title = "High Accurate Simple Approximation of Normal
Distribution Integral",
journal = "Mathematical Problems in Engineering",
volume = "2012",
pages = "1--22",
year = "2012",
DOI = "https://doi.org/10.1155/2012/124029",
ISSN = "1024-123X (print), 1563-5147 (electronic)",
bibdate = "Sat Dec 16 17:54:09 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.hindawi.com/journals/mpe/2012/124029/",
acknowledgement = ack-nhfb,
}
@Article{Veberic:2012:LFA,
author = "Darko Veberi{\v{c}}",
title = "{Lambert} {$W$} function for applications in physics",
journal = j-COMP-PHYS-COMM,
volume = "183",
number = "12",
pages = "2622--2628",
month = dec,
year = "2012",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2012.07.008",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Tue Aug 28 17:36:53 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465512002366",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Willis:2012:AGH,
author = "Joshua L. Willis",
title = "Acceleration of generalized hypergeometric functions
through precise remainder asymptotics",
journal = j-NUMER-ALGORITHMS,
volume = "59",
number = "??",
pages = "??--??",
month = "????",
year = "2012",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-011-9499-9",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Nov 30 06:42:07 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arxiv.org/abs/1102.3003;
http://www.springerlink.com/content/k413064448600815/",
abstract = "We express the asymptotics of the remainders of the
partial sums $ \{ s_n \} $ of the generalized
hypergeometric function through an inverse power series
$ z^n n^\lambda \sum c_k / n_k $, where the exponent $
\lambda $ and the asymptotic coefficients $ \{ c_k \} $
may be recursively computed to any desired order from
the hypergeometric parameters and argument. From this
we derive a new series acceleration technique that can
be applied to any such function, even with complex
parameters and at the branch point $ z = 1 $. For
moderate parameters (up to approximately ten) a C
implementation at fixed precision is very effective at
computing these functions; for larger parameters an
implementation in higher than machine precision would
be needed. Even for larger parameters, however, our C
implementation is able to correctly determine whether
or not it has converged; and when it converges, its
estimate of its error is accurate.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Generalized hypergeometric functions; Recurrence
asymptotics; Series acceleration",
}
@InCollection{Arfken:2013:BF,
author = "George B. (George Brown) Arfken and Hans-J{\"u}rgen
Weber and Frank E. Harris",
title = "{Bessel} Functions",
crossref = "Arfken:2013:MMP",
chapter = "14",
pages = "643--713",
year = "2013",
bibdate = "Thu Dec 5 05:54:14 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B9780123846549000141",
acknowledgement = ack-nhfb,
}
@InCollection{Arfken:2013:GFb,
author = "George B. (George Brown) Arfken and Hans-J{\"u}rgen
Weber and Frank E. Harris",
title = "{Gamma} Function",
crossref = "Arfken:2013:MMP",
chapter = "13",
pages = "599--641",
year = "2013",
bibdate = "Thu Dec 5 05:54:14 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B978012384654900013X",
acknowledgement = ack-nhfb,
}
@Article{Babusci:2013:SME,
author = "D. Babusci and G. Dattoli and K. G{\'o}rska and K. A.
Penson",
title = "Symbolic methods for the evaluation of sum rules of
{Bessel} functions",
journal = j-J-MATH-PHYS,
volume = "54",
number = "7",
pages = "073501",
month = jul,
year = "2013",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.4812325",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Wed Feb 12 12:24:18 MST 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Beals:2013:MFG,
author = "Richard Beals and Jacek Szmigielski",
title = "{Meijer} {$G$}-functions: a gentle introduction",
journal = j-NAMS,
volume = "60",
number = "7",
pages = "866--872",
month = aug,
year = "2013",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti1016",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "33C60",
MRnumber = "3086637",
MRreviewer = "Gianni Pagnini",
bibdate = "Thu Aug 15 07:17:02 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nams2010.bib",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
}
@Article{Booker:2013:BAB,
author = "Andrew R. Booker and Andreas Str{\"o}mbergsson and
Holger Then",
title = "Bounds and algorithms for the {$K$-Bessel} function of
imaginary order",
journal = j-LMS-J-COMPUT-MATH,
volume = "16",
pages = "78--108",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1112/S1461157013000028",
ISSN = "1461-1570",
ISSN-L = "1461-1570",
MRclass = "26D07; 33C10; 33F05; 34D05; 41A58 (primary); 41A80;
65D05; 40H05; 26B99 (secondary)",
bibdate = "Sat Jun 22 11:29:28 MDT 2013",
bibsource = "http://journals.cambridge.org/action/displayJournal?jid=JCM;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
acknowledgement = ack-nhfb,
ajournal = "LMS J. Comput. Math.",
fjournal = "LMS Journal of Computation and Mathematics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=JCM",
onlinedate = "10 April 2013",
}
@InProceedings{Brent:2013:FCB,
author = "Richard P. Brent and David Harvey",
editor = "D. H. Bailey and H. H. Bauschke and P. Borwein and F.
Garvan and M. Th{\'e}ra and J. D. Vanderwerff and H.
Wolkowicz",
booktitle = "Computational and Analytical Mathematics",
title = "Fast Computation of {Bernoulli}, Tangent and Secant
Numbers",
volume = "50",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xv + 701",
pages = "127--142",
year = "2013",
DOI = "https://doi.org/10.1007/978-1-4614-7621-4_8",
ISBN = "1-4614-7620-8, 1-4614-7621-6 (e-book)",
ISBN-13 = "978-1-4614-7620-7, 978-1-4614-7621-4 (e-book)",
ISSN = "2194-1009",
bibdate = "Sat Jun 8 08:38:45 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Chen:2013:CFE,
author = "Chao-Ping Chen",
title = "Continued fraction estimates for the psi function",
journal = j-APPL-MATH-COMP,
volume = "219",
number = "19",
pages = "9865--9871",
day = "1",
month = jun,
year = "2013",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2013.03.134",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon May 20 19:05:31 MDT 2013",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300313003962",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Chen:2013:LIA,
author = "Chao-Ping Chen and Cristinel Mortici",
title = "Limits and inequalities associated with the
{Euler--Mascheroni} constant",
journal = j-APPL-MATH-COMP,
volume = "219",
number = "18",
pages = "9755--9761",
day = "15",
month = may,
year = "2013",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2013.03.089",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon May 20 19:05:27 MDT 2013",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300313003500",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "asymptotic expansion; Euler-Mascheroni constant;
harmonic numbers; inequality; polygamma functions; psi
function",
}
@Article{Chen:2013:UTS,
author = "Chao-Ping Chen",
title = "Unified treatment of several asymptotic formulas for
the gamma function",
journal = j-NUMER-ALGORITHMS,
volume = "64",
number = "2",
pages = "311--319",
month = oct,
year = "2013",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-012-9667-6",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 2 18:18:08 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=64&issue=2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-012-9667-6",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@InProceedings{Chevillard:2013:MPE,
author = "Sylvain Chevillard and Marc Mezzarobba",
title = "Multiple-Precision Evaluation of the {Airy} {Ai}
Function with Reduced Cancellation",
crossref = "IEEE:2013:PIS",
pages = "175--182",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.33",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Accuracy; Airy Ai function; algorithm; Algorithm
design and analysis; Approximation algorithms;
Approximation methods; arbitrary precision; ARITH-21;
asymptotics; cancellation reduction; classical Miller
algorithm; correct rounding; differential equations;
Equations; error bounds; ill-conditioned three-term
recurrence; linear ordinary differential equation;
Miller method; multiple-precision evaluation;
nonnegative Taylor expansions; numerical evaluation;
series (mathematics); series expansion; Shape; Special
functions; Taylor coefficients; Taylor series",
}
@Article{deDinechin:2013:FPT,
author = "Florent de Dinechin and Matei Istoan and Guillaume
Sergent",
title = "Fixed-point trigonometric functions on {FPGAs}",
journal = j-COMP-ARCH-NEWS,
volume = "41",
number = "5",
pages = "83--88",
month = dec,
year = "2013",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2641361.2641375",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Mon Aug 18 17:12:43 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Three approaches for computing sines and cosines on
FPGAs are studied in this paper, with a focus of
high-throughput pipelined architecture, and
state-of-the-art implementation techniques. The first
approach is the classical CORDIC iteration, for which
we suggest a reduced iteration technique and fine
optimizations in datapath width and latency. The second
is an ad-hoc architecture specifically designed around
trigonometric identities. The third uses a generic
table- and DSP-based polynomial approximator. These
three architectures are implemented and compared in the
FloPoCo framework.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Develi:2013:HAA,
author = "I. Develi and A. Basturk",
title = "Highly Accurate Analytic Approximation to the
{Gaussian} {$Q$}-function Based on the Use of Nonlinear
Least Squares Optimization Algorithm",
journal = j-J-OPT-THEORY-APPL,
volume = "159",
number = "1",
pages = "183--191",
day = "01",
month = oct,
year = "2013",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-012-0217-0",
ISSN = "1573-2878",
ISSN-L = "0022-3239",
bibdate = "Sat Dec 16 16:18:18 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://link.springer.com/article/10.1007/s10957-012-0217-0",
acknowledgement = ack-nhfb,
ajournal = "J. Optim. Theory Appl.",
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
}
@Article{Erricolo:2013:AFS,
author = "Danilo Erricolo and Giuseppe Carluccio",
title = "{Algorithm 934}: {Fortran 90} subroutines to compute
{Mathieu} functions for complex values of the
parameter",
journal = j-TOMS,
volume = "40",
number = "1",
pages = "8:1--8:19",
month = sep,
year = "2013",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2513109.2513117",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 30 16:05:58 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Software to compute angular and radial Mathieu
functions is provided in the case that the parameter q
is a complex variable and the independent variable x is
real. After an introduction on the notation and the
definitions of Mathieu functions and their related
properties, Fortran 90 subroutines to compute them are
described and validated with some comparisons. A sample
application is also provided.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Feng:2013:TFA,
author = "Lei Feng and Weiping Wang",
title = "Two families of approximations for the gamma
function",
journal = j-NUMER-ALGORITHMS,
volume = "64",
number = "3",
pages = "403--416",
month = nov,
year = "2013",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-012-9671-x",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 2 18:18:12 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=64&issue=3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-012-9671-x",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Fukushima:2013:PFC,
author = "Toshio Fukushima",
title = "Precise and fast computation of {Jacobian} elliptic
functions by conditional duplication",
journal = j-NUM-MATH,
volume = "123",
number = "4",
pages = "585--605",
month = apr,
year = "2013",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-012-0498-0",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Apr 27 13:30:29 MDT 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=123&issue=4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
URL = "http://link.springer.com/article/10.1007/s00211-012-0498-0",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Fukushima:2013:RCD,
author = "Toshio Fukushima",
title = "Recursive computation of derivatives of elliptic
functions and of incomplete elliptic integrals",
journal = j-APPL-MATH-COMP,
volume = "221",
number = "??",
pages = "21--31",
day = "15",
month = sep,
year = "2013",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Dec 2 12:34:28 MST 2013",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300313006152",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Gonzalez-Morales:2013:NII,
author = "M. J. Gonz{\'a}lez-Morales and R. Mahillo-Isla and C.
Dehesa-Mart{\'\i}nez",
title = "A new integral identity involving the elliptic
integral {$ E(m) $}",
journal = j-APPL-MATH-COMP,
volume = "221",
number = "??",
pages = "568--570",
day = "15",
month = sep,
year = "2013",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Dec 2 12:34:28 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300313007303",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Hale:2013:FAC,
author = "Nicholas Hale and Alex Townsend",
title = "Fast and Accurate Computation of {Gauss--Legendre} and
{Gauss--Jacobi} Quadrature Nodes and Weights",
journal = j-SIAM-J-SCI-COMP,
volume = "35",
number = "2",
pages = "A652--A674",
month = "????",
year = "2013",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/120889873",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Jul 19 07:43:46 MDT 2013",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2013",
}
@Article{Huang:2013:NNE,
author = "Zhi-Wei Huang and Jueping Liu",
title = "{NumExp}: Numerical epsilon expansion of
hypergeometric functions",
journal = j-COMP-PHYS-COMM,
volume = "184",
number = "8",
pages = "1973--1980",
month = aug,
year = "2013",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2013.03.016",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Wed May 15 07:02:08 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465513001136",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Jablonski:2013:IAC,
author = "A. Jablonski",
title = "Improved algorithm for calculating the {Chandrasekhar}
function",
journal = j-COMP-PHYS-COMM,
volume = "184",
number = "2",
pages = "440--442",
month = feb,
year = "2013",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2012.08.020",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Nov 2 11:55:56 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S001046551200286X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Jiang:2013:AFE,
author = "Hao Jiang and Stef Graillat and Roberto Barrio",
title = "Accurate and Fast Evaluation of Elementary Symmetric
Functions",
crossref = "IEEE:2013:PIS",
pages = "183--190",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.18",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Accuracy; accurate algorithm; Algorithm design and
analysis; ARITH-21; compensated algorithm;
double-double library; elementary symmetric functions;
error-free transformation; error-free transformations;
floating point arithmetic; floating-point arithmetic;
forward roundoff error bound; Libraries; mathematics
computing; MATLAB poly function; Polynomials;
psychological measurement; Rasch model; roundoff error;
Roundoff errors; running error bound; shaper bound;
summation algorithm; Vectors",
}
@Article{Lopez:2013:NSE,
author = "Jos{\'e} L. L{\'o}pez and Nico M. Temme",
title = "New series expansions of the {Gauss} hypergeometric
function",
journal = j-ADV-COMPUT-MATH,
volume = "39",
number = "2",
pages = "349--365",
month = aug,
year = "2013",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/s10444-012-9283-y",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
MRclass = "33C05 (33F05 41A58 65D20)",
MRnumber = "3082518",
MRreviewer = "Jochen Denzler",
bibdate = "Sat Feb 3 18:23:06 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/s10444-012-9283-y",
acknowledgement = ack-nhfb,
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
keywords = "Gauss hypergeometric function $_2F_1(a,b,c; z)$",
remark = "Improvement on
\cite{Buhring:1987:ACH,Buhring:1987:BUA} and \cite[\S
2.3]{Gil:2007:NMS} by removal of points excluded from
the domain of convergence.",
}
@Article{Low:2013:MET,
author = "Joshua Yung Lih Low and Ching Chuen Jong",
title = "A Memory-Efficient Tables-and-Additions Method for
Accurate Computation of Elementary Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "5",
pages = "858--872",
month = may,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.43",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Apr 30 12:26:22 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Mastin:2013:LQB,
author = "Andrew Mastin and Patrick Jaillet",
title = "Log-quadratic bounds for the {Gaussian}
{$Q$}-function",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "9",
month = apr,
year = "2013",
bibdate = "Sat Dec 16 17:09:03 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arxiv.org/abs/1304.2488",
acknowledgement = ack-nhfb,
}
@Article{Nemes:2013:EBE,
author = "Gerg{\H{o}} Nemes",
title = "Error bounds and exponential improvement for
{Hermite}'s asymptotic expansion for the gamma
function",
journal = "Applicable Analysis and Discrete Mathematics ",
volume = "7",
number = "1",
pages = "161--179",
month = apr,
year = "2013",
DOI = "https://doi.org/10.2298/AADM130124002N",
ISSN = "1452-8630 (print), 2406-100X (electronic)",
ISSN-L = "1452-8630",
MRclass = "41A60 (33B15 41A80)",
MRnumber = "3086174",
MRreviewer = "Junesang Choi",
bibdate = "Fri Oct 18 16:34:50 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://doi.org/10.2298/AADM130124002N",
acknowledgement = ack-nhfb,
ajournal = "Appl. Anal. Discrete Math.",
fjournal = "Applicable Analysis and Discrete Mathematics",
journal-URL = "https://pefmath.etf.bg.ac.rs/",
}
@Article{Neta:2013:FHL,
author = "Beny Neta and Melvin Scott",
title = "On a family of {Halley}-like methods to find simple
roots of nonlinear equations",
journal = j-APPL-MATH-COMP,
volume = "219",
number = "15",
pages = "7940--7944",
day = "1",
month = apr,
year = "2013",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2013.02.035",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon May 6 18:04:12 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300313001574",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
keywords = "basin of attraction; Euler--Chebyshev method; Halley
method; nonlinear equations; simple roots",
}
@Book{Osipov:2013:PSW,
author = "Andrei Osipov",
title = "Prolate Spheroidal Wave Functions of Order Zero:
Mathematical Tools for Bandlimited Approximation",
publisher = pub-SV,
address = pub-SV:adr,
pages = "????",
year = "2013",
ISBN = "1-4614-8258-5",
ISBN-13 = "978-1-4614-8258-1",
LCCN = "????",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy1315/2013945079-b.html;
http://www.loc.gov/catdir/enhancements/fy1315/2013945079-d.html;
http://www.loc.gov/catdir/enhancements/fy1315/2013945079-t.html",
acknowledgement = ack-nhfb,
tableofcontents = "Introduction \\
Mathematical and Numerical Preliminaries \\
Overview \\
Analysis of the Differential Operator \\
Analysis of the Integral Operator \\
Rational Approximations of PSWFs \\
Miscellaneous Properties of PSWFs \\
Asymptotic Analysis of PSWFs \\
Quadrature Rules and Interpolation via PSWFs \\
Numerical Algorithms",
}
@Article{Russinoff:2013:CFV,
author = "David M. Russinoff",
title = "Computation and Formal Verification of {SRT} Quotient
and Square Root Digit Selection Tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "5",
pages = "900--913",
month = may,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.40",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Apr 30 12:26:22 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Szmytkowski:2013:EBT,
author = "Rados{\l}aw Szmytkowski",
title = "Erratum to {{\booktitle{Formulas and Theorems for the
Special Functions of Mathematical Physics}} by W.
Magnus, F. Oberhettinger, R. P. Soni}",
journal = j-MATH-COMPUT,
volume = "82",
number = "283",
pages = "1709--1710",
month = "????",
year = "2013",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Apr 30 16:18:02 MDT 2013",
bibsource = "http://www.ams.org/mcom/2013-82-283;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2013-02671-3;
http://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2013-02671-3/S0025-5718-2013-02671-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Thompson:2013:AIG,
author = "Ian Thompson",
title = "{Algorithm 926}: Incomplete {Gamma} Functions with
Negative Arguments",
journal = j-TOMS,
volume = "39",
number = "2",
pages = "14:1--14:9",
month = feb,
year = "2013",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2427023.2427031",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 20 16:46:13 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "An algorithm for accurately computing the lower
incomplete gamma function $ \gamma (a, t) $ in the case
where $ a = n + 1 / 2 $, $ n \in Z $ and $ t < 0 $ is
described. Series expansions and analytic continuation
are employed to compute the function for certain
critical values of $n$, and these results are used to
initiate stable recurrence. The algorithm has been
implemented in Fortran 2003, with precomputations
carried out in Maple.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Zhong:2013:AKF,
author = "Min Zhong and R. J. Loy and R. S. Anderssen",
title = "Approximating the {Kohlrausch} function by sums of
exponentials",
journal = j-ANZIAM-J,
volume = "54",
number = "4",
pages = "306--323",
month = apr,
year = "2013",
CODEN = "AJNOA2",
DOI = "https://doi.org/10.1017/S1446181113000229",
ISSN = "1446-1811 (print), 1446-8735 (electronic)",
ISSN-L = "1446-1811",
bibdate = "Fri Apr 26 16:14:05 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.cambridge.org/core/journals/anziam-journal/article/approximating-the-kohlrausch-function-by-sums-of-exponentials/1F2BD299466198D202D9D2355E34116F",
acknowledgement = ack-nhfb,
ajournal = "ANZIAM J.",
fjournal = "The ANZIAM Journal. The Australian \& New Zealand
Industrial and Applied Mathematics Journal",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
keywords = "Kohlrausch function $\exp(-t^\beta)$, with $\beta \in
(0,1)$",
onlinedate = "04 September 2013",
}
@Article{Adj:2014:SRC,
author = "G. Adj and F. Rodriguez-Henriquez",
title = "Square Root Computation over Even Extension Fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "11",
pages = "2829--2841",
month = nov,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.145",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 06 07:39:04 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Algorithm design and analysis; Complexity theory;
Computational efficiency; Computer science; Elliptic
curve cryptography; Elliptic curves; even extension
fields; finite extension fields; finite field
arithmetic; Modular square root; number theoretical
problem; number theory; square root computation;
Taxonomy",
}
@Misc{Anonymous:2014:CLL,
author = "Anonymous",
title = "{CR-Libm} --- a library of correctly rounded
elementary functions in double-precision",
howpublished = "Web site",
year = "2014",
bibdate = "Sat Oct 31 07:21:21 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://lipforge.ens-lyon.fr/www/crlibm/",
abstract = "CRlibm is a free mathematical library (libm) that
provides: (1) implementations of the double-precision
C99 standard elementary functions; (2) correctly
rounded in the four IEEE-754 rounding modes; (3) with a
comprehensive proof of both the algorithms used and
their implementation; (4) sufficiently efficient in
average time, worst-case time, and memory consumption
to replace existing libms transparently.",
acknowledgement = ack-nhfb,
keywords = "CR-Libm; scslib (software carry save library)",
}
@Article{Babusci:2014:SBS,
author = "D. Babusci and G. Dattoli and K. G{\'o}rska and K. A.
Penson",
title = "The spherical {Bessel} and {Struve} functions and
operational methods",
journal = j-APPL-MATH-COMP,
volume = "238",
number = "??",
pages = "1--6",
day = "1",
month = jul,
year = "2014",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri May 23 10:53:19 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300314005086",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Backeljauw:2014:VES,
author = "Franky Backeljauw and Stefan Becuwe and Annie Cuyt and
Joris {Van Deun} and Daniel W. Lozier",
title = "Validated evaluation of special mathematical
functions",
journal = j-SCI-COMPUT-PROGRAM,
volume = "90 (part A)",
number = "??",
pages = "2--20",
day = "15",
month = sep,
year = "2014",
CODEN = "SCPGD4",
DOI = "https://doi.org/10.1016/j.scico.2013.05.006",
ISSN = "0167-6423 (print), 1872-7964 (electronic)",
ISSN-L = "0167-6423",
bibdate = "Thu May 22 07:49:47 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/scicomputprogram.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167642313001263",
acknowledgement = ack-nhfb,
fjournal = "Science of Computer Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/01676423/",
}
@Book{Bartsch:2014:TMF,
author = "Hans-Jochen Bartsch",
title = "{Taschenbuch mathematischer Formeln f{\"u}r Ingenieure
und Naturwissenschaftler: [F{\"u}r Studium und Beruf]}.
({German}) [{Pocketbook} of mathematical formulas for
engineers and natural sciences: [For study and job]]",
publisher = "Fachbuchverlag Leipzig im Hanser-Verlag",
address = "M{\"u}nchen, Germany",
edition = "Twenty-third",
pages = "832",
year = "2014",
ISBN = "3-446-43800-9",
ISBN-13 = "978-3-446-43800-2",
LCCN = "????",
bibdate = "Wed Mar 1 17:30:07 MST 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://d-nb.info/1045240478/04",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "1 Logik, Mengen, Zahlensysteme / 21 \\
2 Arithmetik / 46 \\
3 Gleichungen und Ungleichungen / 91 \\
4 Elementare Geometrie / 124 \\
5 Lineare Algebra / 168 \\
6 Vektoren, Analytische Geometrie / 244 \\
7 Funktionen und Kurven / 335 \\
8 Differenzialrechnung / 421 \\
9 Integralrechnung / 467 \\
10 Vektoranalysis / 512 \\
11 Differenzialgleichungen / 536 \\
12 Reihen, F- und L-/ Transformation \\
13 Statistik, Stochastik / 643 \\
14 Integraltabellen / 719",
}
@Book{Boyd:2014:STE,
author = "John P. (John Philip) Boyd",
title = "Solving transcendental equations: the {Chebyshev}
polynomial proxy and other numerical rootfinders,
perturbation series, and oracles",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xviii + 460",
year = "2014",
ISBN = "1-61197-351-1 (paperback)",
ISBN-13 = "978-1-61197-351-8 (paperback)",
LCCN = "QA353.T7 B69 2014",
bibdate = "Wed Sep 23 17:10:53 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy1503/2014017078-b.html;
http://www.loc.gov/catdir/enhancements/fy1503/2014017078-d.html;
http://www.loc.gov/catdir/enhancements/fy1503/2014017078-t.html",
acknowledgement = ack-nhfb,
author-dates = "1951--",
subject = "Transcendental functions; Chebyshev polynomials;
Transcendental numbers",
tableofcontents = "I: Introduction and overview \\
Introduction: Key themes in rootfinding \\
II: the Chebyshev-Proxy rootfinder and its
generalizations \\
The Chebyshev-Proxy/Companion matrix rootfinder \\
Adaptive Chebyshev interpolation \\
Adaptive Fourier interpolation and rootfinding \\
Complex zeros: Interpolation on a disk, the
Delves--Lyness algorithm, and contour integrals \\
III: Fundamentals: Iterations, bifurcation, and
continuation \\
Newton iteration and its kin \\
Bifurcation theory \\
Continuation in a parameter \\
IV: Polynomials \\
Polynomial equations and the irony of Galois Theory \\
The Quadratic Equation \\
Roots of a cubic polynomial \\
Roots of a quartic polynomial \\
V: Analytical methods \\
Methods for explicit solutions \\
Regular perturbation methods for roots \\
Singular perturbation methods: fractional powers,
logarithms, and exponential asymptotics \\
VI: Classics, special functions, inverses, and oracles
\\
Classical methods for solving one equation in one
unknown \\
Special algorithms for special functions \\
Inverse functions of one unknown \\
Oracles: Theorems and algorithms for determining the
existence, nonexistence, and number of zeros \\
VII: Bivariate systems \\
Two equations in two unknowns \\
VIII: Challenges \\
Past and future \\
A: Companion matrices \\
B: Chebyshev interpolation and quadrature \\
Marching triangles \\
D: Imbricate-Fourier series and the Poisson Summation
Theorem",
}
@Article{Buehler:2014:CCH,
author = "Stephan Buehler and Claude Duhr",
title = "{CHAPLIN-Complex Harmonic Polylogarithms} in
{Fortran}",
journal = j-COMP-PHYS-COMM,
volume = "185",
number = "10",
pages = "2703--2713",
month = oct,
year = "2014",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Aug 16 08:37:41 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465514001969",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655/",
}
@Article{Choudhury:2014:SAA,
author = "Amit Choudhury",
title = "A simple approximation to the area under standard
normal curve",
journal = "Mathematics and Statistics",
volume = "2",
number = "3",
pages = "147--149",
month = "????",
year = "2014",
DOI = "https://doi.org/10.13189/ms.2014.020307",
ISSN = "2332-2071 (print), 2332-2144 (electronic)",
ISSN-L = "2332-2071",
bibdate = "Sat Dec 16 15:57:04 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.hrpub.org/journals/article_info.php?aid=1470;
https://www.hrpub.org/download/20140305/MS7-13401470.pdf",
acknowledgement = ack-nhfb,
}
@Book{Dunkl:2014:OPS,
author = "Charles F. Dunkl and Yuan Xu",
title = "Orthogonal Polynomials of Several Variables",
volume = "155",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "xvii + 420",
year = "2014",
ISBN = "1-107-07189-5, 1-316-05717-8 (e-book)",
ISBN-13 = "978-1-107-07189-6, 978-1-316-05717-9 (e-book)",
LCCN = "QA404.5 .D86 2014",
bibdate = "Sat Nov 11 06:43:34 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Encyclopedia of mathematics and its applications",
URL = "http://catdir.loc.gov/catdir/enhancements/fy1408/2014001846-b.html;
http://catdir.loc.gov/catdir/enhancements/fy1408/2014001846-d.html;
http://catdir.loc.gov/catdir/enhancements/fy1408/2014001846-t.html;
http://digitale-objekte.hbz-nrw.de/storage2/2014/11/17/file_11/5877666.pdf",
acknowledgement = ack-nhfb,
remark = "See also first edition \cite{Dunkl:2001:OPS}",
shorttableofcontents = "Preface to the Second Edition / xiii \\
Preface to the First Edition / xv \\
1 Background / 1 \\
2 Orthogonal Polynomials in Two Variables / 28 \\
3 General Properties of Orthogonal Polynomials in
Several Variables / 57 \\
4 Orthogonal Polynomials on the Unit Sphere / 114 \\
5 Examples of Orthogonal Polynomials in Several
Variables / 137 \\
6 Root Systems and Coxeter Groups / 174 \\
7 Spherical Harmonics Associated with Reflection Groups
/ 208 \\
8 Generalized Classical Orthogonal Polynomials / 258
\\
9 Summability of Orthogonal Expansions / 289 \\
10 Orthogonal Polynomials Associated with Symmetric
Groups / 318 \\
11 Orthogonal Polynomials Associated with Octahedral
Groups and Applications / 364 \\
References / 396 \\
Author Index / 413 \\
Symbol Index / 416 \\
Subject Index / 418",
subject = "Orthogonal polynomials; Functions of several real
variables; Polyn{\^o}mes orthogonaux; Fonctions de
plusieurs variables r{\'e}elles; Functions of several
real variables; Orthogonal polynomials; Orthogonale
reeksen; Ortogonalpolynom",
tableofcontents = "Preface to the Second Edition / xiii \\
Preface to the First Edition / xv \\
\\
1 Background / 1 \\
1.1 The Gamma and Beta Functions / 1 \\
1.2 Hypergeometric Series / 3 \\
1.2.1 Lauricella series / 5 \\
1.3 Orthogonal Polynomials of One Variable / 6 \\
1.3.1 General properties / 6 \\
1.3.2 Three-term recurrence / 9 \\
1.4 Classical Orthogonal Polynomials / 13 \\
1.4.1 Hermite polynomials / 13 \\
1.4.2 Laguerre polynomials / 14 \\
1.4.3 Gegenbauer polynomials / 16 \\
1.4.4 Jacobi polynomials / 20 \\
1.5 Modified Classical Polynomials / 22 \\
1.5.1 Generalized Hermite polynomials / 24 \\
1.5.2 Generalized Gegenbauer polynomials / 25 \\
1.5.3 A limiting relation / 27 \\
1.6 Notes / 27 \\
\\
2 Orthogonal Polynomials in Two Variables / 28 \\
2.1 Introduction / 28 \\
2.2 Product Orthogonal Polynomials / 29 \\
2.3 Orthogonal Polynomials on the Unit Disk / 30 \\
2.4 Orthogonal Polynomials on the Triangle / 35 \\
2.5 Orthogonal Polynomials and Differential Equations /
37 \\
2.6 Generating Orthogonal Polynomials of Two Variables
/ 38 \\
2.6.1 A method for generating orthogonal polynomials /
38 \\
2.6.2 Orthogonal polynomials for a radial weight / 40
\\
2.6.3 Orthogonal polynomials in complex variables / 41
\\
2.7 First Family of Koornwinder Polynomials / 45 \\
2.8 A Related Family of Orthogonal Polynomials / 43 \\
2.9 Second Family of Koornwinder Polynomials / 50 \\
2.10 Notes / 54 \\
\\
3 General Properties of Orthogonal Polynomials in
Several Variables / 57 \\
3.1 Notation and Preliminaries / 58 \\
3.2 Moment Functionals and Orthogonal Polynomials in
Several Variables / 60 \\
3.2.1 Definition of orthogonal polynomials / 60 \\
3.2.2 Orthogonal polynomials and moment matrices / 64
\\
3.2.3 The moment problem / 67 \\
3.3 The Three-Term Relation / 70 \\
3.3.1 Definition and basic properties / 70 \\
3.3.2 Favard's theorem / 73 \\
3.3.3 Centrally symmetric integrals / 76 \\
3.3.4 Examples / 79 \\
3.4 Jacobi Matrices and Commuting Operators / 82 \\
3.5 Further Properties of the Three-Term Relation / 87
\\
3.5.1 Recurrence formula / 87 \\
3.5.2 General solutions of the three-term relation / 94
\\
3.6 Reproducing Kernels and Fourier Orthogonal Series /
96 \\
3.6.1 Reproducing kernels / 97 \\
3.6.2 Fourier orthogonal series / 101 \\
3.7 Common Zeros of Orthogonal Polynomials in Several
Variables / 103 \\
3.8 Gaussian Cubature Formulae / 107 \\
3.9 Notes / 112 \\
\\
4 Orthogonal Polynomials on the Unit Sphere / 114 \\
4.1 Spherical Harmonics / 114 \\
4.2 Orthogonal Structures on $S^d$ and on $B^d$ / 119
\\
4.3 Orthogonal Structures on $B^d$ and on $S^{d + m -
1}$ / 125 \\
4.4 Orthogonal Structures on the Simplex / 129 \\
4.5 Van der Corput--Schaake Inequality / 133 \\
4.6 Notes / 136 \\
\\
5 Examples of Orthogonal Polynomials in Several
Variables / 137 \\
5.1 Orthogonal Polynomials for Simple Weight Functions
/ 137 \\
5.1.1 Product weight functions / 138 \\
5.1.2 Rotation-invariant weight functions / 138 \\
5.1.3 Multiple Hermite polynomials on $\mathbb{R}^d$ /
139 \\
5.1.4 Multiple Laguerre polynomials on $\mathbb{R}^d__$
/ 141 \\
5.2 Classical Orthogonal Polynomials on the Unit Ball /
141 \\
5.2.1 Orthonormal bases / 142 \\
5.2.2 Appell's monic orthogonal and biorthogonal
polynomials / 143 \\
5.2.3 Reproducing kernel with respect to $W_\mu^B$ on
$B^d$ / 148 \\
53.3 Classical Orthogonal Polynomials on the Simplex /
150 \\
5.4 Orthogonal Polynomials via Symmetric Functions /
154 \\
5.4.1 Two general families of orthogonal polynomials /
154 \\
5.4.2 Common zeros and Gaussian cubature formulae / 156
\\
5.5 Chebyshev Polynomials of Type ${\cal A}_d$ / 165
\\
5.6 Sobolev Orthogonal Polynomials on the Unit Ball /
165 \\
5.6.1 Sobolev orthogonal polynomials defined via the
gradient operator / 165 \\
5.6.2 Sobolev orthogonal polynomials defined via the
Laplacian operator / 168 \\
5.7 Notes / 171 \\
\\
6 Root Systems and Coxeter Groups / 174 \\
6.1 Introduction and Overview / 174 \\
6.2 Root Systems / 176 \\
6.2.1 Type $A_{d - 1}$ / 179 \\
6.2.2 Type $B_d$ / 179 \\
6.2.3 Type $I_2(m)$ / 180 \\
6.2.4 Type $D_d$ / 181 \\
6.2.5 Type $H_3$ / 181 \\
6.2.6 Type $F_4$ / 182 \\
6.2.7 Other types / 182 \\
6.2.8 Miscellaneous results / 182 \\
6.3 Invariant Polynomials / 183 \\
6.3.1 Type $A_{d - 1}$ invariants / 183 \\
6.3.2 Type $B_d$ invariants / 186 \\
6.3.3 Type $D_d$ invariants / 186 \\
6.3.4 Type $I_2(m)$ invariants / 186 \\
6.3.5 Type $H_3$ invariants / 186 \\
6.3.6 Type $F_4$ invariants / 187 \\
6.4 Differential--Difference Operators / 187 \\
6.5 The Intertwining Operator / 192 \\
6.6 The $\kappa$-Analogue of the Exponential / 200 \\
6.7 Invariant Differential Operators / 202 \\
6.8 Notes / 207 \\
\\
7 Spherical Harmonics Associated with Reflection Groups
/ 208 \\
7.1 $h$-Harmonic Polynomials / 208 \\
7.2 Inner Products on Polynomials / 217 \\
7.3 Reproducing Kernels and the Poisson Kernel / 221
\\
7.4 Integration of the Intertwining Operator / 224 \\
7.5 Example: Abelian Group ${\cal Z}_2^d$ / 228 \\
7.5.1 Orthogonal basis for $h$-harmonics / 228 \\
7.5.2 Intertwining and projection operators / 232 \\
7.5.3 Monic orthogonal basis / 235 \\
7.6 Example: Dihedral Groups / 240 \\
7.6.1 An orthonormal basis of ${\cal H}_(h^2_{\alpha,
\beta})$ / 241 \\
7.6.2 Cauchy and Poisson kernels / 248 \\
7.7 The Dunkl Transform / 250 \\
7.8 Notes / 256 \\
\\
8 Generalized Classical Orthogonal Polynomials / 258
\\
8.1 Generalized Classical Orthogonal Polynomials on the
Ball / 258 \\
8.1.1 Definition and differential-difference equations
/ 258 \\
8.1.2 Orthogonal basis and reproducing kernel / 263 \\
8.1.3 Orthogonal polynomials for ${\cal
Z}_2^d$-invariant weight functions / 266 \\
8.1.4 Reproducing kernel for ${\cal Z}_2^d$-invariant
weight functions / 268 \\
8.2 Generalized Classical Orthogonal Polynomials on the
Simplex / 271 \\
8.2.1 Weight function and differential-difference
equation / 271 \\
8.2.2 Orthogonal basis and reproducing kernel / 273 \\
8.2.3 Monic orthogonal polynomials / 287 \\
8.3 Generalized Hermite Polynomials / 278 \\
8.4 Generalized Laguerre Polynomials / 283 \\
8.5 Notes / 287 \\
\\
9 Summability of Orthogonal Expansions / 289 \\
9.1 General Results on Orthogonal Expansions / 289 \\
9.1.1 Uniform convergence of partial sums / 289 \\
9.1.2 Ces{\`a}ro means of the orthogonal expansion /
293 \\
9.2 Orthogonal Expansion on the Sphere / 296 \\
9.3 Orthogonal Expansion on the Ball / 299 \\
9.4 Orthogonal Expansion on the Simplex / 304 \\
9.5 Orthogonal Expansion of Laguerre and Hermite
Polynomials / 306 \\
9.6 Multiple Jacobi Expansion / 311 \\
9.7 Notes / 315 \\
\\
10 Orthogonal Polynomials Associated with Symmetric
Groups / 318 \\
10.1 Partitions, Compositions and Orderings / 318 \\
10.2 Commuting Self-Adjoint Operators / 320 \\
10.3 The Dual Polynomial Basis / 322 \\
10.4 $S_d$-Invariant Subspaces / 329 \\
10.5 Degree-Changing Recurrences / 334 \\
10.6 Norm Formulae / 337 \\
10.6.1 Hook-length products and the pairing norm / 337
\\
10.6.2 The biorthogonal-type norm / 341 \\
10.6.3 The torus inner product / 343 \\
10.6.4 Monic polynomials / 346 \\
10.6.5 Normalizing constants / 346 \\
10.7 Symmetric Functions and Jack Polynomials / 350 \\
10.8 Miscellaneous Topics / 357 \\
10.9 Notes / 362 \\
\\
11 Orthogonal Polynomials Associated with Octahedral
Groups and Applications / 364 \\
11.1 Introduction / 364 \\
11.2 Operators of Type $B$ / 365 \\
11.3 Polynomial Eigenfunctions of Type $B$ / 368 \\
11.4 Generalized Binomial Coefficients / 376 \\
11.5 Hermite Polynomials of Type $B$ / 373 \\
11.6 Calogero--Sutherland Systems / 385 \\
11.6.1 The simple harmonic oscillator / 386 \\
11.6.2 Root systems and the Laplacian / 387 \\
11.6.3 Type $A$ models on the line / 387 \\
11.6.4 Type $A$ models on the circle / 389 \\
11.6.5 Type $B$ models on the line / 392 \\
11.7 Notes / 394 \\
\\
References / 396 \\
Author Index / 413 \\
Symbol Index / 416 \\
Subject Index / 418",
}
@Article{Fukushima:2014:ACG,
author = "Toshio Fukushima",
title = "Analytical computation of generalized {Fermi--Dirac}
integrals by truncated {Sommerfeld} expansions",
journal = j-APPL-MATH-COMP,
volume = "234",
number = "??",
pages = "417--433",
day = "15",
month = may,
year = "2014",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Apr 21 18:04:13 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300314002926",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Fukushima:2014:CGI,
author = "Toshio Fukushima",
title = "Computation of a general integral of {Fermi--Dirac}
distribution by {McDougall--Stoner} method",
journal = j-APPL-MATH-COMP,
volume = "238",
number = "??",
pages = "485--510",
day = "1",
month = jul,
year = "2014",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri May 23 10:53:19 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S009630031400561X",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Gil:2014:ACM,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{Algorithm 939}: Computation of the {Marcum}
{$Q$}-Function",
journal = j-TOMS,
volume = "40",
number = "3",
pages = "20:1--20:21",
month = apr,
year = "2014",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2591004",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Apr 21 17:42:14 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Methods and an algorithm for computing the generalized
Marcum $Q$-function $ (Q_\mu (x, y))$ and the
complementary function $ (P_\mu (x, y))$ are described.
These functions appear in problems of different
technical and scientific areas such as, for example,
radar detection and communications, statistics, and
probability theory, where they are called the
noncentral chi-square or the noncentral gamma
cumulative distribution functions. The algorithm for
computing the Marcum functions combines different
methods of evaluation in different regions: series
expansions, integral representations, asymptotic
expansions, and use of three-term homogeneous
recurrence relations. A relative accuracy close to $
10^{-12}$ can be obtained in the parameter region $ (x,
y, \mu) \in [0, A] \times [0, A] \times [1, A]$, $ A =
200$, while for larger parameters the accuracy
decreases (close to $ 10^{-11}$ for $ A = 1000$ and
close to $ 5 \times 10^{-11}$ for $ A = 10000$).",
acknowledgement = ack-nhfb,
articleno = "20",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gil:2014:CZA,
author = "Amparo Gil and Javier Segura",
title = "On the complex zeros of {Airy} and {Bessel} functions
and those of their derivatives",
journal = j-ANAL-APPL,
volume = "12",
number = "5",
pages = "537--561",
month = aug,
year = "2014",
DOI = "https://doi.org/10.1142/s0219530514500341",
ISSN = "0219-5305 (print), 1793-6861 (electronic)",
ISSN-L = "0219-5305",
bibdate = "Thu Nov 16 07:32:34 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Special Issue: Dedicated to the Memory of Frank Olver
(Part II).",
acknowledgement = ack-nhfb,
ajournal = "Anal. Appl. (Singapore)",
fjournal = "Analysis and Applications (Singapore)",
journal-URL = "https://www.worldscientific.com/worldscinet/aa",
subject-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
}
@Article{Gil:2014:RSD,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Recent software developments for special functions in
the {Santander--Amsterdam} project",
journal = j-SCI-COMPUT-PROGRAM,
volume = "90 (part A)",
number = "??",
pages = "42--54",
day = "15",
month = sep,
year = "2014",
CODEN = "SCPGD4",
DOI = "https://doi.org/10.1016/j.scico.2013.11.004",
ISSN = "0167-6423 (print), 1872-7964 (electronic)",
ISSN-L = "0167-6423",
bibdate = "Thu May 22 07:49:47 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/scicomputprogram.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167642313002888",
acknowledgement = ack-nhfb,
fjournal = "Science of Computer Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/01676423/",
}
@Article{Goerg:2014:ULW,
author = "Georg M. Goerg",
title = "Usage of the {Lambert} {$W$} function in statistics",
journal = j-ANN-APPL-STAT,
volume = "8",
number = "4",
pages = "2567--2567",
month = dec,
year = "2014",
CODEN = "????",
ISSN = "1932-6157 (print), 1941-7330 (electronic)",
ISSN-L = "1932-6157",
bibdate = "Wed Feb 11 19:26:08 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annapplstat.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://projecteuclid.org/euclid.aoas/1419001755",
acknowledgement = ack-nhfb,
fjournal = "Annals of Applied Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoas/;
http://www.jstor.org/journals/19326157.html",
}
@InProceedings{Greuel:2014:SIS,
author = "Gert-Martin Greuel and Wolfram Sperber",
title = "{swMATH} --- an Information Service for Mathematical
Software",
crossref = "Hong:2014:MSI",
pages = "691--701",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2_103",
bibdate = "Tue Sep 26 10:21:48 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Greynat:2014:NAE,
author = "David Greynat and Javier Sesma",
title = "A new approach to the epsilon expansion of generalized
hypergeometric functions",
journal = j-COMP-PHYS-COMM,
volume = "185",
number = "2",
pages = "472--478",
month = feb,
year = "2014",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Dec 2 12:05:01 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S001046551300324X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Harvey:2014:SAC,
author = "David Harvey",
title = "A subquadratic algorithm for computing the $n$-th
{Bernoulli} number",
journal = j-MATH-COMPUT,
volume = "83",
number = "289",
pages = "2471--2477",
year = "2014",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Sep 9 11:37:57 MDT 2014",
bibsource = "http://www.ams.org/mcom/2014-83-289;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02832-9;
http://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02832-9/S0025-5718-2014-02832-9.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Johansson:2014:EIE,
author = "Fredrik Johansson",
title = "Efficient implementation of elementary functions in
the medium-precision range",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "27",
month = oct,
year = "2014",
bibdate = "Mon Jun 12 16:12:02 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://arxiv.org/abs/1410.7176",
abstract = "We describe a new implementation of the elementary
transcendental functions exp, sin, cos, log and atan
for variable precision up to approximately 4096 bits.
Compared to the MPFR library, we achieve a maximum
speedup ranging from a factor 3 for cos to 30 for atan.
Our implementation uses table-based argument reduction
together with rectangular splitting to evaluate Taylor
series. We collect denominators to reduce the number of
divisions in the Taylor series, and avoid overhead by
doing all multiprecision arithmetic using the mpn layer
of the GMP library. Our implementation provides
rigorous error bounds.",
acknowledgement = ack-nhfb,
}
@PhdThesis{Johansson:2014:FRC,
author = "Fredrik Johansson",
title = "Fast and Rigorous Computation of Special Functions to
High Precision",
type = "{Ph.D.} thesis",
school = "Johannes Kepler University",
address = "Linz, Austria",
pages = "ix + 109",
day = "24",
month = mar,
year = "2014",
bibdate = "Sat Aug 09 09:01:13 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://permalink.obvsg.at/AC10776210",
abstract = "The problem of efficiently evaluating special
functions to high precision has been considered by
numerous authors. Important tools used for this purpose
include algorithms for evaluation of linearly recurrent
sequences, and algorithms for power series
arithmetic.\par
In this work, we give new baby-step, giant-step
algorithms for evaluation of linearly recurrent
sequences involving an expensive parameter (such as a
high-precision real number) and for computing
compositional inverses of power series. Our algorithms
do not have the best asymptotic complexity, but they
are faster than previous algorithms in practice over a
large input range.\par
Using a combination of techniques, we also obtain
efficient new algorithms for numerically evaluating the
gamma function $ \Gamma (z) $ and the Hurwitz zeta
function $ \zeta (s, a) $, or Taylor series expansions
of those functions, with rigorous error bounds. Our
methods achieve softly optimal complexity when
computing a large number of derivatives to
proportionally high precision.\par
Finally, we show that isolated values of the integer
partition function $ p(n) $ can be computed rigorously
with softly optimal complexity by means of the
Hardy--Ramanujan--Rademacher formula and careful
numerical evaluation. We provide open source
implementations which run significantly faster than
previously published software. The implementations are
used for record computations of the partition function,
including the tabulation of several billion
Ramanujan-type congruences, and of Taylor series
associated with the Riemann zeta function.",
acknowledgement = ack-nhfb,
remark = "Reviewed in \booktitle{ACM Communications in Computer
Algebra}, {\bf 48}(2) 28--28 (2014).",
}
@Article{Krasikov:2014:ABA,
author = "Ilia Krasikov",
title = "Approximations for the {Bessel} and {Airy} functions
with an explicit error term",
journal = j-LMS-J-COMPUT-MATH,
volume = "17",
number = "1",
pages = "209--225",
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1112/S1461157013000351",
ISSN = "1461-1570",
bibdate = "Tue Sep 9 12:34:08 MDT 2014",
bibsource = "http://journals.cambridge.org/action/displayJournal?jid=JCM;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
acknowledgement = ack-nhfb,
ajournal = "LMS J. Comput. Math.",
fjournal = "LMS Journal of Computation and Mathematics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=JCM",
onlinedate = "19 May 2014",
}
@InProceedings{Kupriianova:2014:MMF,
author = "Olga Kupriianova and Christoph Lauter",
title = "{Metalibm}: A Mathematical Functions Code Generator",
crossref = "Hong:2014:MSI",
pages = "713--717",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2_106",
bibdate = "Tue Sep 26 10:21:48 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Li:2014:ICH,
author = "Dingfang Li and Ping Liu and Jisheng Kou",
title = "An improvement of {Chebyshev--Halley} methods free
from second derivative",
journal = j-APPL-MATH-COMP,
volume = "235",
number = "??",
pages = "221--225",
day = "25",
month = may,
year = "2014",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Apr 21 18:04:20 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300314003312",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Lu:2014:GAF,
author = "Dawei Lu and Jinghai Feng and Congxu Ma",
title = "A general asymptotic formula of the gamma function
based on the {Burnside}'s formula",
journal = j-J-NUMBER-THEORY,
volume = "145",
number = "??",
pages = "317--328",
month = dec,
year = "2014",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2014.06.016",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:09 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X14002224",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Lu:2014:GAG,
author = "Dawei Lu and Lixin Song and Congxu Ma",
title = "A generated approximation of the gamma function
related to {Windschitl}'s formula",
journal = j-J-NUMBER-THEORY,
volume = "140",
number = "??",
pages = "215--225",
month = jul,
year = "2014",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2014.01.023",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:07 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X14000687",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Lu:2014:NAE,
author = "Dawei Lu and Xiaoguang Wang",
title = "A new asymptotic expansion and some inequalities for
the gamma function",
journal = j-J-NUMBER-THEORY,
volume = "140",
number = "??",
pages = "314--323",
month = jul,
year = "2014",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2014.01.025",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:07 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X14000705",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Lu:2014:SNI,
author = "Dawei Lu",
title = "Some new improved classes of convergence towards
{Euler}'s constant",
journal = j-APPL-MATH-COMP,
volume = "243",
number = "??",
pages = "24--32",
day = "15",
month = sep,
year = "2014",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2014.05.098",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Aug 16 10:10:22 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S009630031400798X",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
keywords = "Continued fraction; Euler's constant; Inequalities;
Rate of convergence",
}
@Article{Mortici:2014:SBG,
author = "Cristinel Mortici",
title = "Sharp bounds for gamma function in terms of $ x^{x -
1} $",
journal = j-APPL-MATH-COMP,
volume = "249",
number = "??",
pages = "278--285",
day = "15",
month = dec,
year = "2014",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Nov 26 10:49:00 MST 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300314013939",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Ogburn:2014:FDC,
author = "Daniel X. Ogburn and Colin L. Waters and Murray D.
Sciffer and Jeff A. Hogan and Paul C. Abbott",
title = "A finite difference construction of the spheroidal
wave functions",
journal = j-COMP-PHYS-COMM,
volume = "185",
number = "1",
pages = "244--253",
month = jan,
year = "2014",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Dec 2 12:04:56 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465513002610",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Piparo:2014:SHE,
author = "Danilo Piparo and Vincenzo Innocente and Thomas
Hauth",
title = "Speeding up {HEP} experiment software with a library
of fast and auto-vectorisable mathematical functions",
journal = "Journal of Physics: Conference Series",
volume = "513",
number = "5",
publisher = "IOP Publishing",
pages = "052027",
month = jun,
year = "2014",
DOI = "https://doi.org/10.1088/1742-6596/513/5/052027",
ISSN = "1742-6588 (print), 1742-6596 (electronic)",
ISSN-L = "1742-6588",
bibdate = "Tue Sep 24 14:55:02 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Potter:2014:APC,
author = "Ronald W. Potter",
title = "Arbitrary Precision Calculation of Selected Higher
Functions",
publisher = "Lulu",
address = "????",
pages = "????",
year = "2014",
ISBN = "1-312-59943-X",
ISBN-13 = "978-1-312-59943-7",
LCCN = "QA76.9.A43 P56 2014",
bibdate = "Sat Dec 10 15:39:37 MST 2022",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
subject = "Computer algorithms; Computational complexity;
Functional programming languages; Mathematics;
Algorithms; Algorithmes; Complexit{\'e} de calcul
(Informatique); Langages de programmation fonctionnels;
Math{\'e}matiques; algorithms; mathematics; applied
mathematics; Algorithms; Computational complexity;
Computer algorithms; Functional programming languages;
Mathematics",
tableofcontents = "Preface / ii \\
Introduction / x \\
1: Basic Arithmetic / 1-1 \\
2: High Precision Computational Techniques / 2-1 \\
3: Elementary Functions / 3-1 \\
4: Euler's Constant / 4-1 \\
5: Gamma and Polygamma Functions / 5-1 \\
6: Elliptic Integrals and $ \pi $ / 6-1 \\
7: Jacobian Elliptic Functions / 7-1 \\
8: Theta Functions / 8-1 \\
9: Incomplete Gamma Functions, Chi$^2$ and Inverse
Chi$^2$ Distribution / 9-1 \\
10: Beta and Incomplete Beta Functions, Student's $t$
and $F$-Distributions and Their Inverses / 10-1 \\
11: Error Functions, Gaussian Distribution and Inverse
/ 11-1 \\
12: Modified Bessel Functions / 12-1 \\
13: Ordinary Bessel Functions / 13-1 \\
14: Zeros of Ordinary Bessel Functions / 14-1 \\
15: Spherical Bessel Functions / 15-1 \\
16: Airy Functions and Zeros / 16-1 \\
17: Kelvin Functions / 17-1 \\
18: Struve Functions / 18-1 \\
19: Fresnel Integrals / 19-1 \\
20: Exponential Integrals / 20-1 \\
21: Sine\slash Cosine and Sinh\slash Cosh Integrals /
21-1 \\
22: Orthogonal Polynomials / 22-1 \\
23: Polynomial Roots / 23-1 \\
24: Matrix Operations / 24-1 \\
25: Geometric Operations / 25-1 \\
Appendix A: Fast Fourier Transform (FFT) / A-1 \\
Appendix B: The AGM Algorithm / B-1 \\
Appendix C: Contours of Bessel Function Zeros / C-1 \\
Appendix D: A Few Numbers (6071 digits per number) /
D-1 \\
Appendix E: 315061 Decimal Digits of Euler's Constant /
E-1 \\
Index / I-1 \\
About the Author",
}
@Article{Qi:2014:IRC,
author = "Feng Qi",
title = "Integral representations and complete monotonicity
related to the remainder of {Burnside}'s formula for
the gamma function",
journal = j-J-COMPUT-APPL-MATH,
volume = "268",
number = "??",
pages = "155--167",
day = "1",
month = oct,
year = "2014",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:34:45 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042714001356",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Rappoport:2014:MSM,
author = "Juri Rappoport",
title = "Mathematical Software for Modified {Bessel}
Functions",
crossref = "Hong:2014:MSI",
pages = "325--332",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2_51",
bibdate = "Tue Sep 26 10:17:51 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ratnanather:2014:ATI,
author = "J. Tilak Ratnanather and Jung H. Kim and Sirong Zhang
and Anthony M. J. Davis and Stephen K. Lucas",
title = "{Algorithm 935}: {{\tt IIPBF}}, a {{\tt MATLAB}}
toolbox for infinite integral of products of two
{Bessel} functions",
journal = j-TOMS,
volume = "40",
number = "2",
pages = "14:1--14:12",
month = feb,
year = "2014",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2508435",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Mar 14 06:30:41 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "A {\tt MATLAB} toolbox, {\tt IIPBF}, for calculating
infinite integrals involving a product of two Bessel
functions $ J_a(\rho x) J_b(\tau x) $, $ J_a(\rho x)
Y_b(\tau x) $, and $ Y_a(\rho x) Y_b(\tau x) $, for
non-negative integers $a$, $b$, and a well-behaved
function $ f(x) $, is described. Based on the Lucas
algorithm previously developed for $ J_a(\rho x)
J_b(\tau x) $ only, {\tt IIPBF} recasts each product as
the sum of two functions whose oscillatory behavior is
exploited in the three-step procedure of adaptive
integration, summation, and extrapolation. The toolbox
uses customised {\tt QUADPACK} and {\tt IMSL} functions
from a {\tt MATLAB} conversion of the {\tt SLATEC}
library. In addition, {\tt MATLAB}'s own {\tt quadgk}
function for adaptive Gauss--Kronrod quadrature results
in a significant speed up compared with the original
algorithm. Usage of {\tt IIPBF} is described and
eighteen test cases illustrate the robustness of the
toolbox; five additional ones are used to compare {\tt
IIPBF} with the {\tt BESSELINT} code for rational and
exponential forms of $ f(x) $ with $ J_a(\rho x)
J_b(\tau x) $. Reliability for a broad range of values
of $ \rho $ and $ \tau $ for the three different
product types as well as different orders in one case
is demonstrated. An electronic appendix provides a
novel derivation of formulae for five cases.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Shukla:2014:LLH,
author = "R. Shukla and K. C. Ray",
title = "Low Latency Hybrid {CORDIC} Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "12",
pages = "3066--3078",
month = dec,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.173",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Dec 4 10:36:57 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "adders; Approximation algorithms; communication
systems; Computer architecture; coordinate rotational
digital computer; CORDIC algorithm; Delays; digital
arithmetic; Digital computers; digital computers;
double step branching; fast adders; first order
hardware architecture; hardware complexity; hybrid
CORDIC algorithm; image processing; low latency; low
latency hybrid CORDIC algorithm; Mathematical model;
radix-4; redundant arithmetic; scale factor
calculation; signal processing; Signal processing
algorithms",
}
@Article{Soranzo:2014:VSE,
author = "Alessandro Soranzo and Emanuela Epure",
title = "Very simply explicitly invertible approximations of
normal cumulative and normal quantile function",
journal = j-APPL-MATH-SCI-RUSE,
volume = "8",
pages = "4323--4341",
year = "2014",
DOI = "https://doi.org/10.12988/ams.2014.45338",
ISSN = "1312-885X (print), 1314-7552 (electronic)",
ISSN-L = "1312-885X",
bibdate = "Sat Dec 16 17:41:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://m-hikari.com/ams/ams-2014/ams-85-88-2014/epureAMS85-88-2014.pdf",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematical Sciences (Ruse)",
journal-URL = "http://www.m-hikari.com/ams/",
}
@Article{Wang:2014:CFA,
author = "Dong Wang and Milo{\v{s}} D. Ercegovac and Yang Xiao",
title = "Complex Function Approximation Using Two-Dimensional
Interpolation",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "12",
pages = "2948--2960",
month = dec,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.181",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Dec 4 10:36:57 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "2D convolution algorithm; 2D interpolation;
Approximation error; ASIC; bipartite schemes; bivariate
functions; coefficient table; complex exponential;
complex function approximation; complex function
evaluation; complex reciprocal; Complex reciprocal;
Computational complexity; cubic interpolation;
exponential functions; field programmable gate arrays;
FPGA; Function approximation; generic hardware
architecture; interpolation; interpolation degree;
interpolation kernels; Lagrange interpolation;
Lagrangian functions; linear interpolation; lookup
tables; memory requirements; multipartite schemes;
quadratic interpolation; Quadratic programming; table
lookup; tabulated function; two-dimensional
interpolation",
}
@Article{Wang:2014:FPT,
author = "Dong Wang and Jean-Michel Muller and Nicolas
Brisebarre and Milo D. Ercegovac",
title = "{$ (M, p, k)$-Friendly} Points: a Table-Based Method
to Evaluate Trigonometric Function",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "61",
number = "9",
pages = "711--715",
year = "2014",
DOI = "https://doi.org/10.1109/TCSII.2014.2331094",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Fri Sep 29 10:46:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}
@Article{Xu:2014:SII,
author = "Ai-Min Xu and Zhong-Di Cen",
title = "Some identities involving exponential functions and
{Stirling} numbers and applications",
journal = j-J-COMPUT-APPL-MATH,
volume = "260",
number = "??",
pages = "201--207",
month = apr,
year = "2014",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:34:42 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042713005323",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Yun:2014:AHA,
author = "Beong In Yun",
title = "An ad hoc approximation to the {Gauss} error function
and a correction method",
journal = j-APPL-MATH-SCI-RUSE,
volume = "8",
pages = "4261--4273",
year = "2014",
DOI = "https://doi.org/10.12988/ams.2014.45345",
ISSN = "1312-885X (print), 1314-7552 (electronic)",
bibdate = "Sat Dec 16 18:06:18 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.m-hikari.com/ams/ams-2014/ams-85-88-2014/yunAMS85-88-2014.pdf",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematical Sciences (Ruse)",
journal-URL = "http://www.m-hikari.com/ams/",
}
@InProceedings{Zafar:2014:HAD,
author = "Saad Zafar and Raviteja Adapa",
booktitle = "2014 International Conference on Advances in
Electrical Engineering {(ICAEE)}",
title = "Hardware architecture design and mapping of ``{Fast
Inverse Square Root}'' algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--4",
month = jan,
year = "2014",
DOI = "https://doi.org/10.1109/icaee.2014.6838433",
bibdate = "Wed Dec 20 07:29:37 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Fast Inverse Square Root algorithm has been used
in 3D games of past for lighting and reflection
calculations, because it offers up to four times
performance gains. This paper presents a hardware
implementation of the algorithm on an FPGA board by
designing the complete architecture and successfully
mapping it on Xilinx Spartan 3E after thorough
functional verification. The results show that this
implementation provides a very efficient
single-precision floating point inverse square root
calculator with practically accurate results being made
available after just 12 short clock cycles. This
performance measure is far superior to the software
counterpart of the algorithm, and is not processor
dependent like rsqrtss of x86 SSE instruction set.
Results of this work can aid FPGA based vector
processors or graphic processing units with 3D
rendering. The hardware design can also form part of a
larger floating point arithmetic unit for dedicated
reciprocal square root calculations.",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:2015:L,
author = "Anonymous",
title = "libcerf",
howpublished = "Web site",
year = "2015",
bibdate = "Mon Jun 12 16:08:24 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://apps.jcns.fz-juelich.de/doku/sc/libcerf",
abstract = "This is the home page of libcerf, a self-contained
numeric library that provides an efficient and accurate
implementation of complex error functions, along with
Dawson, Faddeeva, and Voigt functions.",
acknowledgement = ack-nhfb,
}
@Article{Bailey:2015:CCI,
author = "D. H. Bailey and J. M. Borwein",
title = "{Crandall}'s computation of the incomplete Gamma
function and the {Hurwitz} zeta function, with
applications to {Dirichlet} {$L$}-series",
journal = j-APPL-MATH-COMP,
volume = "268",
number = "??",
pages = "462--477",
day = "1",
month = oct,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Sep 16 06:56:32 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315008292",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Beliakov:2015:ARZ,
author = "Gleb Beliakov and Yuri Matiyasevich",
title = "Approximation of {Riemann}'s Zeta Function by Finite
{Dirichlet} Series: A Multiprecision Numerical
Approach",
journal = j-EXP-MATH,
volume = "24",
number = "2",
pages = "150--161",
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2014.976801",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
bibdate = "Mon Jun 8 17:49:44 MDT 2015",
bibsource = "http://www.tandfonline.com/toc/uexm20/24/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@Article{Boyd:2015:FWC,
author = "John P. Boyd",
title = "Four ways to compute the inverse of the complete
elliptic integral of the first kind",
journal = j-COMP-PHYS-COMM,
volume = "196",
number = "??",
pages = "13--18",
month = nov,
year = "2015",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2015.05.006",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Tue Sep 22 13:45:19 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465515001733",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655/",
}
@Article{Brent:2015:BET,
author = "Richard P. Brent and Fredrik Johansson",
title = "A bound for the error term in the {Brent--McMillan}
algorithm",
journal = j-MATH-COMPUT,
volume = "84",
number = "295",
pages = "2351--2359",
month = "",
year = "2015",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Aug 4 08:33:55 MDT 2015",
bibsource = "http://www.ams.org/mcom/2015-84-295;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2015-84-295/S0025-5718-2015-02931-7;
http://www.ams.org/journals/mcom/2015-84-295/S0025-5718-2015-02931-7/S0025-5718-2015-02931-7.pdf",
abstract = "The Brent--McMillan algorithm B3 (1980), when
implemented with binary splitting, is the fastest known
algorithm for high-precision computation of Euler's
constant. However, no rigorous error bound for the
algorithm has ever been published. We provide such a
bound and justify the empirical observations of Brent
and McMillan. We also give bounds on the error in the
asymptotic expansions of functions related to the
Bessel functions $ I_0 (x) $ and $ K_0 (x) $ for
positive real $x$.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Euler's constant; multiple-precision arithmetic",
}
@InProceedings{Brunie:2015:CGM,
author = "Nicolas Brunie and Florent de Dinechin and Olga
Kupriianova and Christoph Lauter",
title = "Code Generators for Mathematical Functions",
crossref = "Muller:2015:ISC",
pages = "66--73",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.22",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Chen:2015:AEC,
author = "Chao-Ping Chen and Neven Elezovi{\'c}",
title = "Asymptotic expansions and completely monotonic
functions associated with the gamma, psi and polygamma
functions",
journal = j-APPL-MATH-COMP,
volume = "269",
number = "??",
pages = "232--241",
day = "15",
month = oct,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Sep 16 06:56:33 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315009637",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Chen:2015:IAEa,
author = "Chao-Ping Chen and Richard B. Paris",
title = "Inequalities, asymptotic expansions and completely
monotonic functions related to the gamma function",
journal = j-APPL-MATH-COMP,
volume = "250",
number = "??",
pages = "514--529",
day = "1",
month = jan,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Jan 7 16:27:08 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S009630031401515X",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Chen:2015:IAEb,
author = "Chao-Ping Chen",
title = "Inequalities and asymptotic expansions associated with
the {Ramanujan} and {Nemes} formulas for the gamma
function",
journal = j-APPL-MATH-COMP,
volume = "261",
number = "??",
pages = "337--350",
day = "15",
month = jun,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed May 13 09:01:41 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315004610",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Chen:2015:ICM,
author = "Chao-Ping Chen",
title = "Inequalities and completely monotonic functions
associated with the ratios of functions resulting from
the gamma function",
journal = j-APPL-MATH-COMP,
volume = "259",
number = "??",
pages = "790--799",
day = "15",
month = may,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Apr 24 18:27:24 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315003148",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@InProceedings{deDinechin:2015:HIF,
author = "Florent de Dinechin and Matei Istoan",
title = "Hardware Implementations of Fixed-Point {Atan2}",
crossref = "Muller:2015:ISC",
pages = "34--41",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.23",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Elezovic:2015:EPF,
author = "Neven Elezovi{\'c}",
title = "Estimations of psi function and harmonic numbers",
journal = j-APPL-MATH-COMP,
volume = "258",
number = "??",
pages = "192--205",
day = "1",
month = may,
year = "2015",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2015.02.008",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu Mar 19 09:03:22 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315001617",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Flocke:2015:AAE,
author = "N. Flocke",
title = "{Algorithm 954}: an Accurate and Efficient Cubic and
Quartic Equation Solver for Physical Applications",
journal = j-TOMS,
volume = "41",
number = "4",
pages = "30:1--30:24",
month = oct,
year = "2015",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2699468",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 26 17:31:15 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We report on an accurate and efficient algorithm for
obtaining all roots of general real cubic and quartic
polynomials. Both the cubic and quartic solvers give
highly accurate roots and place no restrictions on the
magnitude of the polynomial coefficients. The key to
the algorithm is a proper rescaling of both
polynomials. This puts upper bounds on the magnitude of
the roots and is very useful in stabilizing the root
finding process. The cubic solver is based on dividing
the cubic polynomial into six classes. By analyzing the
root surface for each class, a fast convergent
Newton--Raphson starting point for a real root is
obtained at a cost no higher than three additions and
four multiplications. The quartic solver uses the cubic
solver in getting information about stationary points
and, when the quartic has real roots, stable
Newton--Raphson iterations give one of the extreme real
roots. The remaining roots follow by composite
deflation to a cubic. If the quartic has only complex
roots, the present article shows that a stable
Newton--Raphson iteration on a derived symmetric sixth
degree polynomial can be formulated for the real parts
of the complex roots. The imaginary parts follow by
solving suitable quadratics.",
acknowledgement = ack-nhfb,
articleno = "30",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Fukushima:2015:PFCa,
author = "Toshio Fukushima",
title = "Precise and fast computation of inverse {Fermi--Dirac}
integral of order $ 1 / 2 $ by minimax rational
function approximation",
journal = j-APPL-MATH-COMP,
volume = "259",
number = "??",
pages = "698--707",
day = "15",
month = may,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Apr 24 18:27:24 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315003094",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Fukushima:2015:PFCb,
author = "Toshio Fukushima",
title = "Precise and fast computation of {Fermi--Dirac}
integral of integer and half integer order by piecewise
minimax rational approximation",
journal = j-APPL-MATH-COMP,
volume = "259",
number = "??",
pages = "708--729",
day = "15",
month = may,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Apr 24 18:27:24 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315003033",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@InProceedings{Fukushima:2015:PFCc,
author = "Toshio Fukushima",
title = "Precise and Fast Computation of Elliptic Integrals and
Functions",
crossref = "Muller:2015:ISC",
pages = "50--57",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.15",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Fukushima:2015:PFCd,
author = "Toshio Fukushima",
title = "Precise and fast computation of generalized
{Fermi--Dirac} integral by parameter polynomial
approximation",
journal = j-APPL-MATH-COMP,
volume = "270",
number = "??",
pages = "802--807",
day = "1",
month = nov,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu Nov 5 06:24:28 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315011509",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Gil:2015:CKF,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Computing the {Kummer} function {$ U(a, b, z) $} for
small values of the arguments",
journal = j-APPL-MATH-COMP,
volume = "271",
number = "??",
pages = "532--539",
day = "15",
month = nov,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Nov 13 08:52:33 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315012837",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Gil:2015:GPI,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "{GammaCHI}: a package for the inversion and
computation of the gamma and chi-square cumulative
distribution functions (central and noncentral)",
journal = j-COMP-PHYS-COMM,
volume = "191",
number = "??",
pages = "132--139",
month = jun,
year = "2015",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Apr 24 18:44:55 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465515000107",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655/",
}
@Article{Graillat:2015:ECF,
author = "Stef Graillat and Christoph Lauter and Ping Tak Peter
Tang and Naoya Yamanaka and Shin'ichi Oishi",
title = "Efficient Calculations of Faithfully Rounded $
l_2$-Norms of $n$-Vectors",
journal = j-TOMS,
volume = "41",
number = "4",
pages = "24:1--24:20",
month = oct,
year = "2015",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2699469",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 26 17:31:15 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "In this article, we present an efficient algorithm to
compute the faithful rounding of the $ l_2 $-norm of a
floating-point vector. This means that the result is
accurate to within 1 bit of the underlying
floating-point type. This algorithm does not generate
overflows or underflows spuriously, but does so when
the final result calls for such a numerical exception
to be raised. Moreover, the algorithm is well suited
for parallel implementation and vectorization. The
implementation runs up to 3 times faster than the
netlib version on current processors.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Graillat:2015:MRE,
author = "Stef Graillat and Vincent Lef{\`e}vre and Jean-Michel
Muller",
title = "On the maximum relative error when computing integer
powers by iterated multiplications in floating-point
arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "70",
number = "3",
pages = "653--667",
month = nov,
year = "2015",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-015-9967-8",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Sun Oct 25 07:27:50 MDT 2015",
bibsource = "http://link.springer.com/journal/11075/70/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-015-9967-8",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "The authors show via a complex multipage proof that
the iterated product for $ x^n $ in p-bit binary
arithmetic with default IEEE 754 rounding (to nearest
with ties to even) produces a worst-case relative error
in the product that is no larger than $ (n - 1) u $,
where $ u = 2^{-p} $ is the rounding unit.",
}
@InProceedings{Johansson:2015:EIE,
author = "Fredrik Johansson",
title = "Efficient Implementation of Elementary Functions in
the Medium-Precision Range",
crossref = "Muller:2015:ISC",
pages = "83--89",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.16",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Johansson:2015:RHP,
author = "Fredrik Johansson",
title = "Rigorous high-precision computation of the {Hurwitz}
zeta function and its derivatives",
journal = j-NUMER-ALGORITHMS,
volume = "69",
number = "2",
pages = "253--270",
month = jun,
year = "2015",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-014-9893-1",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Thu May 28 15:00:06 MDT 2015",
bibsource = "http://link.springer.com/journal/11075/69/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-014-9893-1",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Kuznetsov:2015:CTT,
author = "A. Kuznetsov",
title = "Computing the truncated theta function via {Mordell}
integral",
journal = j-MATH-COMPUT,
volume = "84",
number = "296",
pages = "2911--2926",
month = "",
year = "2015",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 20 16:30:35 MDT 2015",
bibsource = "http://www.ams.org/mcom/2015-84-296;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2015-84-296/S0025-5718-2015-02953-6;
http://www.ams.org/journals/mcom/2015-84-296/S0025-5718-2015-02953-6/S0025-5718-2015-02953-6.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Lauter:2015:SAF,
author = "Christoph Lauter and Marc Mezzarobba",
title = "Semi-Automatic Floating-Point Implementation of
Special Functions",
crossref = "Muller:2015:ISC",
pages = "58--65",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.12",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Lu:2015:NSC,
author = "Dawei Lu and Lixin Song and Yang Yu",
title = "New sequences with continued fraction towards
{Euler}'s constant",
journal = j-APPL-MATH-COMP,
volume = "259",
number = "??",
pages = "12--20",
day = "15",
month = may,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Apr 24 18:27:24 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315001745",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Lu:2015:SNA,
author = "Dawei Lu and Lixin Song and Congxu Ma",
title = "Some new asymptotic approximations of the gamma
function based on {Nemes}' formula, {Ramanujan}'s
formula and {Burnside}'s formula",
journal = j-APPL-MATH-COMP,
volume = "253",
number = "??",
pages = "1--7",
day = "15",
month = feb,
year = "2015",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2014.12.077",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Feb 18 09:36:23 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300314017317",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Lu:2015:SNQ,
author = "Dawei Lu and Congxu Ma",
title = "Some new quicker continued fraction approximations for
the gamma function related to the {Nemes}' formula",
journal = j-NUMER-ALGORITHMS,
volume = "70",
number = "4",
pages = "825--833",
month = dec,
year = "2015",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-015-9975-8",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Jan 25 08:55:03 MST 2016",
bibsource = "http://link.springer.com/journal/11075/70/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-015-9975-8",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Mortici:2015:PAG,
author = "Cristinel Mortici and Hari M. Srivastava",
title = "A product approximation of the gamma function",
journal = j-NUMER-ALGORITHMS,
volume = "69",
number = "3",
pages = "595--610",
month = jul,
year = "2015",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-014-9915-z",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Sat Aug 8 13:58:48 MDT 2015",
bibsource = "http://link.springer.com/journal/11075/69/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-014-9915-z",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Nadarajah:2015:CGH,
author = "Saralees Nadarajah",
title = "On the Computation of {Gauss} Hypergeometric
Functions",
journal = j-AMER-STAT,
volume = "69",
number = "2",
pages = "146--148",
year = "2015",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1080/00031305.2015.1028595",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Sun Aug 9 16:54:48 MDT 2015",
bibsource = "http://www.tandfonline.com/toc/utas20/69/2;
https://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://amstat.tandfonline.com/loi/utas20",
onlinedate = "24 Mar 2015",
}
@Article{Natalini:2015:BPM,
author = "Pierpaolo Natalini and Paolo Emilio Ricci",
title = "{Bell} polynomials and modified {Bessel} functions of
half-integral order",
journal = j-APPL-MATH-COMP,
volume = "268",
number = "??",
pages = "270--274",
day = "1",
month = oct,
year = "2015",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2015.06.069",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Sep 16 06:56:32 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315008504",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
keywords = "Bell polynomials; Bessel functions; Combinatorial
analysis; Hankel functions",
}
@Article{Qi:2015:SIT,
author = "Feng Qi and Cristinel Mortici",
title = "Some inequalities for the trigamma function in terms
of the digamma function",
journal = j-APPL-MATH-COMP,
volume = "271",
number = "??",
pages = "502--511",
day = "15",
month = nov,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Nov 13 08:52:33 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315012758",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Book{Schwalm:2015:EFE,
author = "William A. Schwalm",
title = "Elliptic Functions and Elliptic Integrals",
publisher = "Morgan and Claypool Publishers and IOP Publishing",
address = "San Rafael, CA, USA and Bristol, UK",
pages = "67",
year = "2015",
DOI = "https://doi.org/10.1088/978-1-6817-4230-4",
ISBN = "1-68174-166-0 (print), 1-68174-230-6 (e-book),
1-68174-102-4 (mobi)",
ISBN-13 = "978-1-68174-166-6 (print), 978-1-68174-230-4 (e-book),
978-1-68174-102-4 (mobi)",
ISSN = "2054-7307",
LCCN = "QA343 .S355 2015",
bibdate = "Tue Mar 14 07:38:46 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "IOP concise physics",
URL = "http://iopscience.iop.org/book/978-1-6817-4230-4",
abstract = "This volume is a basic introduction to certain aspects
of elliptic functions and elliptic integrals.
Primarily, the elliptic functions stand out as closed
solutions to a class of physical and geometrical
problems giving rise to nonlinear differential
equations. While these nonlinear equations may not be
the types of greatest interest currently, the fact that
they are solvable exactly in terms of functions about
which much is known makes up for this. The elliptic
functions of Jacobi, or equivalently the Weierstrass
elliptic functions, inhabit the literature on current
problems in condensed matter and statistical physics,
on solitons and conformal representations, and all
sorts of famous problems in classical mechanics. The
lectures on elliptic functions have evolved as part of
the first semester of a course on theoretical and
mathematical methods given to first- and second-year
graduate students in physics and chemistry at the
University of North Dakota. They are for graduate
students or for researchers who want an elementary
introduction to the subject that nevertheless leaves
them with enough of the details to address real
problems. The style is supposed to be informal. The
intention is to introduce the subject as a moderate
extension of ordinary trigonometry in which the
reference circle is replaced by an ellipse. This entre
depends upon fewer tools and has seemed less
intimidating that other typical introductions to the
subject that depend on some knowledge of complex
variables. The first three lectures assume only
calculus, including the chain rule and elementary
knowledge of differential equations. In the later
lectures, the complex analytic properties are
introduced naturally so that a more complete study
becomes possible",
acknowledgement = ack-nhfb,
tableofcontents = "Preface \\
1. Elliptic functions as trigonometry \\
1.1. Definition of Jacobian elliptic functions and
trigonometric identities \\
1.2. Differential equations \\
1.3. Anharmonic oscillator \\
2. Differential equations satisfied by the Jacobi
elliptic functions: pendula \\
2.1. Oscillatory motion of a pendulum at large
amplitude \\
2.2. Motion traversing the whole circle \\
2.3. The sine-Gordon equation: a series of pendula \\
2.4. Series of pendula: 'super luminal' case \\
3. General reduction of the DE in terms of Jacobi
functions \\
3.1. Linear fractional transformation and cross ratio
\\
3.2. Reduction of general quartic case \\
3.3. Finding the coefficients of the linear fractional
transformation \\
4. Elliptic integrals \\
4.1. Review of complex variables up through residues
\\
4.2. Branching and multi-valued functions in complex
planes \\
4.3. Elliptic integrals and elliptic functions in
complex planes \\
4.4. Example \\
4.5. Reduction of the most general elliptic integral in
terms of the three Legendre forms",
}
@Article{Sun:2015:LEG,
author = "Qiming Sun",
title = "{Libcint}: an efficient general integral library for
{Gaussian} basis functions",
journal = j-J-COMPUT-CHEM,
volume = "36",
number = "22",
pages = "1664--1671",
day = "15",
month = aug,
year = "2015",
CODEN = "JCCHDD",
DOI = "https://doi.org/10.1002/jcc.23981",
ISSN = "0192-8651 (print), 1096-987X (electronic)",
ISSN-L = "0192-8651",
bibdate = "Sat Jul 25 20:32:36 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputchem2010.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0192-8651",
onlinedate = "30 Jun 2015",
}
@Book{Temme:2015:AMI,
author = "Nico M. Temme",
title = "Asymptotic Methods for Integrals",
volume = "6",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xxii + 605",
year = "2015",
ISBN = "981-4612-15-4 (hardcover), 981-4612-16-2 (e-book)",
ISBN-13 = "978-981-4612-15-9 (hardcover), 978-981-4612-16-6
(e-book)",
MRclass = "41-02 (33Cxx 33E20 65D30)",
MRnumber = "3328507",
MRreviewer = "Jos{\'e} Luis L{\'o}pez",
bibdate = "Tue Feb 06 11:44:21 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Series in Analysis",
abstract = "This book gives introductory chapters on the classical
basic and standard methods for asymptotic analysis,
such as Watson's lemma, Laplace's method, the saddle
point and steepest descent methods, stationary phase
and Darboux's method. The methods, explained in great
detail, will obtain asymptotic approximations of the
well-known special functions of mathematical physics
and probability theory. After these introductory
chapters, the methods of uniform asymptotic analysis
are described in which several parameters have
influence on typical phenomena: turning points and
transition points, coinciding saddle and singularities.
In all these examples, the special functions are
indicated that describe the peculiar behavior of the
integrals. The text extensively covers the classical
methods with an emphasis on how to obtain expansions,
and how to use the results for numerical methods, in
particular for approximating special functions. In this
way, we work with a computational mind: how can we use
certain expansions in numerical analysis and in
computer programs, how can we compute coefficients, and
so on.",
acknowledgement = ack-nhfb,
shorttableofcontents = "Basic methods for integrals \\
Basic methods: examples for special functions \\
Other methods for integrals \\
Uniform methods for integrals \\
Uniform methods for Laplace-type integrals \\
Uniform examples for special functions \\
A class of cumulative distribution factors",
tableofcontents = "Preface / vii \\
Acknowledgments / ix \\
Part 1: Basic Methods for Integrals / 1 \\
1. Introduction / 3 \\
1.1 Symbols used in asymptotic estimates / 3 \\
1.2 Asymptotic expansions / 4 \\
1.3 A first example: Exponential integral / 5 \\
1.4 Generalized asymptotic expansions / 7 \\
1.5 Properties of asymptotic power series / 8 \\
1.6 Optimal truncation of asymptotic expansions / 10
\\
2. Expansions of Laplace-type integrals: Watson's lemma
/ 13 \\
2.1 Watson's lemma / 13 \\
2.1.1 Watson's lemma for extended sectors / 14 \\
2.1.2 More general forms of Watson's lemma / 16 \\
2.2 Watson's lemma for loop integrals / 16 \\
2.3 More general forms of Laplace-type integrals / 19
\\
2.3.1 Transformation to the standard form / 19 \\
2.4 How to compute the coefficients / 20 \\
2.4.1 Inversion method for computing the coefficients /
20 \\
2.4.2 Integrating by parts / 22 \\
2.4.3 Manipulating power series / 23 \\
2.4.4 Explicit forms of the coefficients in the
expansion / 25 \\
2.5 Other kernels / 26 \\
2.6 Exponentially improved asymptotic expansions / 27
\\
2.7 Singularities of the integrand / 29 \\
2.7.1 A pole near the endpoint / 29 \\
2.7.2 More general cases / 32 \\
3. The method of Laplace / 33 \\
3.1 A theorem for the general case / 33 \\
3.2 Constructing the expansion / 35 \\
3.2.1 Inversion method for computing the coefficients /
36 \\
3.3 Explicit forms of the coefficients in the expansion
/ 37 \\
3.4 The complementary error function / 38 \\
4. The saddle point method and paths of steepest
descent / 41 \\
4.1 The axis of the valley at the saddle point / 43 \\
4.2 Examples with simple exponentials / 43 \\
4.2.1 A first example / 43 \\
4.2.2 A cosine transform / 44 \\
4.3 Steepest descent paths not through a saddle point /
44 \\
4.3.1 A gamma function example / 45 \\
4.3.2 An integral related to the error function / 46
\\
4.4 An example with strong oscillations: A 100-digit
challenge / 48 \\
4.5 A Laplace inversion formula for $ \erfc z $ / 49
\\
4.6 A non-oscillatory integral for $ \erfc z $, $ z \in
\mathbb{C} $ / 50 \\
4.7 The complex Airy function / 50 \\
4.8 A parabolic cylinder function / 53 \\
5. The Stokes phenomenon / 57 \\
5.1 The Airy function / 57 \\
5.2 The recent interest in the Stokes phenomenon / 58
\\
5.3 Exponentially small terms in the Airy expansions /
59 \\
5.4 Expansions in connection with the Stokes phenomenon
/ 60 \\
5.4.1 Applications to a Kummer function / 61 \\
Part 2: Basic Methods: Examples for Special Functions /
63 \\
6. The gamma function / 65 \\
6.1 $ \Gamma(z) $ by Laplace's method / 66 \\
6.1.1 Calculating the coefficients / 67 \\
6.1.2 Details on the transformation / 68 \\
6.2 $ 1 / \Gamma(z) $ by the saddle point method / 71
\\
6.2.1 Another integral representation of $ 1 /
\Gamma(z) $ / 72 \\
6.3 The logarithm of the gamma function / 72 \\
6.3.1 Estimations of the remainder / 73 \\
6.4 Expansions of $ \Gamma(z + a) $ and $ 1 / \Gamma(z
+ a) $ / 75 \\
6.5 The ratio of two gamma functions / 76 \\
6.5.1 A simple expansion / 77 \\
6.5.2 A more efficient expansion / 78 \\
6.6 A binomial coefficient / 80 \\
6.6.1 A uniform expansion of the binomial coefficient /
83 \\
6.7 Asymptotic expansion of a product of gamma
functions / 85 \\
6.8 Expansions of ratios of three gamma functions / 88
\\
7. Incomplete gamma functions / 91 \\
7.1 Integral representations / 91 \\
7.2 $ \Gamma(a, x) $ : Asymptotic expansion for $ x \gg
a $ / 92 \\
7.3 $ \gamma(a, x) $ : Asymptotic expansion for $ a > x
$ / 93 \\
7.3.1 Singularity of the integrand / 94 \\
7.3.2 More details on the transformation $ u = \phi(t)
$ / 96 \\
7.4 $ \Gamma(a, x) $ : Asymptotic expansion for $ x > a
$ / 97 \\
8. The Airy functions / 101 \\
8.1 Expansions of $ \Ai(z) $, $ \Bi(z) $ / 102 \\
8.1.1 Transforming the saddle point contour / 102 \\
8.2 Expansions of $ \Ai(-z) $, $ \Bi(-z) $ / 105 \\
8.3 Two simple ways to obtain the coefficients / 106
\\
8.4 A generalized form of the Airy function / 107 \\
9. Bessel functions: Large argument / 109 \\
9.1 The modified Bessel function $ K_\nu(z) $ / 109 \\
9.2 The ordinary Bessel functions / 110 \\
9.3 The modified Bessel function $ I_\nu(z) $ / 111
9.3.1 A compound expansion of $ I_\nu(z) $ / 111 9.4
Saddle point method for $ K_\nu(z) $, $ z \in
\mathbb{C} $ / 113 \\
9.4.1 Integral representations from saddle point
analysis / 115 \\
9.4.2 Saddle point method for $ J_\nu(x) $, $ x < \nu $
/ 116 \\
9.5 Debye-type expansions of the modified Bessel
functions / 117 \\
9.6 Modified Bessel functions of purely imaginary order
/ 119 \\
9.6.1 The monotonic case: $ x > \nu > 0 $ / 120 \\
9.6.2 The oscillatory case: $ \nu > x > 0 $ / 123 \\
9.7 A $ J $ -Bessel integral / 126 \\
10. Kummer functions / 129 \\
10.1 General properties / 129 \\
10.2 Asymptotic expansions for large $ z $ / 131 \\
10.3 Expansions for large $ a $ / 132 \\
10.3.1 Tricomi's function $ E_\nu(z) $ / 132 \\
10.3.2 Expansion of $ U(a, c, z) $, $ a \to +\infty $ /
133 \\
10.3.3 Expansion of $ _1F_1(a; c; z) $, $ a \to +\infty
$ / 135 \\
10.3.4 Expansion of $ _1F_1(a; c; z) $, $ a \to -\infty
$ / 137 \\
10.3.5 Expansion of $ U(a, c, z) $, $ a \to -\infty $ /
138 \\
10.3.6 Slater's results for large $ a $ / 140 \\
10.4 Expansions for large $ c $ / 142 \\
10.4.1 Expansion of $ _1F_1(a; c; z) $, $ c \to +\infty
$ / 142 \\
10.4.2 Expansion of $ U(a, c, z) $, $ c \to +\infty $,
$ z < c $ / 143 \\
10.4.3 Expansion of $ U(a, c, z) $, $ c \to +\infty $,
$ z > e $ / 144 \\
10.4.4 Expansion of $ U(a, c, z) $, $ c \to -\infty $ /
145 \\
10.4.5 Expansion of $ _1F_1(a; c; z) $, $ c \to -\infty
$ / 147 \\
10.5 Uniform expansions of the Kummer functions / 147
\\
11. Parabolic cylinder functions: Large argument / 149
\\
11.1 A few properties of the parabolic cylinder
functions / 149 \\
11.2 The function $ U(a, z) $ / 150 \\
11.3 The function $ U(a, -z) $ / 152 \\
11.4 The function $ V(a, z) $ / 153 \\
11.5 Expansions of the derivatives / 154 \\
12. The Gauss hypergeometric function / 155 \\
12.1 Large values of $ c $ / 156 \\
12.1.1 Large positive $ c $; $ |z| < z_0 $ / 156 \\
12.1.2 Large negative $ c $; $ |z| < z_0 $ / 157 \\
12.1.3 Large positive $ c $; $ |z| > z_0 $ / 158 \\
12.1.4 Large negative $ c $; $ |z| > z_0 $ / 158 \\
12.2 Large values of $ b $ / 158 \\
12.2.1 Large negative $ b $; $ |z| > z_0 $ / 159 \\
12.2.2 Large $ b $, $ |z| < z_0 $ / 159 \\
12.3 Other large parameter cases / 160 \\
12.3.1 Jacobi polynomials of large degree / 161 \\
12.3.2 An example of the case $ _2F_1(a, b - \lambda; c
+ \lambda; z) $ / 163 \\
13. Examples of $ _3F_2 $ -polynomials / 167 \\
13.1 A $ _3F_2 $ associated with the
Catalan--Larcombe--French sequence / 167 \\
13.1.1 Transformations / 169 \\
13.1.2 Asymptotic analysis / 170 \\
13.1.3 Asymptotic expansion / 172 \\
13.1.4 An alternative method / 173 \\
13.2 An integral of Laguerre polynomials / 175 \\
13.2.1 A first approach / 176 \\
13.2.2 A generating function approach / 178 \\
Part 3: Other Methods for Integrals / 181 \\
14. The method of stationary phase / 183 \\
14.1 Critical points / 183 \\
14.2 Integrating by parts: No stationary points / 184
\\
14.3 Three critical points: A formal approach / 185 \\
14.4 On the use of neutralizes / 186 \\
14.5 How to avoid neutralizes? / 188 \\
14.5.1 A few details about the Fresnel integral / 190
\\
14.6 Algebraic singularities at both endpoints:
Erdelyi's example / 191 \\
14.6.1 Application: A conical function / 192 \\
14.6.2 Avoiding neutralizes in Erdelyi's example / 193
\\
14.7 Transformation to standard form / 194 \\
14.8 General order stationary points / 196 \\
14.8.1 Integrating by parts / 196 \\
14.9 The method fails: Examples / 197 \\
14.9.1 The Airy function / 198 \\
14.9.2 A more complicated example / 198 \\
15. Coefficients of a power series. Darboux's method /
203 \\
15.1 A first example: A binomial coefficient / 204 \\
15.2 Legendre polynomials of large degree / 205 \\
15.2.1 A paradox in asymptotics / 207 \\
15.3 Gegenbauer polynomials of large degree / 208 \\
15.4 Jacobi polynomials of large degree / 209 \\
15.5 Laguerre polynomials of large degree / 209 \\
15.6 Generalized Bernoulli polynomials $ B_n^{(\mu)}(z)
$ / 210 \\
15.6.1 Asymptotic expansions for large degree / 211 \\
15.6.2 An alternative expansion / 213 \\
15.7 Generalized Euler polynomials $ E_n^{(\mu)}(z) $ /
215 \\
15.7.1 Asymptotic expansions for large degree / 215 \\
15.7.2 An alternative expansion / 216 \\
15.8 Coefficients of expansions of the $ _1F_1 $
-function / 218 \\
15.8.1 Coefficients of Tricomi's expansion / 218 \\
15.8.2 Coefficients of Buchholz's expansion / 221 \\
16. Mellin--Barnes integrals and Mellin convolution
integrals / 225 \\
16.1 Mellin--Barnes integrals / 226 \\
16.2 Mellin convolution integrals / 228 \\
16.3 Error bounds / 230 \\
17. Alternative expansions of Laplace-type integrals /
231 \\
17.1 Hadamard-type expansions / 231 \\
17.2 An expansion in terms of Kummer functions / 233
\\
17.3 An expansion in terms of factorial series / 234
\\
17.4 The Franklin--Friedman expansion / 237 \\
18. Two-point Taylor expansions / 241 \\
18.1 The expansions / 242 \\
18.2 An alternative form of the expansion / 243 \\
18.3 Explicit forms of the coefficients / 244 \\
18.4 Manipulations with two-point Taylor expansions /
245 \\
19. Hermite polynomials as limits of other classical
orthogonal polynomials / 249 \\
19.1 Limits between orthogonal polynomials / 249 \\
19.2 The Askey scheme of orthogonal polynomials / 251
\\
19.3 Asymptotic representations / 251 \\
19.4 Gegenbauer polynomials / 253 \\
19.5 Laguerre polynomials / 254 \\
19.6 Generalized Bessel polynomials / 255 \\
19.7 Meixner--Pollaczek polynomials into Laguerre
polynomials / 257 \\
Part 4: Uniform Methods for Integrals / 259 \\
20. An overview of standard forms / 261 \\
20.1 Comments on the table / 263 \\
21. A saddle point near a pole / 267 \\
21.1 A saddle point near a pole: Van der Waerden's
method / 267 \\
21.2 An alternative expansion / 269 \\
21.3 An example from De Bruijn / 270 \\
21.4 A pole near a double saddle point / 271 \\
21.5 A singular perturbation problem and $ K $ -Bessel
integrals / 272 \\
21.5.1 A Bessel $ K_0 $ integral / 272 \\
21.5.2 A similar Bessel $ K_1 $ integral / 274 \\
21.5.3 A singular perturbation problem / 275 \\
21.6 A double integral with poles near saddle points /
277 \\
21.6.1 Application to a singular perturbation problem /
278 \\
21.7 The Fermi--Dirac integral / 281 \\
22. Saddle point near algebraic singularity / 285 \\
22.1 A saddle point near an endpoint of the interval /
285 \\
22.2 The Bleistein expansion / 286 \\
22.3 Extending the role of the parameter /3 / 289 \\
22.4 Contour integrals / 291 \\
22.5 Kummer functions in terms of parabolic cylinder
functions / 292 \\
22.5.1 Uniform expansion of $ U(a, c, z) $, $ c \to
+\infty $ / 293 \\
22.5.2 Uniform expansion of $ _1F_1(a; c; z) $, $ c \to
+\infty $ / 296 \\
23. Two coalescing saddle points: Airy-type expansions
/ 299 \\
23.1 The standard form / 299 \\
23.2 An integration by parts method / 300 \\
23.3 How to compute the coefficients / 302 \\
23.4 An Airy-type expansion of the Hermite polynomial /
305 \\
23.4.1 The cubic transformation / 306 \\
23.4.2 Details on the coefficients / 308 \\
23.5 An Airy-type expansion of the Bessel function $
J_\nu(z) $ / 309 \\
23.6 A semi-infinite interval: Incomplete Scorer
function / 313 \\
23.6.1 A singular perturbation problem inside a circle
/ 315 \\
24. Hermite-type expansions of integrals / 319 \\
24.1 An expansion in terms of Hermite polynomials / 320
\\
24.1.1 Cauchy-type integrals for the coefficients / 321
\\
24.2 Gegenbauer polynomials / 323 \\
24.2.1 Preliminary steps / 324 \\
24.2.2 A first approximation / 325 \\
24.2.3 Transformation to the standard form / 326 \\
24.2.4 Special cases of the expansion / 331 \\
24.2.5 Approximating the zeros / 332 \\
24.2.6 The relativistic Hermite polynomials / 333 \\
24.3 Tricomi--Carlitz polynomials / 333 \\
24.3.1 Contour integral and saddle points / 335 \\
24.3.2 A first approximation / 337 \\
24.3.3 Transformation to the standard form / 337 \\
24.3.4 Approximating the zeros / 339 \\
24.4 More examples / 340 \\
Part 5: Uniform Methods for Laplace-Type Integrals /
341 \\
25. The vanishing saddle point / 343 \\
25.1 Expanding at the saddle point / 344 \\
25.2 An integration by parts method / 346 \\
25.2.1 Representing coefficients as a Cauchy-type
integral / 347 \\
25.3 Expansions for loop integrals / 348 \\
25.4 Rummer functions / 350 \\
25.5 Generalized zeta function / 350 \\
25.6 Transforming to the standard form / 351 \\
25.6.1 The ratio of two gamma functions / 352 \\
25.6.2 Parabolic cylinder functions / 354 \\
26. A moving endpoint: Incomplete Laplace integrals /
355 \\
26.1 The standard form / 355 \\
26.2 Constructing the expansion / 356 \\
26.2.1 The complementary function / 357 \\
26.3 Application to the incomplete beta function / 358
\\
26.3.1 Expansions of the coefficients / 361 \\
26.4 A corresponding loop integral / 362 \\
26.4.1 Application to the incomplete beta function /
363 \\
27. An essential singularity: Bessel-type expansions /
365 \\
27.1 Expansions in terms of modified Bessel functions /
365 \\
27.2 A corresponding loop integral / 368 \\
27.3 Expansion at the internal saddle point / 368 \\
27.4 Application to Kummer functions / 369 \\
27.4.1 Expansion of $ U(a, c, z) $, $ a \to +\infty $,
$ z > 0 $ / 369 \\
27.4.2 Auxiliary expansions and further details / 372
\\
27.4.3 Expansion of $ _1F_1(a: c; z) $, $ a \to +\infty
$, $ z > 0 $ / 374 \\
27.4.4 Expansion of $ _1F_1(a; c: z) $, $ a \to -\infty
$, $ 0 < z < -4a $ / 375 \\
27.4.5 Expansion of $ U(a, c, z) $, $ a \to -\infty $,
$ 0 < z < -4a $ / 377 \\
27.5 A second uniformity parameter / 378 \\
27.5.1 Expansion of $ U(a, c, z) $, $ a \to \infty $, $
z > 0 $, $ c < 1 $ / 380 \\
27.5.2 Expansion of $ _1F_1(a; c; z), $ a \to \infty $,
$ z > 0 $, $ c > 1 $ / 381 \\
28. Expansions in terms of Kummer functions / 383 \\
28.1 Approximation in terms of the Kummer J7-function /
383 \\
28.1.1 Constructing the expansions / 384 \\
28.1.2 Expansion for the loop integral / 387 \\
28.2 The $ _2F_1 $ function, large $ c $, in terms of $
U $ / 387 \\
28.2.1 Legendre polynomials: Uniform expansions / 388
\\
28.3 The $ _2F_1 $ -function, large $ b $ : in terms of
$ _1F_1 $ / 389 \\
28.3.1 Using a real integral / 390 \\
28.3.2 Using a loop integral / 394 \\
28.4 Jacobi polynomials of large degree: Laguerre-type
expansion / 394 \\
28.4.1 Laguerre-type expansion for large values of /3 /
398 \\
28.5 Expansion of a Dirichlet-type integral / 401 \\
Part 6: Uniform Examples for Special Functions / 403
\\
29. Legendre functions / 405 \\
29.1 Expansions of $ P_\nu^\mu(z) $, $ Q_\nu^\mu(z) $;
$ \nu \to \infty $, $ z \geq 1 $ / 406 \\
29.1.1 Expansions for $ z > z_0 > 1 $ / 400 \\
29.1.2 Expansion in terms of modified Bessel functions
/ 407 \\
29.1.3 Expansions of $ P_\nu^\mu(z) $ and $
Q_\nu^\mu(z) $ in terms of Bessel functions / 411 \\
29.2 Expansions of $ P_\nu^\mu(z) $, $ Q_\nu^\mu(z) $;
$ p \to \infty $, $ z > 1 $ / 412 \\
29.2.1 Expansions for bounded $ z $ / 412 \\
29.2.2 Expansions in terms of modified Bessel functions
/ 412 \\
29.2.3 Expansions of $ P_\nu^\mu(z) $ and $
Q_\nu^\mu(z) $ / 413 \\
29.3 Integrals with nearly coincident branch points /
414 \\
29.3.1 Ursell's expansions of Legendre functions / 415
\\
29.3.2 Coefficients of the expansion / 416 \\
29.3.3 An alternative expansion of $ P_n^m(\cosh z) $ /
417 \\
29.3.4 A related integral with nearly coincident branch
points / 418 \\
29.4 Toroidal harmonics and conical functions / 418 \\
30. Parabolic cylinder functions: Large parameter / 419
\\
30.1 Notation for uniform asymptotic expansions / 419
\\
30.2 The case $ a < 0 $ / 421 \\
30.2.1 The case $ z > 2\sqrt{-a} $ : $ -a + z \to
\infty $ / 421 \\
30.2.2 The case $ z < -2\sqrt{-a} $ : $ -a - z \to
\infty $ / 422 \\
30.2.3 The case -2\sqrt{-a} < z < 2\sqrt{-a} / 423 \\
30.3 The case $ a > 0 $ / 424 \\
30.3.1 The case $ z > 0 $, $ a + z \to \infty $ / 425
\\
30.3.2 The case $ z < 0 $, $ a - z \to \infty $ / 425
\\
30.4 Expansions from integral representations / 426 \\
30.4.1 The case $ a > 0 $, $ z > 0 $; $ a + z \to
\infty $ / 426 \\
30.4.2 The case $ a > 0 $, $ z < 0 $; $ a - z \to
\infty $ / 428 \\
30.4.3 The case $ a < 0 $, $ |z| > 2\sqrt{-a} $; $ -a +
|z| \to \infty $ / 429 \\
30.5 Airy-type expansions / 430 \\
31. Coulomb wave functions / 433 \\
31.1 Contour integrals for Coulomb functions / 434 \\
31.2 Expansions for $ \rho \to \infty $ and bounded $
\eta $ / / 435 \\
31.3 Expansions for $ \eta \to \infty $ and bounded $
\rho $ / 437 \\
31.4 Expansions for $ \eta \to -\infty $ and bounded $
\rho $ / 439 \\
31.5 Expansions for $ \eta \to -\infty and $ \rho \geq
\rho_0 > 0 $ / 440 \\
31.6 Expansions for $ \eta \to -\infty $ and $ \rho
\geq 0 $ / 442 \\
31.7 Expansions for $ \eta $, $ \rho \to \infty $;
Airy-type expansions / 444 \\
32. Laguerre polynomials: Uniform expansions / 449 \\
32.1 An expansion for bounded $ z $ and $ a $ / 449 \\
32.2 An expansion for bounded $ z $; $ a $ depends on $
n $ / 451 \\
32.3 Expansions for bounded $ a $; $ z $ depends on $ n
$ / 454 \\
32.3.1 An expansion in terms of Airy functions / 455
\\
32.3.2 An expansion in terms of Bessel functions / 456
\\
32.4 An expansion in terms of Hermite polynomials;
large $ a $ / 458 \\
32.4.1 A first approximation / 459 \\
32.4.2 Transformation to the standard form / 460 \\
32.4.3 Approximating the zeros / 462 \\
33. Generalized Bessel polynomials / 465 \\
33.1 Relations to Bessel and Kummer functions / 466 \\
33.2 An expansion in terms of Laguerre polynomials /
467 \\
33.3 Expansions in terms of elementary functions / 470
\\
33.3.1 The case $ |\ph z| < \pi/2 $ / 470 \\
33.3.2 The case $ |\ph(-z)| < \pi/2 $ / 471 \\
33.3.3 Integral representations / 472 \\
33.3.4 Construction of the expansions / 472 \\
33.4 Expansions in terms of modified Bessel functions /
476 \\
33.4.1 Construction of the expansion / 476 \\
34. Stirling numbers / 479 \\
34.1 Definitions and integral representations / 479 \\
34.2 Stirling number of the second kind / 481 \\
34.2.1 Higher-order approximations / 483 \\
34.2.2 About the positive saddle point / 486 \\
34.2.3 About the quantity $ A $ / 487 \\
34.3 Stirling numbers of the first kind / 488 \\
35. Asymptotics of the integral $ \int_0^1 \cos(b x + a
/ x) \, dx $ / 491 \\
35.1 The case $ b < a $ / 491 \\
35.2 The case $ a = b $ / 493 \\
35.3 The case $ b > a $ / 494 \\
35.3.1 The contribution from $ \mathcal{P}_1 $ / 495
\\
35.3.2 The contribution from $ \mathcal{P}_2 $ / 496
\\
35.4 A Fresnel-type expansion / 497 \\
Part 7: A Class of Cumulative Distribution Functions /
499 \\
36. Expansions of a class of cumulative distribution
functions / 501 \\
36.1 Cumulative distribution functions: A standard form
/ 501 \\
36.2 An incomplete normal distribution function / 505
\\
36.3 The Sievert integral / 506 \\
36.4 The Pearson type IV distribution / 507 \\
36.5 The Von Mises distribution / 509 \\
36.5.1 An expansion near the lower endpoint of
integration / 511 \\
37. Incomplete gamma functions: Uniform expansions /
513 \\
37.1 Using the standard integral representations / 513
\\
37.2 Representations by contour integrals / 514 \\
37.2.1 Constructing the expansions / 516 \\
37.2.2 Details on the coefficients / 518 \\
37.2.3 Relations to the coefficients of earlier
expansions / 520 \\
37.3 Incomplete gamma functions, negative parameters /
520 \\
37.3.1 Expansions near the transition point / 522 \\
37.3.2 A real expansion of 7*(-a, -z) / 524 \\
38. Incomplete beta function / 525 \\
38.1 A power series expansion for large p / 526 \\
38.2 A uniform expansion for large p / 526 \\
38.3 The nearly symmetric case / 527 \\
38.4 The general error function case / 529 \\
39. Non-central chi-square, Marcum functions / 531 \\
39.1 Properties of the Marcum functions / 532 \\
39.2 More integral representations / 533 \\
39.3 Asymptotic expansion; $ \mu $ fixed, $ \xi $ large
/ 535 \\
39.4 Asymptotic expansion; $ \xi + \mu $ large / 537
\\
39.5 An expansion in terms of the incomplete gamma
function / 540 \\
39.6 Comparison of the expansions numerically / 543 \\
40. A weighted sum of exponentials / 545 \\
40.1 An integral representation / 546 \\
40.2 Saddle point analysis / 547 \\
40.3 Details on the coefficients / 548 \\
40.4 Auxiliary expansions / 550 \\
40.5 Numerical verification / 551 \\
41. A generalized incomplete gamma function / 553 \\
41.1 An expansion in terms of incomplete gamma
functions / 554 \\
41.2 An expansion in terms of Laguerre polynomials /
554 \\
41.3 An expansion in terms of Kummer functions / 555
\\
41.4 An expansion in terms of the error function / 555
\\
42. Asymptotic inversion of cumulative distribution
functions / 559 \\
42.1 The asymptotic inversion method / 559 \\
42.2 Asymptotic inversion of the gamma distribution /
561 \\
42.2.1 Numerical verification / 563 \\
42.2.2 Other asymptotic inversion methods / 564 \\
42.2.3 Asymptotics of the zeros of $ \Gamma(a, z) $ /
565 \\
42.3 Asymptotic inversion of the incomplete beta
function / 567 \\
42.3.1 Inverting by using the error function / 568 \\
42.3.2 Inverting by using the incomplete gamma function
/ 569 \\
42.3.3 Numerical verification / 572 \\
42.4 The hyperbolic cumulative distribution / 573 \\
42.4.1 Numerical verification / 574 \\
42.5 The Marcum functions / 575 \\
42.5.1 Asymptotic inversion / 576 \\
42.5.2 Asymptotic inversion with respect to $ x $ / 576
\\
42.5.3 Asymptotic inversion with respect to $ y $ / 579
\\
Bibliography / 583 \\
Index / 597",
}
@Article{Weiss:2015:ROS,
author = "Alexander K. H. Weiss and Christian Ochsenfeld",
title = "A rigorous and optimized strategy for the evaluation
of the {Boys} function kernel in molecular electronic
structure theory",
journal = j-J-COMPUT-CHEM,
volume = "36",
number = "18",
pages = "1390--1398",
day = "5",
month = jul,
year = "2015",
CODEN = "JCCHDD",
DOI = "https://doi.org/10.1002/jcc.23935",
ISSN = "0192-8651 (print), 1096-987X (electronic)",
ISSN-L = "0192-8651",
bibdate = "Sat Jul 25 20:32:35 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputchem2010.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0192-8651",
onlinedate = "13 May 2015",
}
@Article{Xu:2015:CFC,
author = "Ai-Min Xu and Zhong-Di Cen",
title = "Closed formulas for computing higher-order derivatives
of functions involving exponential functions",
journal = j-APPL-MATH-COMP,
volume = "270",
number = "??",
pages = "136--141",
day = "1",
month = nov,
year = "2015",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2015.08.051",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu Nov 5 06:24:28 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315011066",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
keywords = "closed formula; derivatives of exponential functions;
derivatives of trigonometric functions; higher-order
derivative; hyperbolic function; tangent number;
trigonometric function",
remark = "The authors derive closed-form $n$-term sums for the
$n$-th order derivatives of exponential and
trigonometric functions. The sums involve factorials,
powers, and Stirling numbers of the first and second
kinds. At the end of their paper, they derive a new
computationally-stable formula for the tangent numbers,
$ T_{2 n + 1} = \sum_{k = 1}^n \binom {2 n}{2 k - 1}
T_{2 k - 1} T_{2(n - k) + 1}$, a sum that involves only
positive terms. There is a stable recurrence relation
discussed in the MathCW book that is likely faster,
because it requires only 2 multiplies and 1 add in each
term of the recurrence.",
}
@Article{Yang:2015:AFG,
author = "Zhen-Hang Yang and Yu-Ming Chu",
title = "Asymptotic formulas for gamma function with
applications",
journal = j-APPL-MATH-COMP,
volume = "270",
number = "??",
pages = "665--680",
day = "1",
month = nov,
year = "2015",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2015.08.087",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu Nov 5 06:24:28 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315011431",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Yang:2015:SBP,
author = "Zhen-Hang Yang and Yu-Ming Chu and Xiao-Hui Zhang",
title = "Sharp bounds for psi function",
journal = j-APPL-MATH-COMP,
volume = "268",
number = "??",
pages = "1055--1063",
day = "1",
month = oct,
year = "2015",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2015.07.012",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Sep 16 06:56:32 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315009248",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
keywords = "Gamma function; Monotonicity; Psi function",
}
@Article{Zhang:2015:EAR,
author = "Jianfeng Zhang and Paul Chow and Hengzhu Liu",
title = "An Enhanced Adaptive Recoding Rotation {CORDIC}",
journal = j-TRETS,
volume = "9",
number = "1",
pages = "4:1--4:??",
month = nov,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2812813",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Tue Dec 22 16:19:56 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "The Conventional Coordinate Rotation Digital Computer
(CORDIC) algorithm has been widely used in many
applications, particularly in Direct Digital Frequency
Synthesizers (DDS) and Fast Fourier Transforms (FFT).
However, CORDIC is constrained by the excessive number
of iterations, angle data path, and scaling factor
compensation. In this article, an enhanced adaptive
recoding CORDIC (EARC) is proposed. It uses the
enhanced adaptive recoding method to reduce the
required iterations and adopts the trigonometric
transformation scheme to scale up the rotation angles.
Computing sine and cosine is used first to compare the
core functionality of EARC with basic CORDIC; then a
16-bit DDS and a 1,024-point FFT based on EARC are
evaluated to demonstrate the benefits of EARC in larger
applications. All the proposed architectures are
validated on a Virtex 5 FPGA development platform.
Compared with a commercial implementation of CORDIC,
EARC requires 33.3\% less hardware resources, provides
a twofold speedup, dissipates 70.4\% less power, and
improves accuracy in terms of the Bit Error Position
(BEP). Compared to the state-of-the-art Hybrid CORDIC,
EARC reduces latency by 11.1\% and consumes 17\% less
power. Compared with a commercial implementation of
DDS, the dissipated power of the proposed DDS is
reduced by 27.2\%. The proposed DDS improves
Spurious-Free Dynamic Range (SFDR) by nearly 7 dBc and
dissipates 21.8\% less power when compared with a
recently published DDS circuit. The FFT based on EARC
dissipates a factor of 2.05 less power than the
commercial FFT even when choosing the 100\% toggle rate
for the FFT based on EARC and the 12.5\% toggle rate
for the commercial FFT. Compared with a recently
published FFT, the FFT based on EARC improves
Signal-to-Noise Ratio (SNR) by 8.9 dB and consumes
7.78\% less power.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@Article{Abel:2016:HOA,
author = "Ulrich Abel",
title = "High order algorithms for calculating roots",
journal = j-MATH-GAZ,
volume = "100",
number = "549",
pages = "420--428",
month = nov,
year = "2016",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.1017/mag.2016.106",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Thu Nov 17 10:32:54 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
URL = "https://www.cambridge.org/core/product/2FACD442DB78364B04DA2E64BA06F269",
acknowledgement = ack-nhfb,
ajournal = "Math. Gaz.",
fjournal = "The Mathematical Gazette",
journal-URL = "http://journals.cambridge.org/action/displayIssue?jid=MAG;
http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
onlinedate = "17 October 2016",
}
@Article{Aprahamian:2016:MIT,
author = "Mary Aprahamian and Nicholas J. Higham",
title = "Matrix Inverse Trigonometric and Inverse Hyperbolic
Functions: Theory and Algorithms",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "37",
number = "4",
pages = "1453--1477",
month = "????",
year = "2016",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/16M1057577",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Aug 25 09:01:43 MDT 2017",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2016",
}
@Article{Bailey:2016:CSC,
author = "D. H. Bailey and J. M. Borwein",
title = "Computation and structure of character polylogarithms
with applications to character
{Mordell--Tornheim--Witten} sums",
journal = j-MATH-COMPUT,
volume = "85",
number = "297",
pages = "295--324",
month = "",
year = "2016",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/2974",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Feb 8 17:02:07 MST 2016",
bibsource = "http://www.ams.org/mcom/2016-85-297;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3;
http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3/S0025-5718-2015-02974-3.pdf;
http://www.ams.org/mathscinet/search/author.html?authorName=Borwein%2C%20J.%20M;
http://www.ams.org/mathscinet/search/author.html?mrauthid=29355",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bao:2016:SAO,
author = "Vo Nguyen Quoc Bao and Luu Pham Tuyen and Huynh Huu
Tue",
title = "A Survey on Approximations of One-Dimensional
{Gaussian} {$Q$}-Function",
journal = "{REV} Journal on Electronics and Communications",
volume = "5",
number = "1--2",
month = feb,
year = "2016",
DOI = "https://doi.org/10.21553/rev-jec.92",
bibdate = "Sat Dec 16 15:18:22 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.rev-jec.org/index.php/rev-jec/article/view/92",
acknowledgement = ack-nhfb,
journal-URL = "http://www.rev-jec.org/index.php/rev-jec/",
}
@Article{Bytev:2016:HHF,
author = "Vladimir V. Bytev and Bernd A. Kniehl",
title = "{HYPERDIRE} --- {HYPERgeometric functions DIfferential
REduction}: {Mathematica}-based packages for the
differential reduction of generalized hypergeometric
functions: {Lauricella} function {$ F_c $} of three
variables",
journal = j-COMP-PHYS-COMM,
volume = "206",
number = "??",
pages = "78--83",
month = sep,
year = "2016",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2016.04.016",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 10 18:27:25 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465516301059",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655/",
}
@Article{Chen:2016:AEG,
author = "Chao-Ping Chen",
title = "On the asymptotic expansions of the gamma function
related to the {Nemes}, {Gosper} and {Burnside}
formulas",
journal = j-APPL-MATH-COMP,
volume = "276",
number = "??",
pages = "417--431",
day = "5",
month = mar,
year = "2016",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Jan 26 17:22:21 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315016057",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Chen:2016:IAEa,
author = "Chao-Ping Chen and Long Lin",
title = "Inequalities and asymptotic expansions for the gamma
function related to {Mortici}'s formula",
journal = j-J-NUMBER-THEORY,
volume = "162",
number = "??",
pages = "578--588",
month = may,
year = "2016",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2015.09.014",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:20 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X15003133",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Chen:2016:IAEb,
author = "Chao-Ping Chen",
title = "Inequalities and asymptotic expansions for the psi
function and the {Euler--Mascheroni} constant",
journal = j-J-NUMBER-THEORY,
volume = "163",
number = "??",
pages = "596--607",
month = jun,
year = "2016",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2015.10.013",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:20 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X15003558",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Chen:2016:IAEc,
author = "Chao-Ping Chen",
title = "Inequalities and asymptotics for the
{Euler--Mascheroni} constant based on {DeTemple's}
result",
journal = j-NUMER-ALGORITHMS,
volume = "73",
number = "3",
pages = "761--774",
month = nov,
year = "2016",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-016-0116-9",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Mar 1 09:12:13 MST 2017",
bibsource = "http://link.springer.com/journal/11075/73/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-016-0116-9",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Chen:2016:MAA,
author = "Chao-Ping Chen",
title = "A more accurate approximation for the gamma function",
journal = j-J-NUMBER-THEORY,
volume = "164",
number = "??",
pages = "417--428",
month = jul,
year = "2016",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2015.11.007",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:21 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X16000068",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Chen:2016:MPI,
author = "Chao-Ping Chen",
title = "Monotonicity properties, inequalities and asymptotic
expansions associated with the gamma function",
journal = j-APPL-MATH-COMP,
volume = "283",
number = "??",
pages = "385--396",
day = "20",
month = jun,
year = "2016",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Apr 5 07:51:07 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300316301515",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Chen:2016:SIAa,
author = "Chao-Ping Chen and Wei-Wei Tong",
title = "Sharp inequalities and asymptotic expansions for the
gamma function",
journal = j-J-NUMBER-THEORY,
volume = "160",
number = "??",
pages = "418--431",
month = mar,
year = "2016",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2015.09.021",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:18 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X15003200",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Erascu:2016:RQE,
author = "Madalina Erascu and Hoon Hong",
title = "Real quantifier elimination for the synthesis of
optimal numerical algorithms (Case study: Square root
computation)",
journal = j-J-SYMBOLIC-COMP,
volume = "75",
number = "??",
pages = "110--126",
month = jul # "\slash " # aug,
year = "2016",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Mon Jan 25 06:25:01 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0747717115001091",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171/",
keywords = "interval arithmetic; interval square root",
}
@TechReport{Fateman:2016:CUA,
author = "Richard J. Fateman",
title = "Comments on Unrestricted Algorithms for {Bessel}
Functions in Computer Algebra: Arbitrary Precision, The
Backwards Recurrence, {Taylor} Series, {Hermite}
Interpolation",
type = "Report",
institution = "University of California, Berkeley",
address = "Berkeley, CA 947220-1776, USA",
day = "4",
month = jun,
year = "2016",
bibdate = "Fri Feb 24 09:55:02 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://people.eecs.berkeley.edu/~fateman/papers/hermite.pdf",
abstract = "We explore various ways of implementing ``unrestricted
algorithms'' [3] for approximating Bessel ($J$)
functions. An unrestricted algorithm for a function $
f(x)$ provides a result to any requested precision in
the answer. The emphasis is on higher-than-normal
precision with the precision specified as an extra
argument to the function. That is, the precision is
specified at run-time. We require that the algorithm
provide at least the requested number of correct
digits, contrary to some existing codes which provide
only ``absolute error'' near critical points. We use $
J_0 $ of real non-negative argument as an example,
although much of the reasoning generalizes to other
Bessel functions or related functions.\par
Since it is plausible that there will be requests for
additional values of $ J_0 $ at the same (high)
precision at a collection of nearby arguments, we
consider implementations that cache certain re-usable
key constants (namely zeros of $ J_0 $ near the
argument values).",
acknowledgement = ack-nhfb,
}
@Article{Gautschi:2016:AER,
author = "Walter Gautschi",
title = "Algorithm 957: Evaluation of the Repeated Integral of
the Coerror Function by Half-Range {Gauss--Hermite}
Quadrature",
journal = j-TOMS,
volume = "42",
number = "1",
pages = "9:1--9:10",
month = feb,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2735626",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 1 17:07:56 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Nonstandard Gaussian quadrature is applied to evaluate
the repeated integral $ i^n \erfc x $ of the coerror
function for $ n \in N_0 $, $ x \in R $ in an
appropriate domain of the $ (n, x)$-plane. Relevant
software in MATLAB is provided: in particular, two
routines evaluating the function to an accuracy of 12
respective 30-decimal digits.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gil:2016:ACI,
author = "Amparo Gil and Diego Ruiz-Antol{\'\i}n and Javier
Segura and Nico M. Temme",
title = "{Algorithm 969}: Computation of the Incomplete Gamma
Function for Negative Values of the Argument",
journal = j-TOMS,
volume = "43",
number = "3",
pages = "26:1--26:9",
month = nov,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2972951",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Nov 22 17:45:25 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://dl.acm.org/citation.cfm?id=2972951",
abstract = "An algorithm for computing the incomplete gamma
function $ \gamma^(a, z) $ for real values of the
parameter $a$ and negative real values of the argument
$z$ is presented. The algorithm combines the use of
series expansions, Poincar{\'e}-type expansions,
uniform asymptotic expansions, and recurrence
relations, depending on the parameter region. A
relative accuracy $ \approx 10^{-13}$ in the parameter
region $ (a, z) \in [500, 500] \times [500, 0)$ can be
obtained when computing the function $ \gamma^\ast (a,
z)$ with the Fortran 90 module IncgamNEG implementing
the algorithm.",
acknowledgement = ack-nhfb,
articleno = "26",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Giles:2016:AAI,
author = "Michael B. Giles",
title = "Algorithm 955: Approximation of the Inverse {Poisson}
Cumulative Distribution Function",
journal = j-TOMS,
volume = "42",
number = "1",
pages = "7:1--7:22",
month = feb,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2699466",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 1 17:07:56 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "New approximations for the inverse of the incomplete
gamma function are derived, which are used to develop
efficient evaluations of the inverse Poisson cumulative
distribution function. An asymptotic approximation
based on the standard Normal approximation is
particularly good for CPUs with MIMD cores, while for
GPUs and other hardware with vector units, a second
asymptotic approximation based on Temme's approximation
of the incomplete gamma function is more efficient due
to conditional branching within each vector. The
accuracy and efficiency of the software implementations
is assessed on both CPUs and GPUs.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Jameson:2016:IGF,
author = "G. J. O. Jameson",
title = "The incomplete gamma functions",
journal = j-MATH-GAZ,
volume = "100",
number = "548",
pages = "298--306",
month = jul,
year = "2016",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.1017/mag.2016.67",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Tue Sep 27 10:11:13 MDT 2016",
bibsource = "http://journals.cambridge.org/action/displayIssue?jid=MAG;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
URL = "https://www.cambridge.org/core/product/9373A31AD28D793AB5431E35EA5C2AF6",
acknowledgement = ack-nhfb,
ajournal = "Math. Gaz.",
fjournal = "The Mathematical Gazette",
journal-URL = "http://journals.cambridge.org/action/displayIssue?jid=MAG;
http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
onlinedate = "14 June 2016",
remark = "This paper exhibits and proves several useful
identities for the incomplete gamma functions, but does
not discuss their stable numerical computation.",
}
@Article{Johansson:2016:CHF,
author = "Fredrik Johansson",
title = "Computing hypergeometric functions rigorously",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "2--29",
day = "22",
month = jun,
year = "2016",
bibdate = "Thu Jun 23 07:39:32 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://arxiv.org/abs/1606.06977",
abstract = "We present an efficient implementation of
hypergeometric functions in arbitrary-precision
interval arithmetic. The functions 0F1, 1F1, 2F1 and
2F0 (or the Kummer U-function) are supported for
unrestricted complex parameters and argument, and by
extension, we cover exponential and trigonometric
integrals, error functions, Fresnel integrals,
incomplete gamma and beta functions, Bessel functions,
Airy functions, Legendre functions, Jacobi polynomials,
complete elliptic integrals, and other special
functions. The output can be used directly for interval
computations or to generate provably correct
floating-point approximations in any format.
Performance is competitive with earlier
arbitrary-precision software, and sometimes orders of
magnitude faster. We also partially cover the
generalized hypergeometric function pFq and computation
of high-order parameter derivatives.",
acknowledgement = ack-nhfb,
}
@Article{Johansson:2016:FAE,
author = "H. T. Johansson and C. Forss{\'e}n",
title = "Fast and Accurate Evaluation of {Wigner} 3$j$, 6$j$,
and 9$j$ Symbols Using Prime Factorization and
Multiword Integer Arithmetic",
journal = j-SIAM-J-SCI-COMP,
volume = "38",
number = "1",
pages = "A376--A384",
month = "????",
year = "2016",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/15M1021908",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Tue Jun 21 08:11:55 MDT 2016",
bibsource = "http://epubs.siam.org/toc/sjoce3/38/1;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2016",
}
@Article{Koelink:2016:AST,
author = "Erik Koelink",
title = "Applications of spectral theory to special functions",
journal = "ArXiv e-prints",
volume = "??",
pages = "1--63",
month = dec,
year = "2016",
bibdate = "Sat Feb 18 09:23:20 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://arxiv.org/abs/1612.07035",
abstract = "Many special functions are eigenfunctions to explicit
operators, such as difference and differential
operators, which is in particular true for the special
functions occurring in the Askey-scheme, its
$q$-analogue and extensions. The study of the spectral
properties of such operators leads to explicit
information for the corresponding special functions. We
discuss several instances of this application,
involving orthogonal polynomials and their
matrix-valued analogues.",
acknowledgement = ack-nhfb,
eprint = "1612.07035",
keywords = "Mathematics --- Classical Analysis and ODEs;
Mathematics --- Functional Analysis",
primaryclass = "math.CA",
}
@Article{Kutsuna:2016:ARM,
author = "Takuro Kutsuna and Yoshinao Ishii",
title = "Abstraction and refinement of mathematical functions
toward {SMT}-based test-case generation",
journal = j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
volume = "18",
number = "1",
pages = "109--120",
month = feb,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10009-015-0389-7",
ISSN = "1433-2779 (print), 1433-2787 (electronic)",
ISSN-L = "1433-2779",
bibdate = "Mon Jan 25 08:12:53 MST 2016",
bibsource = "http://link.springer.com/journal/10009/18/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
https://www.math.utah.edu/pub/tex/bib/sttt.bib",
URL = "http://link.springer.com/article/10.1007/s10009-015-0389-7",
acknowledgement = ack-nhfb,
fjournal = "International Journal on Software Tools for Technology
Transfer (STTT)",
journal-URL = "http://link.springer.com/journal/10009",
}
@InProceedings{Langhammer:2016:SPN,
author = "Martin Langhammer and Bogdan Pasca",
title = "Single Precision Natural Logarithm Architecture for
Hard Floating-Point and {DSP}-Enabled {FPGAs}",
crossref = "Montuschi:2016:ISC",
pages = "164--171",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.20",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@InProceedings{LeMaire:2016:CFP,
author = "Julien {Le Maire} and Nicolas Brunie and Florent de
Dinechin and Jean-Michel Muller",
title = "Computing floating-point logarithms with fixed-point
operations",
crossref = "Montuschi:2016:ISC",
pages = "156--163",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.24",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Lu:2016:QCF,
author = "Dawei Lu and Lixin Song and Congxu Ma",
title = "A quicker continued fraction approximation of the
gamma function related to the {Windschitl}'s formula",
journal = j-NUMER-ALGORITHMS,
volume = "72",
number = "4",
pages = "865--874",
month = aug,
year = "2016",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-015-0070-y",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Tue Sep 20 10:57:47 MDT 2016",
bibsource = "http://link.springer.com/journal/11075/72/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-015-0070-y",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "The tables at the end of this paper compare six
algorithms for approximating $ n! $ for $ n = 50, 100,
500, 2500 $. The Burnside, Nemes, and Windschitl
formulas are slightly less accurate than the
traditional Stirling approximation. The new formula,
and the Mortici formula, are slightly better than
Stirling's.",
}
@Article{Maignan:2016:FGL,
author = "Aude Maignan and Tony C. Scott",
title = "Fleshing out the generalized {Lambert} {$W$}
function",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "50",
number = "2",
pages = "45--60",
month = jun,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2992274.2992275",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Thu Aug 25 17:57:39 MDT 2016",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
abstract = "Herein, we use Hardy's notion of the ``false
derivative'' to obtain exact multiple roots in closed
form of the transcendental--algebraic equations
representing the generalized Lambert $W$ function. In
this fashion, we flesh out the generalized Lambert $W$
function by complementing previous developments to
produce a more complete and integrated body of work.
Finally, we demonstrate the usefulness of this special
function with some applications.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Martin-Dorel:2016:PTB,
author = "{\'E}rik Martin-Dorel and Guillaume Melquiond",
title = "Proving Tight Bounds on Univariate Expressions with
Elementary Functions in {Coq}",
journal = j-J-AUTOM-REASON,
volume = "57",
number = "3",
pages = "187--217",
month = oct,
year = "2016",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-015-9350-4",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Fri Sep 2 06:39:36 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/s10817-015-9350-4",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
}
@Article{Mohankumar:2016:VAN,
author = "N. Mohankumar and A. Natarajan",
title = "On the very accurate numerical evaluation of the
{Generalized Fermi--Dirac Integrals}",
journal = j-COMP-PHYS-COMM,
volume = "207",
number = "??",
pages = "193--201",
month = oct,
year = "2016",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Tue Aug 30 18:08:51 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465516301667",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655/",
}
@Article{Moroz:2016:FCI,
author = "Leonid V. Moroz and Cezary J. Walczyk and Andriy
Hrynchyshyn and Vijay Holimath and Jan L.
Cie{\'s}li{\'n}ski",
title = "Fast calculation of inverse square root with the use
of magic constant --- analytical approach",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--23",
day = "14",
month = mar,
year = "2016",
DOI = "https://doi.org/10.48550/arXiv.1603.04483",
bibdate = "Wed Dec 20 07:34:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/pdf/1603.04483.pdf",
abstract = "We present a mathematical analysis of transformations
used in fast calculation of inverse square root for
single-precision floating-point numbers. Optimal values
of the so called magic constants are derived in a
systematic way, minimizing either absolute or relative
errors at subsequent stages of the discussed
algorithm.",
acknowledgement = ack-nhfb,
}
@Misc{Munshi:2016:OCS,
author = "Aaftab Munshi and Lee Howes and Bartosz Sochacki and
{Khronos OpenCL Working Group}",
title = "The {OpenCL} {C} Specification Version: 2.0 Document
Revision: 33",
howpublished = "Web document.",
pages = "205",
day = "13",
month = apr,
year = "2016",
bibdate = "Mon Apr 16 14:05:49 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "https://www.khronos.org/registry/OpenCL/specs/opencl-2.0-openclc.pdf",
acknowledgement = ack-nhfb,
remark = "Section 6.1.3.2 Math Functions, pages 74ff, defines a
function repertoire extended beyond that of ISO C,
including {\tt acospi}, {\tt asinpi}, {\tt atanpi},
{\tt atan2pi}, {\tt cospi}, {\tt sinpi}, {\tt tanpi},
{\tt cospi}, {\tt fract}, {\tt lgamma\_r}, {\tt mad}
(approximation to {\tt a * b + c}), {\tt minmag}, {\tt
pown}, {\tt rootn}, {\tt sincos}, {\tt sinpi}, and {\tt
tanpi}.",
}
@InProceedings{Navas-Palencia:2016:CCH,
author = "Guillermo Navas-Palencia and Argimiro Arratia",
title = "On the Computation of Confluent Hypergeometric
Functions for Large Imaginary Part of Parameters $b$
and $z$",
crossref = "Greuel:2016:MSI",
pages = "241--248",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-42432-3_30",
bibdate = "Mon Feb 5 08:27:34 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{OSullivan:2016:ZD,
author = "Cormac O'Sullivan",
title = "Zeros of the dilogarithm",
journal = j-MATH-COMPUT,
volume = "85",
number = "302",
pages = "2967--2993",
month = nov,
year = "2016",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3065",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sat Nov 5 12:22:19 MDT 2016",
bibsource = "http://www.ams.org/mcom/2016-85-302;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2016-85-302/S0025-5718-2016-03065-3;
http://www.ams.org/journals/mcom/2016-85-302/S0025-5718-2016-03065-3/S0025-5718-2016-03065-3.pdf;
http://www.ams.org/mathscinet/search/author.html?mrauthid=658848",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Ozcag:2016:RPI,
author = "Emin {\"O}zc{\d{a}}{\u{g}} and {\.I}nci Ege",
title = "Remarks on polygamma and incomplete gamma type
functions",
journal = j-J-NUMBER-THEORY,
volume = "169",
number = "??",
pages = "369--387",
month = dec,
year = "2016",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2016.05.021",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:24 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X16301378",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Paris:2016:UAE,
author = "R. B. Paris",
title = "A uniform asymptotic expansion for the incomplete
gamma functions revisited",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "1--9",
day = "2",
month = nov,
year = "2016",
bibdate = "Sat Feb 18 09:13:43 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://arxiv.org/abs/1611.00548",
abstract = "A new uniform asymptotic expansion for the incomplete
gamma function $ \Gamma (a, z) $ valid for large values
of $z$ was given by the author in
\cite{Paris:2002:UAE}. This expansion contains a
complementary error function of an argument measuring
transition across the point $ z = a$, with easily
computable coefficients that do not involve a removable
singularity in the neighbourhood of this point. In this
note we correct a misprint in the listing of certain
coefficients in this expansion and discuss in more
detail the situation corresponding to $ \Gamma (a,
a)$.",
acknowledgement = ack-nhfb,
remark = "Page 9 gives corrections to \cite[Eq.
8.12.18--8.12.20]{Olver:2010:NHM}.",
}
@Article{Piparo:2016:CPT,
author = "D. Piparo and V. Innocente",
title = "The {CptnHook Profiler} --- a tool to investigate
usage patterns of mathematical functions",
journal = "Journal of Physics: Conference Series",
volume = "762",
pages = "012038:1--012038:",
month = oct,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1088/1742-6596/762/1/012038",
ISSN = "1742-6588 (print), 1742-6596 (electronic)",
ISSN-L = "1742-6588",
bibdate = "Thu Sep 19 14:53:02 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Revy:2016:ADF,
author = "Guillaume Revy",
title = "Automated Design of Floating-Point Logarithm Functions
on Integer Processors",
crossref = "Montuschi:2016:ISC",
pages = "172--180",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.28",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Sayed:2016:WCR,
author = "Wafaa S. Sayed and Hossam A. H. Fahmy",
title = "What are the Correct Results for the Special Values of
the Operands of the Power Operation?",
journal = j-TOMS,
volume = "42",
number = "2",
pages = "14:1--14:17",
month = jun,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2809783",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Jun 3 18:52:21 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Language standards such as C99 and C11, as well as the
IEEE Standard for Floating-Point Arithmetic 754 (IEEE
Std 754-2008) specify the expected behavior of binary
and decimal floating-point arithmetic in
computer-programming environments and the handling of
special values and exception conditions. Many
researchers focus on verifying the compliance of
implementations for binary and decimal floating-point
operations with these standards. In this article, we
are concerned with the special values of the operands
of the power function Z = X$^Y$. We study how the
standards define the correct results for this
operation, propose a mathematically justified
definition for the correct results of the power
function on the occurrence of these special values as
its operands, test how different software
implementations for the power function deal with these
special values, and classify the behavior of different
programming languages from the viewpoint of how much
they conform to the standards and our proposed
mathematical definition. We present inconsistencies
between the implementations and the standards, and
discuss incompatibilities between different versions of
the same software.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Schmidt:2016:ZSG,
author = "Maxie D. Schmidt",
title = "Zeta Series Generating Function Transformations
Related to Generalized {Stirling} Numbers and Partial
Sums of the {Hurwitz} Zeta Function",
journal = "arxiv.org",
month = nov,
year = "2016",
bibdate = "Sat Feb 18 09:26:39 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://adsabs.harvard.edu/abs/2016arXiv161100957S",
abstract = "We define a generalized class of modified zeta series
transformations generating the partial sums of the
Hurwitz zeta function and series expansions of the
Lerch transcendent function. The new transformation
coefficients we define within the article satisfy
expansions by generalized harmonic number sequences, or
the partial sums of the Hurwitz zeta function, which
are analogous to known properties for the Stirling
numbers of the first kind and for the known
transformation coefficients employed to enumerate
variants of the polylogarithm function series.
Applications of the new results we prove in the article
include new series expansions of the Dirichlet beta
function, the Legendre chi function, BBP-type series
identities for special constants, alternating and
exotic Euler sum variants, alternating zeta functions
with powers of quadratic denominators, and particular
series defining special cases of the Riemann zeta
function constants at the positive integers $ s \geq 3
$.",
acknowledgement = ack-nhfb,
eprint = "1611.00957",
keywords = "Mathematics - Combinatorics, Mathematics - Number
Theory",
primaryclass = "math.CO",
}
@Article{Stange:2016:CAM,
author = "J. Stange and N. Loginova and T. Dickhaus",
title = "Computing and approximating multivariate chi-square
probabilities",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "86",
number = "6",
pages = "1233--1247",
year = "2016",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949655.2015.1058798",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Thu Feb 4 07:57:25 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00949655.2015.1058798",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Stefanica:2016:SAA,
author = "Dan Stefanica and Rado{\v{s}} Radoi{\v{c}}i{\'c}",
title = "A sharp approximation for {ATM}-forward option prices
and implied volatilities",
journal = "International Journal of Financial Engineering",
volume = "3",
number = "1",
pages = "1650002",
month = mar,
year = "2016",
DOI = "https://doi.org/10.1142/s242478631650002x",
ISSN = "2424-7863",
bibdate = "Sat Dec 16 17:46:33 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Wang:2016:AFG,
author = "Miao-Kun Wang and Yu-Ming Chu and Ying-Qing Song",
title = "Asymptotical formulas for {Gaussian} and generalized
hypergeometric functions",
journal = j-APPL-MATH-COMP,
volume = "276",
number = "??",
pages = "44--60",
day = "5",
month = mar,
year = "2016",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Jan 26 17:22:21 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315015908",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Wang:2016:UAA,
author = "Weiping Wang",
title = "Unified approaches to the approximations of the gamma
function",
journal = j-J-NUMBER-THEORY,
volume = "163",
number = "??",
pages = "570--595",
month = jun,
year = "2016",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2015.12.016",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:20 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X16000470",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Xu:2016:AEG,
author = "Aimin Xu and Yongcai Hu and Peipei Tang",
title = "Asymptotic expansions for the gamma function",
journal = j-J-NUMBER-THEORY,
volume = "169",
number = "??",
pages = "134--143",
month = dec,
year = "2016",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2016.05.020",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:24 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X16301366",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Zaghloul:2016:RAC,
author = "Mofreh R. Zaghloul",
title = "Remark on {``Algorithm 916: Computing the Faddeyeva
and Voigt Functions''}: Efficiency Improvements and
{Fortran} Translation",
journal = j-TOMS,
volume = "42",
number = "3",
pages = "26:1--26:9",
month = may,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2806884",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon May 23 16:40:02 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Zaghloul:2011:ACF}.",
abstract = "This remark describes efficiency improvements to
Algorithm 916 [Zaghloul and Ali 2011]. It is shown that
the execution time required by the algorithm, when run
at its highest accuracy, may be improved by more than a
factor of 2. A better accuracy vs efficiency tradeoff
scheme is also implemented; this requires the user to
supply the number of significant figures desired in the
computed values as an extra input argument to the
function. Using this tradeoff, it is shown that the
efficiency of the algorithm may be further improved
significantly while maintaining reasonably accurate and
safe results that are free of the pitfalls and complete
loss of accuracy seen in other competitive techniques.
The current version of the code is provided in Matlab
and Scilab in addition to a Fortran translation
prepared to meet the needs of real-world problems where
very large numbers of function evaluations would
require the use of a compiled language. To fulfill this
last requirement, a recently proposed reformed version
of Huml{\'\i}cek's w4 routine, shown to maintain the
claimed accuracy of the algorithm over a wide and fine
grid, is implemented in the present Fortran translation
for the case of four significant figures. This latter
modification assures the reliability of the code in the
solution of practical problems requiring numerous
evaluation of the function for applications requiring
low-accuracy computations ($ < 10^{-4}$).",
acknowledgement = ack-nhfb,
articleno = "26",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Alonso:2017:EAA,
author = "Pedro Alonso and Javier Ib{\'a}{\~n}ez and Jorge
Sastre and Jes{\'u}s Peinado and Emilio Defez",
title = "Efficient and accurate algorithms for computing matrix
trigonometric functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "309",
number = "??",
pages = "325--332",
day = "1",
month = jan,
year = "2017",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:35:53 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042716302321",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Baikov:2017:AID,
author = "Nikita Baikov",
title = "Algorithm and Implementation Details for Complementary
Error Function",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "7",
pages = "1106--1118",
month = jul,
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2016.2641960",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jun 8 10:22:00 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "https://www.computer.org/csdl/trans/tc/2017/07/07792222-abs.html",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Beebe:2017:MFC,
author = "Nelson H. F. Beebe",
title = "The Mathematical-Function Computation Handbook:
Programming Using the {MathCW} Portable Software
Library",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxvi + 1114",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-64110-2",
ISBN = "3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)",
ISBN-13 = "978-3-319-64109-6 (hardcover), 978-3-319-64110-2
(e-book)",
LCCN = "QA75.5-76.95",
bibdate = "Sat Jul 15 19:34:43 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/mupad.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
URL = "http://www.springer.com/us/book/9783319641096",
acknowledgement = ack-nhfb,
ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
tableofcontents = "List of figures / xxv \\
List of tables / xxxi \\
Quick start / xxxv \\
1: Introduction / 1 \\
1.1: Programming conventions / 2 \\
1.2: Naming conventions / 4 \\
1.3: Library contributions and coverage / 5 \\
1.4: Summary / 6 \\
2: Iterative solutions and other tools / 7 \\
2.1: Polynomials and Taylor series / 7 \\
2.2: First-order Taylor series approximation / 8 \\
2.3: Second-order Taylor series approximation / 9 \\
2.4: Another second-order Taylor series approximation /
9 \\
2.5: Convergence of second-order methods / 10 \\
2.6: Taylor series for elementary functions / 10 \\
2.7: Continued fractions / 12 \\
2.8: Summation of continued fractions / 17 \\
2.9: Asymptotic expansions / 19 \\
2.10: Series inversion / 20 \\
2.11: Summary / 22 \\
3: Polynomial approximations / 23 \\
3.1: Computation of odd series / 23 \\
3.2: Computation of even series / 25 \\
3.3: Computation of general series / 25 \\
3.4: Limitations of Cody\slash Waite polynomials / 28
\\
3.5: Polynomial fits with Maple / 32 \\
3.6: Polynomial fits with Mathematica / 33 \\
3.7: Exact polynomial coefficients / 42 \\
3.8: Cody\slash Waite rational polynomials / 43 \\
3.9: Chebyshev polynomial economization / 43 \\
3.10: Evaluating Chebyshev polynomials / 48 \\
3.11: Error compensation in Chebyshev fits / 50 \\
3.12: Improving Chebyshev fits / 51 \\
3.13: Chebyshev fits in rational form / 52 \\
3.14: Chebyshev fits with Mathematica / 56 \\
3.15: Chebyshev fits for function representation / 57
\\
3.16: Extending the library / 57 \\
3.17: Summary and further reading / 58 \\
4: Implementation issues / 61 \\
4.1: Error magnification / 61 \\
4.2: Machine representation and machine epsilon / 62
\\
4.3: IEEE 754 arithmetic / 63 \\
4.4: Evaluation order in C / 64 \\
4.5: The {\tt volatile} type qualifier / 65 \\
4.6: Rounding in floating-point arithmetic / 66 \\
4.7: Signed zero / 69 \\
4.8: Floating-point zero divide / 70 \\
4.9: Floating-point overflow / 71 \\
4.10: Integer overflow / 72 \\
4.11: Floating-point underflow / 77 \\
4.12: Subnormal numbers / 78 \\
4.13: Floating-point inexact operation / 79 \\
4.14: Floating-point invalid operation / 79 \\
4.15: Remarks on NaN tests / 80 \\
4.16: Ulps --- units in the last place / 81 \\
4.17: Fused multiply-add / 85 \\
4.18: Fused multiply-add and polynomials / 88 \\
4.19: Significance loss / 89 \\
4.20: Error handling and reporting / 89 \\
4.21: Interpreting error codes / 93 \\
4.22: C99 changes to error reporting / 94 \\
4.23: Error reporting with threads / 95 \\
4.24: Comments on error reporting / 95 \\
4.25: Testing function implementations / 96 \\
4.26: Extended data types on Hewlett--Packard HP-UX
IA-64 / 100 \\
4.27: Extensions for decimal arithmetic / 101 \\
4.28: Further reading / 103 \\
4.29: Summary / 104 \\
5: The floating-point environment / 105 \\
5.1: IEEE 754 and programming languages / 105 \\
5.2: IEEE 754 and the mathcw library / 106 \\
5.3: Exceptions and traps / 106 \\
5.4: Access to exception flags and rounding control /
107 \\
5.5: The environment access pragma / 110 \\
5.6: Implementation of exception-flag and
rounding-control access / 110 \\
5.7: Using exception flags: simple cases / 112 \\
5.8: Using rounding control / 115 \\
5.9: Additional exception flag access / 116 \\
5.10: Using exception flags: complex case / 120 \\
5.11: Access to precision control / 123 \\
5.12: Using precision control / 126 \\
5.13: Summary / 127 \\
6: Converting floating-point values to integers / 129
\\
6.1: Integer conversion in programming languages / 129
\\
6.2: Programming issues for conversions to integers /
130 \\
6.3: Hardware out-of-range conversions / 131 \\
6.4: Rounding modes and integer conversions / 132 \\
6.5: Extracting integral and fractional parts / 132 \\
6.6: Truncation functions / 135 \\
6.7: Ceiling and floor functions / 136 \\
6.8: Floating-point rounding functions with fixed
rounding / 137 \\
6.9: Floating-point rounding functions: current
rounding / 138 \\
6.10: Floating-point rounding functions without {\em
inexact\/} exception / 139 \\
6.11: Integer rounding functions with fixed rounding /
140 \\
6.12: Integer rounding functions with current rounding
/ 142 \\
6.13: Remainder / 143 \\
6.14: Why the remainder functions are hard / 144 \\
6.15: Computing {\tt fmod} / 146 \\
6.16: Computing {\tt remainder} / 148 \\
6.17: Computing {\tt remquo} / 150 \\
6.18: Computing one remainder from the other / 152 \\
6.19: Computing the remainder in nonbinary bases / 155
\\
6.20: Summary / 156 \\
7: Random numbers / 157 \\
7.1: Guidelines for random-number software / 157 \\
7.2: Creating generator seeds / 158 \\
7.3: Random floating-point values / 160 \\
7.4: Random integers from floating-point generator /
165 \\
7.5: Random integers from an integer generator / 166
\\
7.6: Random integers in ascending order / 168 \\
7.7: How random numbers are generated / 169 \\
7.8: Removing generator bias / 178 \\
7.9: Improving a poor random number generator / 178 \\
7.10: Why long periods matter / 179 \\
7.11: Inversive congruential generators / 180 \\
7.12: Inversive congruential generators, revisited /
189 \\
7.13: Distributions of random numbers / 189 \\
7.14: Other distributions / 195 \\
7.15: Testing random-number generators / 196 \\
7.16: Applications of random numbers / 202 \\
7.17: The \textsf {mathcw} random number routines / 208
\\
7.18: Summary, advice, and further reading / 214 \\
8: Roots / 215 \\
8.1: Square root / 215 \\
8.2: Hypotenuse and vector norms / 222 \\
8.3: Hypotenuse by iteration / 227 \\
8.4: Reciprocal square root / 233 \\
8.5: Cube root / 237 \\
8.6: Roots in hardware / 240 \\
8.7: Summary / 242 \\
9: Argument reduction / 243 \\
9.1: Simple argument reduction / 243 \\
9.2: Exact argument reduction / 250 \\
9.3: Implementing exact argument reduction / 253 \\
9.4: Testing argument reduction / 265 \\
9.5: Retrospective on argument reduction / 265 \\
10: Exponential and logarithm / 267 \\
10.1: Exponential functions / 267 \\
10.2: Exponential near zero / 273 \\
10.3: Logarithm functions / 282 \\
10.4: Logarithm near one / 290 \\
10.5: Exponential and logarithm in hardware / 292 \\
10.6: Compound interest and annuities / 294 \\
10.7: Summary / 298 \\
11: Trigonometric functions / 299 \\
11.1: Sine and cosine properties / 299 \\
11.2: Tangent properties / 302 \\
11.3: Argument conventions and units / 304 \\
11.4: Computing the cosine and sine / 306 \\
11.5: Computing the tangent / 310 \\
11.6: Trigonometric functions in degrees / 313 \\
11.7: Trigonometric functions in units of $ \pi $ / 315
\\
11.8: Computing the cosine and sine together / 320 \\
11.9: Inverse sine and cosine / 323 \\
11.10: Inverse tangent / 331 \\
11.11: Inverse tangent, take two / 336 \\
11.12: Trigonometric functions in hardware / 338 \\
11.13: Testing trigonometric functions / 339 \\
11.14: Retrospective on trigonometric functions / 340
\\
12: Hyperbolic functions / 341 \\
12.1: Hyperbolic functions / 341 \\
12.2: Improving the hyperbolic functions / 345 \\
12.3: Computing the hyperbolic functions together / 348
\\
12.4: Inverse hyperbolic functions / 348 \\
12.5: Hyperbolic functions in hardware / 350 \\
12.6: Summary / 352 \\
13: Pair-precision arithmetic / 353 \\
13.1: Limitations of pair-precision arithmetic / 354
\\
13.2: Design of the pair-precision software interface /
355 \\
13.3: Pair-precision initialization / 356 \\
13.4: Pair-precision evaluation / 357 \\
13.5: Pair-precision high part / 357 \\
13.6: Pair-precision low part / 357 \\
13.7: Pair-precision copy / 357 \\
13.8: Pair-precision negation / 358 \\
13.9: Pair-precision absolute value / 358 \\
13.10: Pair-precision sum / 358 \\
13.11: Splitting numbers into pair sums / 359 \\
13.12: Premature overflow in splitting / 362 \\
13.13: Pair-precision addition / 365 \\
13.14: Pair-precision subtraction / 367 \\
13.15: Pair-precision comparison / 368 \\
13.16: Pair-precision multiplication / 368 \\
13.17: Pair-precision division / 371 \\
13.18: Pair-precision square root / 373 \\
13.19: Pair-precision cube root / 377 \\
13.20: Accuracy of pair-precision arithmetic / 379 \\
13.21: Pair-precision vector sum / 384 \\
13.22: Exact vector sums / 385 \\
13.23: Pair-precision dot product / 385 \\
13.24: Pair-precision product sum / 386 \\
13.25: Pair-precision decimal arithmetic / 387 \\
13.26: Fused multiply-add with pair precision / 388 \\
13.27: Higher intermediate precision and the FMA / 393
\\
13.28: Fused multiply-add without pair precision / 395
\\
13.29: Fused multiply-add with multiple precision / 401
\\
13.30: Fused multiply-add, Boldo/\penalty
\exhyphenpenalty Melquiond style / 403 \\
13.31: Error correction in fused multiply-add / 406 \\
13.32: Retrospective on pair-precision arithmetic / 407
\\
14: Power function / 411 \\
14.1: Why the power function is hard to compute / 411
\\
14.2: Special cases for the power function / 412 \\
14.3: Integer powers / 414 \\
14.4: Integer powers, revisited / 420 \\
14.5: Outline of the power-function algorithm / 421 \\
14.6: Finding $a$ and $p$ / 423 \\
14.7: Table searching / 424 \\
14.8: Computing $\log_n(g/a)$ / 426 \\
14.9: Accuracy required for $\log_n(g/a)$ / 429 \\
14.10: Exact products / 430 \\
14.11: Computing $w$, $w_1$ and $w_2$ / 433 \\
14.12: Computing $n^{w_2}$ / 437 \\
14.13: The choice of $q$ / 438 \\
14.14: Testing the power function / 438 \\
14.15: Retrospective on the power function / 440 \\
15: Complex arithmetic primitives / 441 \\
15.1: Support macros and type definitions / 442 \\
15.2: Complex absolute value / 443 \\
15.3: Complex addition / 445 \\
15.4: Complex argument / 445 \\
15.5: Complex conjugate / 446 \\
15.6: Complex conjugation symmetry / 446 \\
15.7: Complex conversion / 448 \\
15.8: Complex copy / 448 \\
15.9: Complex division: C99 style / 449 \\
15.10: Complex division: Smith style / 451 \\
15.11: Complex division: Stewart style / 452 \\
15.12: Complex division: Priest style / 453 \\
15.13: Complex division: avoiding subtraction loss /
455 \\
15.14: Complex imaginary part / 456 \\
15.15: Complex multiplication / 456 \\
15.16: Complex multiplication: error analysis / 458 \\
15.17: Complex negation / 459 \\
15.18: Complex projection / 460 \\
15.19: Complex real part / 460 \\
15.20: Complex subtraction / 461 \\
15.21: Complex infinity test / 462 \\
15.22: Complex NaN test / 462 \\
15.23: Summary / 463 \\
16: Quadratic equations / 465 \\
16.1: Solving quadratic equations / 465 \\
16.2: Root sensitivity / 471 \\
16.3: Testing a quadratic-equation solver / 472 \\
16.4: Summary / 474 \\
17: Elementary functions in complex arithmetic / 475
\\
17.1: Research on complex elementary functions / 475
\\
17.2: Principal values / 476 \\
17.3: Branch cuts / 476 \\
17.4: Software problems with negative zeros / 478 \\
17.5: Complex elementary function tree / 479 \\
17.6: Series for complex functions / 479 \\
17.7: Complex square root / 480 \\
17.8: Complex cube root / 485 \\
17.9: Complex exponential / 487 \\
17.10: Complex exponential near zero / 492 \\
17.11: Complex logarithm / 495 \\
17.12: Complex logarithm near one / 497 \\
17.13: Complex power / 500 \\
17.14: Complex trigonometric functions / 502 \\
17.15: Complex inverse trigonometric functions / 504
\\
17.16: Complex hyperbolic functions / 509 \\
17.17: Complex inverse hyperbolic functions / 514 \\
17.18: Summary / 520 \\
18: The Greek functions: gamma, psi, and zeta / 521 \\
18.1: Gamma and log-gamma functions / 521 \\
18.2: The {\tt psi} and {\tt psiln} functions / 536 \\
18.3: Polygamma functions / 547 \\
18.4: Incomplete gamma functions / 560 \\
18.5: A Swiss diversion: Bernoulli and Euler / 568 \\
18.6: An Italian excursion: Fibonacci numbers / 575 \\
18.7: A German gem: the Riemann zeta function / 579 \\
18.8: Further reading / 590 \\
18.9: Summary / 591 \\
19: Error and probability functions / 593 \\
19.1: Error functions / 593 \\
19.2: Scaled complementary error function / 598 \\
19.3: Inverse error functions / 600 \\
19.4: Normal distribution functions and inverses / 610
\\
19.5: Summary / 617 \\
20: Elliptic integral functions / 619 \\
20.1: The arithmetic-geometric mean / 619 \\
20.2: Elliptic integral functions of the first kind /
624 \\
20.3: Elliptic integral functions of the second kind /
627 \\
20.4: Elliptic integral functions of the third kind /
630 \\
20.5: Computing $K(m)$ and $K'(m)$ / 631 \\
20.6: Computing $E(m)$ and $E'(m)$ / 637 \\
20.7: Historical algorithms for elliptic integrals /
643 \\
20.8: Auxiliary functions for elliptic integrals / 645
\\
20.9: Computing the elliptic auxiliary functions / 648
\\
20.10: Historical elliptic functions / 650 \\
20.11: Elliptic functions in software / 652 \\
20.12: Applications of elliptic auxiliary functions /
653 \\
20.13: Elementary functions from elliptic auxiliary
functions / 654 \\
20.14: Computing elementary functions via $R_C(x,y)$ /
655 \\
20.15: Jacobian elliptic functions / 657 \\
20.16: Inverses of Jacobian elliptic functions / 664
\\
20.17: The modulus and the nome / 668 \\
20.18: Jacobian theta functions / 673 \\
20.19: Logarithmic derivatives of the Jacobian theta
functions / 675 \\
20.20: Neville theta functions / 678 \\
20.21: Jacobian Eta, Theta, and Zeta functions / 679
\\
20.22: Weierstrass elliptic functions / 682 \\
20.23: Weierstrass functions by duplication / 689 \\
20.24: Complete elliptic functions, revisited / 690 \\
20.25: Summary / 691 \\
21: Bessel functions / 693 \\
21.1: Cylindrical Bessel functions / 694 \\
21.2: Behavior of $J_n(x)$ and $Y_n(x)$ / 695 \\
21.3: Properties of $J_n(z)$ and $Y_n(z)$ / 697 \\
21.4: Experiments with recurrences for $J_0(x)$ / 705
\\
21.5: Computing $J_0(x)$ and $J_1(x)$ / 707 \\
21.6: Computing $J_n(x)$ / 710 \\
21.7: Computing $Y_0(x)$ and $Y_1(x)$ / 713 \\
21.8: Computing $Y_n(x)$ / 715 \\
21.9: Improving Bessel code near zeros / 716 \\
21.10: Properties of $I_n(z)$ and $K_n(z)$ / 718 \\
21.11: Computing $I_0(x)$ and $I_1(x)$ / 724 \\
21.12: Computing $K_0(x)$ and $K_1(x)$ / 726 \\
21.13: Computing $I_n(x)$ and $K_n(x)$ / 728 \\
21.14: Properties of spherical Bessel functions / 731
\\
21.15: Computing $j_n(x)$ and $y_n(x)$ / 735 \\
21.16: Improving $j_1(x)$ and $y_1(x)$ / 740 \\
21.17: Modified spherical Bessel functions / 743 \\
21.18: Software for Bessel-function sequences / 755 \\
21.19: Retrospective on Bessel functions / 761 \\
22: Testing the library / 763 \\
22.1: Testing {\tt tgamma} and {\tt lgamma} / 765 \\
22.2: Testing {\tt psi} and {\tt psiln} / 768 \\
22.3: Testing {\tt erf} and {\tt erfc} / 768 \\
22.4: Testing cylindrical Bessel functions / 769 \\
22.5: Testing exponent/\penalty \exhyphenpenalty
significand manipulation / 769 \\
22.6: Testing inline assembly code / 769 \\
22.7: Testing with Maple / 770 \\
22.8: Testing floating-point arithmetic / 773 \\
22.9: The Berkeley Elementary Functions Test Suite /
774 \\
22.10: The AT\&T floating-point test package / 775 \\
22.11: The Antwerp test suite / 776 \\
22.12: Summary / 776 \\
23: Pair-precision elementary functions / 777 \\
23.1: Pair-precision integer power / 777 \\
23.2: Pair-precision machine epsilon / 779 \\
23.3: Pair-precision exponential / 780 \\
23.4: Pair-precision logarithm / 787 \\
23.5: Pair-precision logarithm near one / 793 \\
23.6: Pair-precision exponential near zero / 793 \\
23.7: Pair-precision base-$n$ exponentials / 795 \\
23.8: Pair-precision trigonometric functions / 796 \\
23.9: Pair-precision inverse trigonometric functions /
801 \\
23.10: Pair-precision hyperbolic functions / 804 \\
23.11: Pair-precision inverse hyperbolic functions /
808 \\
23.12: Summary / 808 \\
24: Accuracy of the Cody\slash Waite algorithms / 811
\\
25: Improving upon the Cody\slash Waite algorithms /
823 \\
25.1: The Bell Labs libraries / 823 \\
25.2: The {Cephes} library / 823 \\
25.3: The {Sun} libraries / 824 \\
25.4: Mathematical functions on EPIC / 824 \\
25.5: The GNU libraries / 825 \\
25.6: The French libraries / 825 \\
25.7: The NIST effort / 826 \\
25.8: Commercial mathematical libraries / 826 \\
25.9: Mathematical libraries for decimal arithmetic /
826 \\
25.10: Mathematical library research publications / 826
\\
25.11: Books on computing mathematical functions / 827
\\
25.12: Summary / 828 \\
26: Floating-point output / 829 \\
26.1: Output character string design issues / 830 \\
26.2: Exact output conversion / 831 \\
26.3: Hexadecimal floating-point output / 832 \\
26.4: Octal floating-point output / 850 \\
26.5: Binary floating-point output / 851 \\
26.6: Decimal floating-point output / 851 \\
26.7: Accuracy of output conversion / 865 \\
26.8: Output conversion to a general base / 865 \\
26.9: Output conversion of Infinity / 866 \\
26.10: Output conversion of NaN / 866 \\
26.11: Number-to-string conversion / 867 \\
26.12: The {\tt printf} family / 867 \\
26.13: Summary / 878 \\
27: Floating-point input / 879 \\
27.1: Binary floating-point input / 879 \\
27.2: Octal floating-point input / 894 \\
27.3: Hexadecimal floating-point input / 895 \\
27.4: Decimal floating-point input / 895 \\
27.5: Based-number input / 899 \\
27.6: General floating-point input / 900 \\
27.7: The {\tt scanf} family / 901 \\
27.8: Summary / 910 \\
A: Ada interface / 911 \\
A.1: Building the Ada interface / 911 \\
A.2: Programming the Ada interface / 912 \\
A.3: Using the Ada interface / 915 \\
B: C\# interface / 917 \\
B.1: C\# on the CLI virtual machine / 917 \\
B.2: Building the C\# interface / 918 \\
B.3: Programming the C\# interface / 920 \\
B.4: Using the C\# interface / 922 \\
C: C++ interface / 923 \\
C.1: Building the C++ interface / 923 \\
C.2: Programming the C++ interface / 924 \\
C.3: Using the C++ interface / 925 \\
D: Decimal arithmetic / 927 \\
D.1: Why we need decimal floating-point arithmetic /
927 \\
D.2: Decimal floating-point arithmetic design issues /
928 \\
D.3: How decimal and binary arithmetic differ / 931 \\
D.4: Initialization of decimal floating-point storage /
935 \\
D.5: The {\tt <decfloat.h>} header file / 936 \\
D.6: Rounding in decimal arithmetic / 936 \\
D.7: Exact scaling in decimal arithmetic / 937 \\
E: Errata in the Cody\slash Waite book / 939 \\
F: Fortran interface / 941 \\
F.1: Building the Fortran interface / 943 \\
F.2: Programming the Fortran interface / 944 \\
F.3: Using the Fortran interface / 945 \\
H: Historical floating-point architectures / 947 \\
H.1: CDC family / 949 \\
H.2: Cray family / 952 \\
H.3: DEC PDP-10 / 953 \\
H.4: DEC PDP-11 and VAX / 956 \\
H.5: General Electric 600 series / 958 \\
H.6: IBM family / 959 \\
H.7: Lawrence Livermore S-1 Mark IIA / 965 \\
H.8: Unusual floating-point systems / 966 \\
H.9: Historical retrospective / 967 \\
I: Integer arithmetic / 969 \\
I.1: Memory addressing and integers / 971 \\
I.2: Representations of signed integers / 971 \\
I.3: Parity testing / 975 \\
I.4: Sign testing / 975 \\
I.5: Arithmetic exceptions / 975 \\
I.6: Notations for binary numbers / 977 \\
I.7: Summary / 978 \\
J: Java interface / 979 \\
J.1: Building the Java interface / 979 \\
J.2: Programming the Java MathCW class / 980 \\
J.3: Programming the Java C interface / 982 \\
J.4: Using the Java interface / 985 \\
L: Letter notation / 987 \\
P: Pascal interface / 989 \\
P.1: Building the Pascal interface / 989 \\
P.2: Programming the Pascal MathCW module / 990 \\
P.3: Using the Pascal module interface / 993 \\
P.4: Pascal and numeric programming / 994 \\
Bibliography / 995 \\
Author/editor index / 1039 \\
Function and macro index / 1049 \\
Subject index / 1065 \\
Colophon / 1115",
}
@TechReport{Brent:2017:JBP,
author = "Richard P. Brent",
title = "{Jonathan Borwein}, Pi and the {AGM}",
type = "Talk slides",
institution = "Australian National University and CARMA, University
of Newcastle",
address = "Canberra, ACT and Newcastle, NSW, Australia",
pages = "76",
day = "26",
month = sep,
year = "2017",
bibdate = "Fri Sep 04 17:08:54 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://carma.newcastle.edu.au/meetings/jbcc/abstracts/pdf/JBCC-Richard_Brent.pdf",
abstract = "We consider some of Jon Borwein's contributions to the
high-precision computation of $ \pi $ and the
elementary functions, with particular reference to the
fascinating book \booktitle{Pi and the AGM}(Wiley,
1987) by Jon and his brother Peter Borwein. Here
``AGM'' is the arithmetic-geometric mean, first studied
by Euler, Gauss and Legendre. Because the AGM has
second-order convergence, it can be combined with fast
multiplication algorithms to give fast algorithms for
the $n$-bit computation of $ \pi $, and more generally
the elementary functions. These algorithms run in
``almost linear' time $ O(M(n) \log n)$, where $ M(n)$
is the time for $n$-bit multiplication. The talk will
survey some of the results and algorithms, from the
time of Archimedes to the present day, that were of
interest to Jon. In several cases they were discovered
or improved by him",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
}
@Article{Chen:2017:UTS,
author = "Chao-Ping Chen and Junesang Choi",
title = "Unified treatment of several asymptotic expansions
concerning some mathematical constants",
journal = j-APPL-MATH-COMP,
volume = "305",
number = "??",
pages = "348--363",
day = "15",
month = jul,
year = "2017",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2017.02.001",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sun Mar 12 13:31:57 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300317300978",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "Asymptotic expansion; Choi--Srivastava constants;
constants of Landau and Lebesgue; Euler--Mascheroni
constant; Glaisher--Kinkelin constant; psi function
(logarithmic derivative of gamma function)",
}
@Article{Gil:2017:ECL,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Efficient computation of {Laguerre} polynomials",
journal = j-COMP-PHYS-COMM,
volume = "210",
number = "??",
pages = "124--131",
month = jan,
year = "2017",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.17632/3jkk659cn8.1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Dec 1 14:31:09 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465516302727",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655/",
}
@Article{Horsley:2017:BPF,
author = "David E. Horsley",
title = "{Bessel} phase functions: calculation and
application",
journal = j-NUM-MATH,
volume = "136",
number = "3",
pages = "679--702",
month = jul,
year = "2017",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Wed Jun 7 17:52:44 MDT 2017",
bibsource = "http://link.springer.com/journal/211/136/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Istoan:2017:FFP,
author = "M. Istoan and B. Pasca",
title = "Flexible Fixed-Point Function Generation for {FPGAs}",
crossref = "Burgess:2017:ISC",
pages = "123--130",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.31",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Efficient fixed-point function implementation is
critical in many FPGA application domains including
convolutional neural networks, computer vision, and
communication systems. In this work we focus on
functions of the form $ x^p $, with $ p \in \{ - 1, - 1
/ 2, 1 / 2 \} $ as part of a function generator
targeting FPGAs. The generator implements architectures
based on new but also existing algorithms. In this work
we present three distinct methods implemented in this
generator that outperform state-of-the-art
implementations for certain configurations.
Traditionally, fixed-point function implementation
requires a normalization stage, compute and
denormalization (reconstruction) of the result. The
first proposed method implements the function
holistically, thus saving the logic and latency
required during the normalize and reconstruct stages.
The second proposed method is based on a novel second
order Taylor implementation. The third method is based
on the cubic convergence of Halley's method, which is
novel in this context. The proposed methods are
compared and contrasted against state-of-the art
implementations in the context of FPGA targets.",
acknowledgement = ack-nhfb,
keywords = "arithmetic; communication systems; computer vision;
convolutional neural networks; cubic convergence;
Digital signal processing; Field programmable gate
arrays; field programmable gate arrays; fixed point
arithmetic; fixed-point; flexible fixed-point function
generation; FPGA; FPGAs; generator; Generators; Halley
method; Kernel; Memory management; reciprocal;
reciprocal sqrt; second order Taylor implementation;
Signal generators; sqrt",
}
@InProceedings{Jeannerod:2017:REC,
author = "Claude-Pierre Jeannerod and Jean-Michel Muller",
editor = "Michael B. Matthews",
booktitle = "{2017 51st Asilomar Conference on Signals, Systems,
and Computers. October 29--November 1, 2017. Pacific
Grove, California}",
title = "On the relative error of computing complex square
roots in floating-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "737--740",
year = "2017",
DOI = "https://doi.org/10.1109/ACSSC.2017.8335442",
ISBN = "1-5386-1823-0",
ISBN-13 = "978-1-5386-1823-3",
bibdate = "Fri Sep 29 10:59:32 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We study the accuracy of a classical approach to
computing complex square-roots in floating-point
arithmetic. Our analyses are done in binary
floating-point arithmetic in precision p, and we assume
that the (real) arithmetic operations $+$, $-$, $
\times $, $ \div $, $ \sqrt {} $ are rounded to
nearest, so the unit roundoff is $ u = 2^{-p} $. We
show that in the absence of underflow and overflow, the
componentwise and normwise relative errors of this
approach are at most $ 7 / 2 u $ and $ \sqrt {37} / 2 u
$, respectively, and this without having to neglect
terms of higher order in $u$. We then provide some
input examples showing that these bounds are reasonably
sharp for the three basic binary interchange formats
(binary32, binary64, and binary128) of the IEEE 754
standard for floating-point arithmetic.",
acknowledgement = ack-nhfb,
}
@Article{Jeffrey:2017:BSI,
author = "David J. Jeffrey",
title = "Branch Structure and Implementation of {Lambert}
{$W$}",
journal = j-MATH-COMPUT-SCI,
volume = "11",
number = "3--4",
pages = "341--350",
month = dec,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11786-017-0320-6",
ISSN = "1661-8270 (print), 1661-8289 (electronic)",
ISSN-L = "1661-8270",
bibdate = "Mon Oct 2 10:24:36 MDT 2017",
bibsource = "http://link.springer.com/journal/11786/11/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics in Computer Science",
journal-URL = "http://link.springer.com/journal/11786",
}
@InProceedings{Langhammer:2017:FPT,
author = "M. Langhammer and B. Pasca",
title = "Floating Point Tangent Implementation for {FPGAs}",
crossref = "Burgess:2017:ISC",
pages = "64--65",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.25",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents an implementation of the
floating-point (FP) tangent function, optimized for an
FPGA containing hard floating point (HFP) DSP Blocks.
This function inputs values in the interval [- /2, /2],
uses the IEEE-754 single-precision (SP) format, and has
an accuracy conforming to OpenCL requirements. The
presented architecture is based on a combination of
mathematical identities and properties of the tangent
function in FP. The resultant design outperforms
generic polynomial approximation methods targeting the
same resource utilization spectrum, and provides better
resource trade-offs than classical CORDIC-based
implementations. The presented work is widely available
as part of the Intel DSP Builder Advanced Blockset.",
acknowledgement = ack-nhfb,
keywords = "Approximation methods; classical CORDIC-based
implementations; Digital arithmetic; Digital signal
processing; digital signal processing chips; field
programmable gate arrays; Field programmable gate
arrays; fixed point arithmetic; floating point
arithmetic; floating point tangent function; FPGAs;
generic polynomial approximation methods; hard floating
point DSP blocks; HFP DSP; IEEE-754 single-precision
format; Intel DSP Builder Advanced Blockset; OpenCL;
reconfigurable architectures; Resource management;
resource utilization spectrum; Table lookup",
}
@Article{Langhammer:2017:SPL,
author = "Martin Langhammer and Bogdan Pasca",
title = "Single Precision Logarithm and Exponential
Architectures for Hard Floating-Point Enabled {FPGAs}",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2031--2043",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2703923",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7927449/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Matic:2017:PBA,
author = "Ivan Mati{\'c} and Rado{\v{s}} Radoi{\v{c}}i{\'c} and
Dan Stefanica",
title = "{P{\'o}lya}-based approximation for the {ATM}-forward
implied volatility",
journal = "International Journal of Financial Engineering",
volume = "4",
number = "2--3",
pages = "1--15",
month = jun # "\slash " # sep,
year = "2017",
DOI = "https://doi.org/10.1142/S2424786317500323",
ISSN = "2424-7863",
bibdate = "Sat Dec 16 17:12:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.worldscientific.com/doi/abs/10.1142/S2424786317500323",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Finan. Eng.",
journal-URL = "http://www.worldscientific.com/worldscinet/ijfe",
}
@Article{Pearson:2017:NMC,
author = "John W. Pearson and Sheehan Olver and Mason A.
Porter",
title = "Numerical methods for the computation of the confluent
and {Gauss} hypergeometric functions",
journal = j-NUMER-ALGORITHMS,
volume = "74",
number = "3",
pages = "821--866",
month = mar,
year = "2017",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-016-0173-0",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Mar 1 09:12:15 MST 2017",
bibsource = "http://link.springer.com/journal/11075/74/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-016-0173-0",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Saint-Genies:2017:ELT,
author = "Hugues de Lassus Saint-Geni{\`e}s and David Defour and
Guillaume Revy",
title = "Exact Lookup Tables for the Evaluation of
Trigonometric and Hyperbolic Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2058--2071",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2703870",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7927421/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Staunton:2017:PP,
author = "Mike Staunton",
title = "Power to {P{\'o}lya}",
journal = "Wilmott Magazine",
volume = "90",
pages = "36--37",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1002/wilm.10605",
bibdate = "Sat Dec 16 17:41:48 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1002/wilm.10605/full",
acknowledgement = ack-nhfb,
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1541-8286;
https://www.wilmott.com/category/magazine/",
remark = "No issues online at Wiley before year 2011, or at
Wilmott before 2006.",
}
@Article{Tihanyi:2017:CEL,
author = "Norbert Tihanyi and Attila Kov{\'a}cs and J{\'o}zsef
Kov{\'a}cs",
title = "Computing Extremely Large Values of the {Riemann} Zeta
Function",
journal = j-J-GRID-COMP,
volume = "15",
number = "4",
pages = "527--534",
month = dec,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10723-017-9416-0",
ISSN = "1570-7873 (print), 1572-9184 (electronic)",
ISSN-L = "1570-7873",
bibdate = "Sat Jan 6 08:41:37 MST 2018",
bibsource = "http://link.springer.com/journal/10723/15/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jgridcomp.bib",
URL = "https://link.springer.com/article/10.1007/s10723-017-9416-0",
acknowledgement = ack-nhfb,
fjournal = "Journal of Grid Computing",
journal-URL = "http://link.springer.com/journal/10723",
}
@Article{Xu:2017:AEP,
author = "Aimin Xu and Zhongdi Cen",
title = "Asymptotic expansions for the psi function and the
{Euler--Mascheroni} constant",
journal = j-J-NUMBER-THEORY,
volume = "180",
number = "??",
pages = "360--372",
month = nov,
year = "2017",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2017.04.014",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Wed Jul 15 08:49:31 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X17302007",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Ye:2017:SDP,
author = "Liangjie Ye",
title = "A symbolic decision procedure for relations arising
among {Taylor} coefficients of classical {Jacobi} theta
functions",
journal = j-J-SYMBOLIC-COMP,
volume = "82",
number = "??",
pages = "134--163",
month = sep # "\slash " # oct,
year = "2017",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1016/j.jsc.2017.01.005",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Fri Feb 17 12:14:20 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0747717117300135",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171/",
}
@Article{Zaghloul:2017:ASE,
author = "Mofreh R. Zaghloul",
title = "Algorithm 985: Simple, Efficient, and Relatively
Accurate Approximation for the Evaluation of the
{Faddeyeva} Function",
journal = j-TOMS,
volume = "44",
number = "2",
pages = "22:1--22:9",
month = sep,
year = "2017",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3119904",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Sep 19 17:19:59 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://dl.acm.org/citation.cfm?id=3119904",
abstract = "We present a new simple algorithm for efficient, and
relatively accurate computation of the Faddeyeva
function $ w(z) $. The algorithm carefully exploits
previous approximations by Hui et al. (1978) and
Huml{\'\i}cek (1982) along with asymptotic expressions
from Laplace continued fractions. Over a wide and fine
grid of the complex argument, $ z = x + i y $,
numerical results from the present approximation show a
maximum relative error less than $ 4.0 \times 10^{-5} $
for both real and imaginary parts of $w$ while running
in a relatively shorter execution time than other
competitive techniques. In addition to the calculation
of the Faddeyeva function, $w$, partial derivatives of
the real and imaginary parts of the function can easily
be calculated and returned as optional output.",
acknowledgement = ack-nhfb,
articleno = "22",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Abrarov:2018:RAD,
author = "Sanjar M. Abrarov and Brendan M. Quine",
title = "A rational approximation of the {Dawson}'s integral
for efficient computation of the complex error
function",
journal = j-APPL-MATH-COMP,
volume = "321",
number = "??",
pages = "526--543",
day = "15",
month = mar,
year = "2018",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Dec 9 07:21:49 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300317307312",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Bober:2018:NCR,
author = "Jonathan W. Bober and Ghaith A. Hiary",
title = "New Computations of the {Riemann} Zeta Function on the
Critical Line",
journal = j-EXP-MATH,
volume = "27",
number = "2",
pages = "125--137",
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2016.1233083",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
bibdate = "Thu Sep 27 18:22:33 MDT 2018",
bibsource = "http://www.tandfonline.com/toc/uexm20/27/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1233083",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "14 Oct 2016",
}
@Article{Borwein:2018:GFM,
author = "Jonathan M. Borwein and Robert M. Corless",
title = "Gamma and Factorial in the {{\booktitle{Monthly}}}",
journal = j-AMER-MATH-MONTHLY,
volume = "125",
number = "5",
pages = "400--424",
month = may,
year = "2018",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.1080/00029890.2018.1420983",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "33B15",
MRnumber = "3785875",
bibdate = "Tue Apr 17 09:02:26 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Since its inception in 1894, the Monthly has printed
50 articles on the $ \Gamma $ function or Stirling's
asymptotic formula, including the magisterial 1959
paper by Phillip J. Davis, which won the 1963 Chauvenet
prize, and the eye-opening 2000 paper by the Fields
medalist Manjul Bhargava. In this article, we look back
and comment on what has been said, and why, and try to
guess what will be said about the $ \Gamma $ function
in future Monthly issues.1 We also identify some gaps,
which surprised us: phase plots, Riemann surfaces, and
the functional inverse of $ \Gamma $ make their first
appearance in the Monthly here. We also give a new
elementary treatment of the asymptotics of $ n! $ and
the first few terms of a new asymptotic formula for
inv$ \Gamma $.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Braumann:2018:RGF,
author = "C. A. Braumann and J.-C. Cort{\'e}s and L. J{\'o}dar
and L. Villafuerte",
title = "On the random gamma function: Theory and computing",
journal = j-J-COMPUT-APPL-MATH,
volume = "335",
number = "??",
pages = "142--155",
month = jun,
year = "2018",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2017.11.045",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Tue Mar 6 07:50:18 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042717306064",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Bremer:2018:ANE,
author = "James Bremer",
title = "An algorithm for the numerical evaluation of the
associated {Legendre} functions that runs in time
independent of degree and order",
journal = j-J-COMPUT-PHYS,
volume = "360",
number = "??",
pages = "15--38",
day = "1",
month = may,
year = "2018",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2018.01.014",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Thu Mar 15 15:42:48 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S002199911830024X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Ceretani:2018:AME,
author = "Andrea N. Ceretani and Natalia N. Salva and Domingo A.
Tarzia",
title = "Approximation of the modified error function",
journal = j-APPL-MATH-COMP,
volume = "337",
number = "??",
pages = "591--606",
day = "15",
month = nov,
year = "2018",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2018.05.054",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Sep 14 08:14:13 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300318304715",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Chen:2018:NEH,
author = "Ruyun Chen and Gang Yang",
title = "Numerical evaluation of highly oscillatory {Bessel}
transforms",
journal = j-J-COMPUT-APPL-MATH,
volume = "342",
number = "??",
pages = "16--24",
month = nov,
year = "2018",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2018.03.026",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Fri Aug 10 18:10:42 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042718301894",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{DelPunta:2018:LRC,
author = "Jessica A. {Del Punta} and Gustavo Gasaneo and Lorenzo
U. Ancarani",
title = "On the {Laguerre} Representation of {Coulomb}
Functions and the Relation to Orthogonal Polynomials",
chapter = "4",
journal = j-ADV-QUANTUM-CHEM,
volume = "76",
pages = "79--101",
year = "2018",
CODEN = "AQCHA9",
DOI = "https://doi.org/10.1016/bs.aiq.2017.06.005",
ISSN = "0065-3276",
ISSN-L = "0065-3276",
bibdate = "Thu Feb 1 07:08:30 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S0065327617300643",
acknowledgement = ack-nhfb,
ajournal = "Adv. Quantum Chem.",
fjournal = "Advances in Quantum Chemistry",
journal-URL = "http://www.sciencedirect.com/science/bookseries/00653276/",
keywords = "Coulomb functions; Laguerre basis; Orthogonal
polynomials",
}
@Article{Dunster:2018:UAE,
author = "T. M. Dunster and A. Gil and J. Segura",
title = "Uniform asymptotic expansions for {Laguerre}
polynomials and related confluent hypergeometric
functions",
journal = j-ADV-COMPUT-MATH,
volume = "44",
number = "5",
pages = "1441--1474",
month = oct,
year = "2018",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/s10444-018-9589-5",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
bibdate = "Thu May 30 08:11:44 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://link.springer.com/article/10.1007/s10444-018-9589-5",
acknowledgement = ack-nhfb,
ajournal = "Adv. Comput. Math.",
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
}
@Article{Hanson:2018:RAM,
author = "Richard J. Hanson and Tim Hopkins",
title = "Remark on {Algorithm 539: A Modern Fortran Reference
Implementation for Carefully Computing the Euclidean
Norm}",
journal = j-TOMS,
volume = "44",
number = "3",
pages = "24:1--24:23",
month = apr,
year = "2018",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3134441",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Jan 22 17:49:32 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3134441",
abstract = "We propose a set of new Fortran reference
implementations, based on an algorithm proposed by
Kahan, for the Level 1 BLAS routines *NRM2 that compute
the Euclidean norm of a real or complex input vector.
The principal advantage of these routines over the
current offerings is that, rather than losing accuracy
as the length of the vector increases, they generate
results that are accurate to almost machine precision
for vectors of length $ N < N_{\rm max} $ where $
N_{\rm max} $ depends upon the precision of the
floating point arithmetic being used. In addition, we
make use of intrinsic modules, introduced in the latest
Fortran standards, to detect occurrences of non-finite
numbers in the input data and return suitable values as
well as setting IEEE floating point status flags as
appropriate. A set of C interface routines is also
provided to allow simple, portable access to the new
routines. To improve execution speed, we advocate a
hybrid algorithm; a simple loop is used first and, only
if IEEE floating point exception flags signal, do we
fall back on Kahan's algorithm. Since most input
vectors are ``easy,'' i.e., they do not require the
sophistication of Kahan's algorithm, the simple loop
improves performance while the use of compensated
summation ensures high accuracy. We also report on a
comprehensive suite of test problems that has been
developed to test both our new implementation and
existing codes for both accuracy and the appropriate
settings of the IEEE arithmetic status flags.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
xxnote = "See \cite{Lawson:1979:ABL}.",
}
@Article{Higham:2018:UN,
author = "Nicholas J. Higham",
title = "The Unwinding Number",
journal = j-SIAM-NEWS,
volume = "51",
number = "8",
pages = "??--??",
month = oct,
year = "2018",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Oct 06 08:46:15 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sinews.siam.org/Details-Page/the-unwinding-number",
abstract = "While Fortran 66 had a complex data type, this was not
true of most other early programming languages, such as
Algol 60. As a result, programmers had to write their
own procedures to implement complex arithmetic and
transcendental functions in terms of separately stored
real and imaginary parts. They quickly realized that
this is not a trivial task; in the early 1960s, it took
five published attempts over three years to obtain a
correct implementation of the complex logarithm in
Algol 60.",
acknowledgement = ack-nhfb,
}
@Article{Johansson:2018:FRA,
author = "Fredrik Johansson and Marc Mezzarobba",
title = "Fast and Rigorous Arbitrary-Precision Computation of
{Gauss--Legendre} Quadrature Nodes and Weights",
journal = j-SIAM-J-SCI-COMP,
volume = "40",
number = "6",
pages = "C726--C747",
month = "????",
year = "2018",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1170133",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Jan 25 18:37:30 MST 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/40/6;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
ajournal = "SIAM J. Sci. Comput.",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2018",
}
@Misc{Kahan:2018:TD,
author = "William Kahan",
title = "The tanpi Dilemma",
howpublished = "Web document.",
day = "16",
month = apr,
year = "2018",
bibdate = "Tue Apr 17 06:52:47 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://754r.ucbtest.org/background/tanpi.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The function tanpi(x) satisfies two familiar
identities, tanpi(-x) = -tanpi(x), and tanpi(x +
integer) = tanpi(x), that cannot both be satisfied {\em
everywhere\/} by IEEE 754's arithmetic; the obvious
failures occur when tanpi is infinite: does tanpi(-2.5)
= -tanpi(2.5) or does tanpi(-2.5) = tanpi(-2.5 + 4) =
+tanpi(2.5)? Whoever puts a tanpi subprogram into the
Math library has no choice but to disappoint
somebody.",
acknowledgement = ack-nhfb,
}
@Article{Lopez:2018:CEB,
author = "Jos{\'e} L. L{\'o}pez",
title = "Convergent expansions of the {Bessel} functions in
terms of elementary functions",
journal = j-ADV-COMPUT-MATH,
volume = "44",
number = "1",
pages = "277--294",
month = feb,
year = "2018",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/s10444-017-9543-y",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
MRclass = "33C10 (41A58)",
MRnumber = "3755750",
bibdate = "Sat Feb 3 18:23:33 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/s10444-017-9543-y",
acknowledgement = ack-nhfb,
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
}
@Article{Matic:2018:SPB,
author = "Ivan Mati{\'c} and Rado{\v{s}} Radoi{\v{c}}i{\'c} and
Dan Stefanica",
title = "A sharp {P{\'o}lya}-based approximation to the normal
cumulative distribution function",
journal = j-APPL-MATH-COMP,
volume = "322",
number = "??",
pages = "111--122",
day = "1",
month = apr,
year = "2018",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2017.10.019",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Dec 15 10:03:09 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S009630031730718X",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
remark = "Although the accuracy of the approximations developed
is low (6 to 10 digits), the article shows how it can
be increased by taking more series terms. The article
is an excellent overview of prior work on computing the
normal and inverse normal cumulative distribution
function, almost all of which is low accuracy (2 to 4
digits). The authors supply 89 references to prior
work, all of which are now in this bibliography as of
16 December 2017.",
}
@InProceedings{Mikaitis:2018:AFP,
author = "Mantas Mikaitis and David R. Lester and Delong Shang
and Steve Furber and Gengting Liu and Jim Garside and
Stefan Scholze and Sebastian H{\"o}ppner and Andreas
Dixius",
title = "Approximate Fixed-Point Elementary Function
Accelerator for the {SpiNNaker-2} Neuromorphic Chip",
crossref = "Tenca:2018:PIS",
pages = "37--44",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464785",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Neuromorphic chips are used to model biologically
inspired Spiking-Neural-Networks (SNNs) where most
models are based on differential equations. Equations
for most SNN algorithms usually contain variables with
one or more ex components. SpiNNaker is a digital
neuromorphic chip that has so far been using
pre-calculated look-up tables for exponential function.
However this approach is limited because the memory
requirements grow as more complex neural models are
developed. To save already limited memory resources in
the next generation SpiNNaker chip, we are including a
fast exponential function in the silicon. In this paper
we analyse iterative algorithms for elementary
functions and show how to build a single hardware
accelerator for exp and natural log, for a neuromorphic
chip prototype, to be manufactured in a 22 nm FDSOI
process. We present the accelerator that has
algorithmic level approximation control, allowing it to
trade precision for latency and energy efficiency. As
an addition to neuromorphic chip application, we
provide analysis of a parameterized elementary function
unit that can be tailored for other systems with
different power, area, accuracy and latency
constraints.",
acknowledgement = ack-nhfb,
keywords = "Adders; algorithmic level approximation control;
approximate arithmetic; approximate fixed-point
elementary function accelerator; ARITH-25; Biological
system modeling; biologically inspired
spiking-neural-networks; complex neural models;
Computational modeling; Convergence; differential
equations; digital neuromorphic chip; energy
efficiency; exponential function; fast exponential
function; FDSOI process; fixed-point arithmetic;
hardware accelerators; iterative algorithms; iterative
methods; logarithm function; Mathematical model; memory
requirements; memory resources; MPSoC; neural chips;
neuromorphic chip prototype; neuromorphic computing;
Neuromorphics; next generation SpiNNaker chip;
parameterized elementary function unit; pre-calculated
look-up tables; single hardware accelerator; size 22.0
nm; SNN algorithms; SpiNNaker-2 neuromorphic chip;
SpiNNaker2; table lookup; Table lookup",
}
@Article{Moroz:2018:FCI,
author = "Leonid V. Moroz and Cezary J. Walczyk and Andriy
Hrynchyshyn and Vijay Holimath and Jan L.
Cie{\'s}li{\'n}ski",
title = "Fast calculation of inverse square root with the use
of magic constant --- analytical approach",
journal = j-APPL-MATH-COMP,
volume = "316",
number = "??",
pages = "245--255",
day = "1",
month = jan,
year = "2018",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2017.08.025",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Oct 10 15:56:03 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300317305763",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "single-precision 32-bit IEEE 754 binary arithmetic",
}
@Article{Munoz-Coreas:2018:CQO,
author = "Edgard Mu{\~n}oz-Coreas and Himanshu Thapliyal",
title = "{T}-count and Qubit Optimized Quantum Circuit Design
of the Non-Restoring Square Root Algorithm",
journal = j-JETC,
volume = "14",
number = "3",
pages = "36:1--36:15",
month = oct,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3264816",
ISSN = "1550-4832",
bibdate = "Thu Nov 1 16:44:41 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jetc.bib",
abstract = "Quantum circuits for basic mathematical functions such
as the square root are required to implement scientific
computing algorithms on quantum computers. Quantum
circuits that are based on Clifford+T gates can easily
be made fault tolerant, but the T gate is very costly
to implement. As a result, reducing T-count has become
an important optimization goal. Further, quantum
circuits with many qubits are difficult to realize,
making designs that save qubits and produce no garbage
outputs desirable. In this work, we present a T-count
optimized quantum square root circuit with only $ 2 s n
+ 1 $ qubits and no garbage output. To make a fair
comparison against existing work, the Bennett's garbage
removal scheme is used to remove garbage output from
existing works. We determined that our proposed design
achieves an average T-count savings of 43.44\%,
98.95\%, 41.06\%, and 20.28\% as well as qubit savings
of 85.46\%, 95.16\%, 90.59\%, and 86.77\% compared to
existing works.",
acknowledgement = ack-nhfb,
articleno = "36",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J967",
}
@Article{Myland:2018:JEF,
author = "Jan C. Myland and Keith B. Oldham",
title = "{Jacobian} elliptic functions describe the properties
of the diffuse charge region in narrow electrochemical
cells",
journal = j-J-MATH-CHEM,
volume = "56",
number = "4",
pages = "1184--1205",
month = apr,
year = "2018",
CODEN = "JMCHEG",
DOI = "https://doi.org/10.1007/s10910-017-0847-4",
ISSN = "0259-9791 (print), 1572-8897 (electronic)",
ISSN-L = "0259-9791",
bibdate = "Tue Mar 6 07:08:26 MST 2018",
bibsource = "http://link.springer.com/journal/10910/56/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
URL = "https://link.springer.com/article/10.1007/s10910-017-0847-4",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Chemistry",
journal-URL = "http://link.springer.com/journal/10910",
journalabr = "J. Math. Chem.",
}
@Article{Navas-Palencia:2018:FAA,
author = "Guillermo Navas-Palencia",
title = "Fast and accurate algorithm for the generalized
exponential integral {$ E_\nu (x) $} for positive real
order",
journal = j-NUMER-ALGORITHMS,
volume = "77",
number = "2",
pages = "603--630",
month = feb,
year = "2018",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-017-0331-z",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Thu Jan 25 09:50:15 MST 2018",
bibsource = "http://link.springer.com/journal/11075/77/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-017-0331-z",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Navas-Palencia:2018:HPC,
author = "Guillermo Navas-Palencia",
title = "High-precision computation of the confluent
hypergeometric functions via {Franklin--Friedman}
expansion",
journal = j-ADV-COMPUT-MATH,
volume = "44",
number = "3",
pages = "841--859",
month = jun,
year = "2018",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/s10444-017-9565-5",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
bibdate = "Thu May 30 08:11:42 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://link.springer.com/article/10.1007/s10444-017-9565-5",
acknowledgement = ack-nhfb,
ajournal = "Adv. Comput. Math.",
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
keywords = "Arbitrary-precision arithmetic; confluent
hypergeometric functions; Franklin--Friedman expansion;
generalized exponential integer $E_\nu(z) = z^{\nu - 1}
U(\nu, \nu, z)$; Kummer function $U(a,b,z)$; modified
Bessel function $K_\nu(z)$; uniform series expansion",
}
@Article{Pakes:2018:LFN,
author = "Anthony G. Pakes",
title = "The {Lambert} {$W$} function, {Nuttall}'s integral,
and the {Lambert} law",
journal = j-STAT-PROB-LETT,
volume = "139",
number = "??",
pages = "53--60",
month = aug,
year = "2018",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.spl.2018.03.015",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Thu Nov 8 12:34:02 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/statproblett2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715218301354",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
}
@Article{Patterson:2018:SCS,
author = "T. N. L. Patterson",
title = "Sines, Cosines, Square Roots, and Binary Bits",
journal = j-AMER-MATH-MONTHLY,
volume = "125",
number = "8",
pages = "750--754",
year = "2018",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.1080/00029890.2018.1498695",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Dec 13 17:59:05 MST 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html;
https://www.tandfonline.com/loi/uamm20",
onlinedate = "28 Sep 2018",
}
@Article{Punta:2018:CFL,
author = "Jessica A. Del Punta and Gustavo Gasaneo and Lorenzo
U. Ancarani",
title = "On the {Laguerre} Representation of {Coulomb}
Functions and the Relation to Orthogonal Polynomials",
chapter = "4",
journal = j-ADV-QUANTUM-CHEM,
volume = "76",
pages = "79--101",
year = "2018",
CODEN = "AQCHA9",
DOI = "https://doi.org/10.1016/bs.aiq.2017.06.005",
ISSN = "0065-3276",
ISSN-L = "0065-3276",
bibdate = "Thu Feb 1 07:08:30 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S0065327617300643",
acknowledgement = ack-nhfb,
fjournal = "Advances in Quantum Chemistry",
journal-URL = "http://www.sciencedirect.com/science/bookseries/00653276",
keywords = "Coulomb functions; Laguerre basis; Orthogonal
polynomials",
}
@Article{Qi:2018:DME,
author = "Hongyuan Qi and Jinchen Xu and Shaozhong Guo",
title = "Detection of the maximum error of mathematical
functions",
journal = j-J-SUPERCOMPUTING,
volume = "74",
number = "11",
pages = "6275--6290",
month = nov,
year = "2018",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-018-2552-x",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Thu Oct 10 15:31:09 MDT 2019",
bibsource = "http://link.springer.com/journal/11227/74/11;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Quan:2018:ACA,
author = "Le Phuong Quan and Th{\'a}i Anh Nhan",
title = "Applying Computer Algebra Systems in Approximating the
Trigonometric Functions",
journal = j-MATH-COMPUT-APPL,
volume = "23",
number = "3",
pages = "??--??",
month = sep,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.3390/mca23030037",
ISSN = "2297-8747",
ISSN-L = "2297-8747",
bibdate = "Sun Feb 18 06:28:34 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
URL = "https://www.mdpi.com/2297-8747/23/3/37",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput. Appl.",
articleno = "37",
fjournal = "Mathematical and Computational Applications",
journal-URL = "https://www.mdpi.com/journal/mca",
}
@Article{Quan:2018:CMM,
author = "Le Phuong Quan",
title = "A Computational Method with {MAPLE} for a Piecewise
Polynomial Approximation to the Trigonometric
Functions",
journal = j-MATH-COMPUT-APPL,
volume = "23",
number = "4",
pages = "??--??",
month = dec,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.3390/mca23040063",
ISSN = "2297-8747",
ISSN-L = "2297-8747",
bibdate = "Sun Feb 18 06:28:34 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
URL = "https://www.mdpi.com/2297-8747/23/4/63",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput. Appl.",
articleno = "63",
fjournal = "Mathematical and Computational Applications",
journal-URL = "https://www.mdpi.com/journal/mca",
}
@PhdThesis{Saint-Genies:2018:EFT,
author = "Hugues de Lassus Saint-Geni{\`e}s",
title = "Elementary functions: towards automatically generated,
efficient, and vectorizable implementations",
type = "{Ph.D.} thesis",
school = "Universit{\'e} de Perpignan",
address = "Perpignan, France",
pages = "xxxviii + 128",
day = "17",
month = jul,
year = "2018",
bibdate = "Tue Mar 01 06:09:03 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://tel.archives-ouvertes.fr/tel-01841424/document",
acknowledgement = ack-nhfb,
}
@Article{Schneider:2018:NFP,
author = "Barry I. Schneider and Javier Segura and Amparo Gil
and Xiaoxu Guan and Klaus Bartschat",
title = "A new {Fortran 90} program to compute regular and
irregular associated {Legendre} functions (new version
announcement)",
journal = j-COMP-PHYS-COMM,
volume = "225",
number = "??",
pages = "192--193",
month = apr,
year = "2018",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2017.12.013",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Wed Feb 28 14:39:27 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465517304186",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Walczyk:2018:IAF,
author = "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
Cie{\'s}li{\'n}ski",
title = "Improving the accuracy of the fast inverse square root
algorithm",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--21",
day = "17",
month = feb,
year = "2018",
DOI = "https://doi.org/10.48550/arXiv.1802.06302",
bibdate = "Wed Dec 20 07:55:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1802.06302",
abstract = "We present improved algorithms for fast calculation of
the inverse square root for single-precision
floating-point numbers. The algorithms are much more
accurate than the famous fast inverse square root
algorithm and have the same or similar computational
cost. The main idea of our work consists in modifying
the Newton-Raphson method and demanding that the
maximal error is as small as possible. Such
modification is possible when the distribution of
Newton-Raphson corrections is not symmetric (e.g., if
they are non-positive functions).",
acknowledgement = ack-nhfb,
}
@Article{Xue:2018:RCL,
author = "Changfeng Xue and Shaozhong Deng",
title = "Recursive Computation of Logarithmic Derivatives,
Ratios, and Products of Spheroidal Harmonics and
Modified {Bessel} Functions and Applications",
journal = j-J-SCI-COMPUT,
volume = "75",
number = "1",
pages = "128--156",
month = oct,
year = "2018",
CODEN = "JSCOEB",
DOI = "https://doi.org/10.1007/s10915-017-0527-3",
ISSN = "0885-7474 (print), 1573-7691 (electronic)",
ISSN-L = "0885-7474",
bibdate = "Fri Mar 29 16:29:33 MDT 2019",
bibsource = "http://link.springer.com/journal/10915/75/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jscicomput.bib",
URL = "https://link.springer.com/article/10.1007/s10915-017-0527-3;
https://link.springer.com/content/pdf/10.1007/s10915-017-0527-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Scientific Computing",
journal-URL = "http://link.springer.com/journal/10915",
}
@Article{Alonso:2019:CMT,
author = "Pedro Alonso and Jes{\'u}s Peinado and Javier
Ib{\'a}{\~n}ez and Jorge Sastre and Emilio Defez",
title = "Computing matrix trigonometric functions with {GPUs}
through {Matlab}",
journal = j-J-SUPERCOMPUTING,
volume = "75",
number = "3",
pages = "1227--1240",
month = mar,
year = "2019",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-018-2354-1",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Thu Oct 10 15:31:18 MDT 2019",
bibsource = "http://link.springer.com/journal/11227/75/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@InProceedings{Arzelier:2019:EAE,
author = "Denis Arzelier and Florent Br{\'e}hard and Mioara
Joldes",
title = "Exchange Algorithm for Evaluation and Approximation
Error-Optimized Polynomials",
crossref = "Takagi:2019:ISC",
pages = "30--37",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00014",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Machine implementation of mathematical functions often
relies on polynomial approximations. The particularity
is that rounding errors occur both when representing
the polynomial coefficients on a finite number of bits,
and when evaluating it in finite precision. Hence, for
finding the best polynomial (for a given fixed degree,
norm and interval), one has to consider both types of
errors: approximation and evaluation. While efficient
algorithms were already developed for taking into
account the approximation error, the evaluation part is
usually a posteriori handled, in an ad-hoc manner.
Here, we formulate a semi-infinite linear optimization
problem whose solution is the best polynomial with
respect to the supremum norm of the sum of both errors.
This problem is then solved with an iterative exchange
algorithm, which can be seen as an extension of the
well-known Remez algorithm. A discussion and comparison
of the obtained results on different examples are
finally presented.",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; Approximation error;
approximation error; approximation error-optimized
polynomials; ARITH-26; Digital arithmetic; evaluation
error; exchange algorithm; function approximation;
Indexes; Input variables; iterative exchange algorithm;
iterative methods; learning (artificial intelligence);
libm; linear programming; machine implementation;
mathematical functions; mathematics computing;
optimisation; Optimization; polynomial approximation;
polynomial approximations; polynomial coefficients;
Programming; remez algorithm; Remez algorithm;
semi-infinite programming; semiinfinite linear
optimization problem",
}
@Article{Batista:2019:ECM,
author = "Milan Batista",
title = "\pkg{Elfun18} --- a collection of {MATLAB} functions
for the computation of elliptic integrals and
{Jacobian} elliptic functions of real arguments",
journal = j-SOFTWAREX,
volume = "10",
number = "??",
pages = "Article 100245",
month = jul # "\slash " # dec,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.softx.2019.100245",
ISSN = "2352-7110",
ISSN-L = "2352-7110",
bibdate = "Fri Apr 9 16:04:36 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/softwarex.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S2352711018302796",
acknowledgement = ack-nhfb,
fjournal = "SoftwareX",
journal-URL = "https://www.sciencedirect.com/journal/softwarex/issues",
}
@TechReport{Bernstein:2019:FCT,
author = "Daniel J. Bernstein and Bo-Yin Yang",
title = "Fast constant-time gcd computation and modular
inversion",
institution = "International Association for Cryptologic Research",
address = "????",
pages = "1--59",
day = "13",
month = apr,
year = "2019",
bibdate = "Tue May 24 07:23:13 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://eprint.iacr.org/2019/266.pdf",
abstract = "This paper introduces streamlined constant-time
variants of Euclid's algorithm, both for polynomial
inputs and for integer inputs. As concrete
applications, this paper saves time in (1) modular
inversion for Curve25519, which was previously believed
to be handled much more efficiently by Fermat's method,
and (2) key generation for the ntruhrss701 and
sntrup4591761 lattice-based cryptosystems",
acknowledgement = ack-nhfb,
keywords = "algorithm design; branchless algorithms; constant-time
computations; Curve25519; Euclid's algorithm; gcd;
greatest common divisor; modular inversion; modular
reciprocal; NTRU",
}
@Article{Borges:2019:IAH,
author = "Carlos F. Borges",
title = "An Improved Algorithm for {\tt hypot(a,b)}",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--15",
day = "14",
month = jun,
year = "2019",
bibdate = "Fri Apr 19 05:40:55 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1904.09481",
abstract = "We develop a fast and accurate algorithm for
evaluating $ \sqrt {x^2 + y^2} $ for two floating point
numbers $a$ and $b$. Library functions that perform
this computation are generally named {\tt hypot(a,b)}.
We will compare four approaches that we will develop in
this paper to the current resident library function
that is delivered with Julia 1.1 and to the code that
has been distributed with the C math library for
decades. We will demonstrate the performance of our
algorithms by simulation.",
acknowledgement = ack-nhfb,
}
@Article{Bremer:2019:ARN,
author = "James Bremer",
title = "An algorithm for the rapid numerical evaluation of
{Bessel} functions of real orders and arguments",
journal = j-ADV-COMPUT-MATH,
volume = "45",
number = "1",
pages = "173--211",
month = feb,
year = "2019",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/s10444-018-9613-9",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
bibdate = "Thu May 30 08:11:46 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://link.springer.com/article/10.1007/s10444-018-9613-9",
acknowledgement = ack-nhfb,
ajournal = "Adv. Comput. Math.",
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
}
@Article{Bujanda:2019:CEC,
author = "Blanca Bujanda and Jos{\'e} and L. L{\'o}pez and Pedro
J. Pagola",
title = "Convergent expansions of the confluent hypergeometric
functions in terms of elementary functions",
journal = j-MATH-COMPUT,
volume = "88",
number = "318",
pages = "1773--1789",
month = apr,
year = "2019",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3389",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Jul 14 06:45:40 MDT 2020",
bibsource = "http://www.ams.org/mcom/2019-88-318;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "https://www.ams.org/journals/mcom/2019-88-318/S0025-5718-2018-03389-0;
https://www.ams.org/journals/mcom/2019-88-318/S0025-5718-2018-03389-0/S0025-5718-2018-03389-0.pdf;
https://www.ams.org/mathscinet/search/authors.html?authorName=Lopez%2C%20Jose%20L.;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=636519;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=806866",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Campos-Pinto:2019:APP,
author = "Martin Campos-Pinto and Fr{\'e}d{\'e}rique Charles and
Bruno Despr{\'e}s",
title = "Algorithms For Positive Polynomial Approximation",
journal = j-SIAM-J-NUMER-ANAL,
volume = "57",
number = "1",
pages = "148--172",
month = "????",
year = "2019",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/17M1131891",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Mon Mar 18 13:37:59 MDT 2019",
bibsource = "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/57/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
onlinedate = "January 2019",
}
@Article{Cardoso:2019:CMG,
author = "Jo{\~a}o R. Cardoso and Amir Sadeghi",
title = "Computation of matrix gamma function",
journal = j-BIT-NUM-MATH,
volume = "59",
number = "2",
pages = "343--370",
month = jun,
year = "2019",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-018-00744-1",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Fri Sep 6 09:16:11 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/s10543-018-00744-1",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Fedotov:2019:CWM,
author = "Alexander Fedotov and Fr{\'e}d{\'e}ric Klopp",
title = "The Complex {WKB} Method for Difference Equations and
{Airy} Functions",
journal = j-SIAM-J-MATH-ANA,
volume = "51",
number = "6",
pages = "4413--4447",
month = "????",
year = "2019",
CODEN = "SJMAAH",
DOI = "https://doi.org/10.1137/18M1228694",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Fri Apr 24 15:47:49 MDT 2020",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/51/6;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
onlinedate = "January 2019",
}
@Article{Green:2019:DFE,
author = "Kevin R. Green and Tanner A. Bohn and Raymond J.
Spiteri",
title = "Direct Function Evaluation versus Lookup Tables: When
to Use Which?",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "3",
pages = "C194--C218",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1201421",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Thu Oct 10 06:58:05 MDT 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2019",
}
@Article{Greengard:2019:AEI,
author = "Philip Greengard and Vladimir Rokhlin",
title = "An algorithm for the evaluation of the incomplete
gamma function",
journal = j-ADV-COMPUT-MATH,
volume = "45",
number = "1",
pages = "23--49",
month = feb,
year = "2019",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1007/s10444-018-9604-x",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
bibdate = "Thu May 30 08:11:46 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://link.springer.com/article/10.1007/s10444-018-9604-x",
acknowledgement = ack-nhfb,
ajournal = "Adv. Comput. Math.",
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
}
@Article{Horyachyy:2019:SEF,
author = "Oleh Horyachyy and Leonid Moroz and Viktor Otenko",
title = "Simple Effective Fast Inverse Square Root Algorithm
with Two Magic Constants",
journal = "International Journal of Computing",
volume = "18",
number = "4",
pages = "461--470",
month = dec,
year = "2019",
ISSN = "1727-6209 (print), 2312-5381 (electronic)",
ISSN-L = "1727-6209",
bibdate = "Thu Feb 11 11:01:47 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.computingonline.net/computing/article/view/1616;
https://www.researchgate.net/publication/349173096_SIMPLE_EFFECTIVE_FAST_INVERSE_SQUARE_ROOT_ALGORITHM_WITH_TWO_MAGIC_CONSTANTS",
acknowledgement = ack-nhfb,
keywords = "FISR algorithm; floating-point arithmetic; FMA
function; Householder.; IEEE 754 standard; initial
approximation; inverse square root; magic constant;
maximum relative error; Newton-Raphson",
}
@Article{Johansson:2019:CHF,
author = "Fredrik Johansson",
title = "Computing Hypergeometric Functions Rigorously",
journal = j-TOMS,
volume = "45",
number = "3",
pages = "30:1--30:26",
month = aug,
year = "2019",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3328732",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Sep 3 17:49:22 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3328732",
abstract = "We present an efficient implementation of
hypergeometric functions in arbitrary-precision
interval arithmetic. The functions $_0 F_1$, $_1 F_1$,
$_2 F_1$, and $_2 F_0$ (or the Kummer $U$-function) are
supported for unrestricted complex parameters and
argument, and, by extension, we cover exponential and
trigonometric integrals, error functions, Fresnel
integrals, incomplete gamma and beta functions, Bessel
functions, Airy functions, Legendre functions, Jacobi
polynomials, complete elliptic integrals, and other
special functions. The output can be used directly for
interval computations or to generate provably correct
floating-point approximations in any format.
Performance is competitive with earlier
arbitrary-precision software and sometimes orders of
magnitude faster. We also partially cover the
generalized hypergeometric function $_p F_q$ and
computation of high-order parameter derivatives.",
acknowledgement = ack-nhfb,
articleno = "30",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Lemire:2019:FRD,
author = "Daniel Lemire and Owen Kaser and Nathan Kurz",
title = "Faster remainder by direct computation: Applications
to compilers and software libraries",
journal = j-SPE,
volume = "49",
number = "6",
pages = "953--970",
month = jun,
year = "2019",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.2689",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat Oct 12 09:43:47 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "integer division; integer remainder",
onlinedate = "27 February 2019",
}
@InProceedings{Melquiond:2019:FVS,
author = "Guillaume Melquiond and Raphael Rieu-Helft",
title = "Formal Verification of a State-of-the-Art Integer
Square Root",
crossref = "Takagi:2019:ISC",
pages = "183--186",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00041",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present the automatic formal verification of a
state-of-the-art algorithm from the GMP library that
computes the square root of a 64-bit integer. Although
it uses only integer operations, the best way to
understand the program is to view it as a fixed-point
arithmetic algorithm that implements Newton's method.
The C code is short but intricate, involving magic
constants and intentional arithmetic overflows. We have
verified the algorithm using the Why3 tool and
automated solvers such as Gappa.",
acknowledgement = ack-nhfb,
keywords = "64-bit integer; Approximation algorithms; ARITH-26;
automatic formal verification; C code; C language;
Convergence; Digital arithmetic; electronic engineering
computing; fixed point arithmetic; Fixed-point
arithmetic; fixed-point arithmetic algorithm; floating
point arithmetic; Floors; Formal verification; GMP
library; integer operations; integer square root;
intentional arithmetic overflows; Libraries; Newton
method; program verification; programming; Tools; Why3
tool",
}
@Article{Miyajima:2019:VCM,
author = "Shinya Miyajima",
title = "Verified computation for the matrix {Lambert} {$W$}
function",
journal = j-APPL-MATH-COMP,
volume = "362",
number = "??",
pages = "Article 124555",
day = "1",
month = dec,
year = "2019",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Sep 6 09:21:26 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S0096300319305387",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Nemes:2019:AEI,
author = "Gerg{\H{o}} Nemes and Adri B. Olde Daalhuis",
title = "Asymptotic expansions for the incomplete gamma
function in the transition regions",
journal = j-MATH-COMPUT,
volume = "88",
number = "318",
pages = "1805--1827",
month = apr,
year = "2019",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3391",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Jul 14 06:45:40 MDT 2020",
bibsource = "http://www.ams.org/mcom/2019-88-318;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "https://www.ams.org/journals/mcom/2019-88-318/S0025-5718-2018-03391-9;
https://www.ams.org/journals/mcom/2019-88-318/S0025-5718-2018-03391-9/S0025-5718-2018-03391-9.pdf;
https://www.ams.org/mathscinet/search/authors.html?authorName=Nemes%2C%20Gergo;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=293428",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Parhi:2019:CAF,
author = "Keshab K. Parhi and Yin Liu",
title = "Computing Arithmetic Functions Using Stochastic Logic
by Series Expansion",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "7",
number = "1",
pages = "44--59",
month = jan # "\slash " # mar,
year = "2019",
DOI = "https://doi.org/10.1109/TETC.2016.2618750",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
abstract = "Stochastic logic implementations of complex arithmetic
functions, such as trigonometric, exponential, and
sigmoid, are derived based on truncated versions of
their Maclaurin series expansions. This paper makes
three contributions. First, it is shown that a
polynomial can be implemented using multiple levels of
NAND gates based on Horner's rule, if the coefficients
are alternately positive and negative and their
magnitudes are monotonically decreasing. Truncated
Maclaurin series expansions of arithmetic functions are
used to generate polynomials which satisfy these
constraints. The input and output in these functions
are represented by unipolar representation. Functions
including sine, cosine, tangent hyperbolic, logarithm
and exponential can be implemented using this method.
Second, for a polynomial that does not satisfy these
constraints, it still can be implemented based on
Horner's rule if each factor of the polynomial
satisfies these constraints. It is shown that functions
such as $ \sin \pi x / \pi $, $ e^{-a x} $, $ \tanh a x
$ and $ \sigmoid (a x^3) $ (for values of $ a > 1$) can
be implemented using stochastic logic using
factorization in combination with Horner's rule. Third,
format conversion is proposed for arithmetic functions
with input and output represented in different formats,
such as $ \cos \pi x$ given $ x \in [0, 1]$ and $
\sigmoid (x)$ given $ x \in [ - 1, 1]$. Polynomials are
transformed to equivalent forms that naturally exploit
format conversions. The proposed stochastic logic
circuits outperform the well-known Bernstein polynomial
based and finite-state-machine (FSM) based
implementations. Furthermore, the hardware complexity
and the critical path of the proposed implementations
are less than the well-known Bernstein polynomial based
and FSM based implementations for most cases",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Qi:2019:CMD,
author = "Feng Qi and Ai-Qi Liu",
title = "Completely monotonic degrees for a difference between
the logarithmic and psi functions",
journal = j-J-COMPUT-APPL-MATH,
volume = "361",
number = "??",
pages = "366--371",
day = "1",
month = dec,
year = "2019",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Fri Sep 6 08:23:29 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S0377042719302298",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Shterenlikht:2019:QIF,
author = "A. Shterenlikht",
title = "On Quality of Implementation of {Fortran 2008} Complex
Intrinsic Functions on Branch Cuts",
journal = j-TOMS,
volume = "45",
number = "1",
pages = "11:1--11:9",
month = mar,
year = "2019",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3301318",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon May 6 18:23:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3301318",
abstract = "Branch cuts in complex functions have important uses
in fracture mechanics, jet flow, and aerofoil analysis.
This article introduces tests for validating Fortran
2008 complex functions-LOG, SQRT, ASIN, ACOS, ATAN,
ASINH, ACOSH, and ATANH-on branch cuts with arguments
of all 3 IEEE floating-point binary formats: binary32,
binary64, and binary128, including signed zero and
signed infinity. Multiple test failures were revealed,
such as wrong signs of results or unexpected overflow,
underflow, or NaN. We conclude that the quality of
implementation of these Fortran 2008 intrinsics in many
compilers is not yet sufficient to remove the need for
special code for branch cuts. The electronic appendix
contains the full test results with 8 Fortran 2008
compilers: GCC, Flang, Cray, Oracle, PGI, Intel, NAG,
and IBM, detailed derivations of the values of these
functions on branch cuts and conformal maps of the
branch cuts, to be used as a reference. The tests and
the results are freely available from
https://cmplx.sourceforge.io. This work will be of
interest to engineers who use complex functions, as
well as to compiler and math library developers.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Volkova:2019:SAI,
author = "Anastasia Volkova and Jean-Michel Muller",
title = "Semi-Automatic Implementation of the Complementary
Error Function",
crossref = "Takagi:2019:ISC",
pages = "167--174",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00039",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The normal and complementary error functions are
ubiquitous special functions for any mathematical
library. They have a wide range of applications.
Practical applications call for customized
implementations that have strict accuracy requirements.
Accurate numerical implementation of these functions
is, however, non-trivial. In particular, the
complementary error function erfc for large positive
arguments heavily suffers from cancellation, which is
largely due to its asymptotic behavior. We provide a
semi-automatic code generator for the erfc function
which is parameterized by the user-given bound on the
relative error. Our solution exploits the asymptotic
expression of erfc and leverages the automatic code
generator Metalibm that provides accurate polynomial
approximations. A fine-grained a priori error analysis
provides a libm developer with the required accuracy
for each step of the evaluation. In critical parts, we
exploit double-word arithmetic to achieve
implementations that are fast, yet accurate up to 50
bits, even for large input arguments. We demonstrate
that for high required accuracies the automatically
generated code has performance comparable to that of
the standard libm and for lower ones our code
demonstrated roughly 25\% speedup.",
acknowledgement = ack-nhfb,
keywords = "a priori error analysis; ARITH-26; asymptotic
behavior; asymptotic expression; complementary error
functions; Digital arithmetic; Error analysis; error
analysis; error function; floating-point arithmetic;
Generators; Libraries; Lips; mathematical library;
Metalibm; normal error functions; polynomial
approximation; polynomial approximations; program
compilers; semi-automated code generation;
semiautomatic code generator; semiautomatic
implementation; Standards; Tools; ubiquitous special
functions",
}
@Article{Zaghloul:2019:RO,
author = "Mofreh R. Zaghloul",
title = "Remark on {`Algorithm 680: Evaluation of the Complex
Error Function': Cause and Remedy for the Loss of
Accuracy Near the Real Axis}",
journal = j-TOMS,
volume = "45",
number = "2",
pages = "24:1--24:3",
month = apr,
year = "2019",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3309681",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon May 6 18:23:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3309681",
abstract = "In this remark, we identify the cause of the loss of
accuracy in the computation of the Faddeyeva function,
$ w(z) $, near the real axis when using Algorithm 680.
We provide a simple correction to this problem that
allows us to restore this code as one of the important
reference routines for accuracy comparisons.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Abergel:2020:AFA,
author = "R{\'e}my Abergel and Lionel Moisan",
title = "{Algorithm 1006}: Fast and Accurate Evaluation of a
Generalized Incomplete Gamma Function",
journal = j-TOMS,
volume = "46",
number = "1",
pages = "10:1--10:24",
month = mar,
year = "2020",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3365983",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Apr 7 10:39:23 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3365983",
abstract = "We present a computational procedure to evaluate the
integral $ \int^y_x s^{p - 1} e^{- \mu s} \, d s $ for
$ 0 \leq x < y \leq + \infty $, $ \mu = \pm 1 $, $ p >
0 $, which generalizes the lower $ (x = 0) $ and upper
$ (y = + \infty) $ incomplete gamma functions. To allow
for large values of $x$, $y$, and $p$ while avoiding
under\slash overflow issues in the standard double
precision floating point arithmetic, we use an explicit
normalization that is much more efficient than the
classical ratio with the complete gamma function. The
generalized incomplete gamma function is estimated with
continued fractions, with integrations by parts, or,
when $ x \approx y$, with the Romberg numerical
integration algorithm. We show that the accuracy
reached by our algorithm improves a recent
state-of-the-art method by two orders of magnitude, and
it is essentially optimal considering the limitations
imposed by floating point arithmetic. Moreover, the
admissible parameter range of our algorithm $ (0 \leq
p, x, y \leq 10^{15})$ is much larger than competing
algorithms, and its robustness is assessed through
massive usage in an image processing application.",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Adell:2020:RAE,
author = "Jos{\'e} A. Adell and Alberto Lekuona",
title = "Rational approximation to {Euler}'s constant at a
geometric rate of convergence",
journal = j-MATH-COMPUT,
volume = "89",
number = "325",
pages = "2553--2561",
month = jan,
year = "2020",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3528",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Jul 14 07:56:12 MDT 2020",
bibsource = "http://www.ams.org/mcom/2020-89-325;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2020.bib",
URL = "https://www.ams.org/AMSMathViewer;
https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03528-5;
https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03528-5/S0025-5718-2020-03528-5.pdf;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=340766;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=663604",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Chin:2020:PPW,
author = "Wooyoung Chin",
title = "A Probabilistic Proof of a {Wallis}-type Formula for
the Gamma Function",
journal = j-AMER-MATH-MONTHLY,
volume = "127",
number = "1",
pages = "75--79",
year = "2020",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.1080/00029890.2020.1668708",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Dec 13 15:45:45 MST 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html;
https://www.tandfonline.com/loi/uamm20",
onlinedate = "19 Dec 2019",
}
@Article{Ewart:2020:PES,
author = "Timoth{\'e}e Ewart and Francesco Cremonesi and Felix
Sch{\"u}rmann and Fabien Delalondre",
title = "Polynomial Evaluation on Superscalar Architecture,
Applied to the Elementary Function $ e^x $",
journal = j-TOMS,
volume = "46",
number = "3",
pages = "28:1--28:22",
month = sep,
year = "2020",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3408893",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Sep 26 07:28:19 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3408893",
abstract = "The evaluation of small degree polynomials is critical
for the computation of elementary functions. It has
been extensively studied and is well documented. In
this article, we evaluate existing methods for
polynomial evaluation on superscalar architecture. In
addition, we have completed this work with a
factorization method, which is surprisingly neglected
in the literature. This work focuses on out-of-order
Intel processors, amongst others, of which
computational units are available. Moreover, we applied
our work on the elementary function $ e^x $ that
requires, in the current implementation, an evaluation
of a polynomial of degree 10 for a satisfying precision
and performance. Our results show that the
factorization scheme is the fastest in benchmarks, and
that latency and throughput are intrinsically dependent
on each other on superscalar architecture.",
acknowledgement = ack-nhfb,
articleno = "28",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gil:2020:NEA,
author = "A. Gil and J. Segura and N. M. Temme",
title = "Numerical evaluation of {Airy}-type integrals arising
in uniform asymptotic analysis",
journal = j-J-COMPUT-APPL-MATH,
volume = "371",
number = "??",
pages = "Article 112717",
month = jun,
year = "2020",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Wed May 13 06:58:32 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704272030008X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Gimbutas:2020:EAF,
author = "Zydrunas Gimbutas and Shidong Jiang and Li-Shi Luo",
title = "Evaluation of {Abramowitz} functions in the right half
of the complex plane",
journal = j-J-COMPUT-PHYS,
volume = "405",
number = "??",
pages = "Article 109169",
day = "15",
month = mar,
year = "2020",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2019.109169",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Mar 9 18:28:24 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999119308745",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
keywords = "Abramowitz functions; Laurent series; Least squares
method",
remark = "The Abramowitz functions of order n, defined by $
J_n(z) = \int_0^\infty t^n \exp ( - t^2 - z / t) \, d t
$, for $ n \in \mathbb {Z} $.",
}
@Article{Godunov:2020:ACC,
author = "A. Godunov",
title = "Algorithms for Calculating Correctly Rounded
Exponential Function in Double-Precision Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "9",
pages = "1388--1400",
month = sep,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2020.2972901",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Aug 12 14:58:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
abstract = "Correct rounding provides the best approximation of
the exponential function by double-precision numbers.
To obtain the correctly rounded exponential of some
arguments, the exponential should be calculated with
high accuracy. For small arguments, even higher
accuracy is required. This article presents simple and
very fast algorithms for small arguments. Yet another
algorithm presented here demonstrates a good maximum
execution time, which may be important for critical
applications. This algorithm can be combined with some
other already existing algorithms to achieve the best
maximum and average execution times. All proposed
algorithms calculate the correctly rounded exponential
function for all rounding modes and use only
double-precision arithmetic for computation. In the
argument reduction step, precalculated tables are used.
Test implementations of these algorithms were developed
in C language and are portable. Full proofs are
presented either in this article itself or in its
appendices.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Harper:2020:AGH,
author = "J. F. Harper",
title = "Asymptotics of a {Gauss} hypergeometric function with
two large parameters: a new case",
journal = j-ANZIAM-J,
volume = "62",
number = "4",
pages = "446--452",
month = oct,
year = "2020",
CODEN = "AJNOA2",
DOI = "https://doi.org/10.1017/S1446181119000166",
ISSN = "1446-1811 (print), 1446-8735 (electronic)",
ISSN-L = "1446-1811",
bibdate = "Fri May 14 17:04:43 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.cambridge.org/core/journals/anziam-journal/article/asymptotics-of-a-gauss-hypergeometric-function-with-two-large-parameters-a-new-case/32B40986E7DB85F500FC9024F846E527",
acknowledgement = ack-nhfb,
ajournal = "ANZIAM J.",
fjournal = "The ANZIAM Journal. The Australian \& New Zealand
Industrial and Applied Mathematics Journal",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
onlinedate = "10 December 2019",
}
@Article{Hrycak:2020:ELP,
author = "Tomasz Hrycak and Sebastian Schmutzhard",
title = "Evaluation of {Legendre} polynomials by a three-term
recurrence in floating-point arithmetic",
journal = j-IMA-J-NUMER-ANAL,
volume = "40",
number = "1",
pages = "587--605",
month = jan,
year = "2020",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/dry079",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Sat Feb 29 14:22:43 MST 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
URL = "http://academic.oup.com/imajna/article/40/1/587/5162990",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Jablonski:2020:IAC,
author = "A. Jablonski",
title = "Improved algorithm for calculating high accuracy
values of the {Chandrasekhar} function",
journal = j-COMP-PHYS-COMM,
volume = "251",
number = "??",
pages = "Article 107237",
month = jun,
year = "2020",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2020.107237",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri May 29 07:03:02 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465520300709",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Johansson:2020:CLW,
author = "Fredrik Johansson",
title = "Computing the {Lambert $W$} function in
arbitrary-precision complex interval arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "83",
number = "1",
pages = "221--242",
month = jan,
year = "2020",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-019-00678-x",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Jan 22 08:40:22 MST 2020",
bibsource = "http://link.springer.com/journal/11075/83/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@InCollection{Johansson:2020:FSL,
author = "Fredrik Johansson",
title = "{FunGrim}: A Symbolic Library for Special Functions",
crossref = "Bigatti:2020:MSI",
pages = "315--323",
year = "2020",
DOI = "https://doi.org/10.1007/978-3-030-52200-1_31",
bibdate = "Sat Sep 23 06:47:37 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Johnson:2020:EAHa,
author = "Jeff Johnson",
title = "Efficient, arbitrarily high precision hardware
logarithmic arithmetic for linear algebra",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "1--8",
day = "14",
month = may,
year = "2020",
bibdate = "Tue Jul 06 18:17:13 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/pdf/2004.09313.pdf",
abstract = "The logarithmic number system (LNS) is arguably not
broadly used due to exponential circuit overheads for
summation tables relative to arithmetic precision.
Methods to reduce this overhead have been proposed, yet
still yield designs with high chip area and power
requirements. Use remains limited to lower precision or
high multiply/add ratio cases, while much of linear
algebra (near 1:1 multiply/add ratio) does not
qualify.\par
We present a dual-base approximate logarithmic
arithmetic comparable to floating point in use, yet
unlike LNS it is easily fully pipelined, extendable to
arbitrary precision with $ O(n^2) $ overhead, and
energy efficient at a 1:1 multiply/add ratio.Compared
to float32 or float64 vector inner product with FMA,
our design is respectively $ 2.3 \times $ and $ 4.6
\times $ more energy efficient in 7 nm CMOS. It depends
on exp and log evaluation $ 5.4 \times $ and $ 3.2
\times $ more energy efficient, at $ 0.23 \times $ and
$ 0.37 \times $ the chip area for equivalent accuracy
versus standard hyperbolic CORDIC using shift-and-add
and approximated ODE integration in the style of Revol
and Yakoubsohn. This technique is a novel alternative
for low power, high precision hardened linear algebra
in computer vision, graphics and machine learning
applications.",
acknowledgement = ack-nhfb,
keywords = "approximate arithmetic; elementary function
evaluation; hardware linear algebra; logarithmic
arithmetic",
remark = "Published in \cite{Johnson:2020:EAHb}.",
}
@InProceedings{Johnson:2020:EAHb,
author = "Jeff Johnson",
title = "Efficient, arbitrarily high precision hardware
logarithmic arithmetic for linear algebra",
crossref = "Cornea:2020:ISC",
pages = "25--32",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00013",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The logarithmic number system (LNS) is arguably not
broadly used due to exponential circuit overheads for
summation tables relative to arithmetic precision.
Methods to reduce this overhead have been proposed, yet
still yield designs with high chip area and power
requirements. Use remains limited to lower precision or
high multiply/add ratio cases, while much of linear
algebra (near 1:1 multiply/add ratio) does not qualify.
We present a dual-base approximate logarithmic
arithmetic comparable to floating point in use, yet
unlike LNS it is easily fully pipelined, extendable to
arbitrary precision with $ O(n^2) $ overhead, and
energy efficient at a 1:1 multiply/add ratio. Compared
to float32 or float64 vector inner product with FMA,
our design is respectively $ 2.3 \times $ and $ 4.6
\times $ more energy efficient in 7 nm CMOS. It depends
on exp and log evaluation 5.4 and $ 3.2 \times $ more
energy efficient, at $ 0.23 \times $ and $ 0.37 \times
$ the chip area for equivalent accuracy versus standard
hyperbolic CORDIC using shift-and-add and approximated
ODE integration in the style of Revol and Yakoubsohn.
This technique is a novel alternative for low power,
high precision hardened linear algebra in computer
vision, graphics and machine learning applications.",
acknowledgement = ack-nhfb,
keywords = "Adders; approximate arithmetic; Clocks; elementary
function evaluation; Hardware; hardware linear algebra;
Linear algebra; logarithmic arithmetic; Pipeline
processing; Read only memory; Switches",
}
@Book{Korotkov:2020:IRE,
author = "N. E. (Nikola{\'y}i Efimovich) Korotkov and Alexander
N. Korotkov",
title = "Integrals Related to the Error Function",
publisher = "CRC Press, Taylor and Francis Group",
address = "Boca Raton, FL, USA",
pages = "xx + 227",
year = "2020",
ISBN = "0-367-40820-1 (hardcover), 0-367-80923-0 (e-book),
1-000-03307-4 (e-book), 1-000-03308-2 (Mobipocket
e-book), 1-000-03309-0 (e-Pub)",
ISBN-13 = "978-0-367-40820-6 (hardcover), 978-0-367-80923-2
(e-book), 978-1-000-03307-6 (e-book), 978-1-000-03308-3
(Mobipocket e-book), 978-1-000-03309-0 (e-Pub)",
LCCN = "QA308 .K67 2020",
bibdate = "Fri Feb 5 17:54:22 MST 2021",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "\booktitle{Integrals Related to the Error Function}
presents a table of integrals related to the error
function, including indefinite and improper definite
integrals. Most of the formulas in this book have not
been presented in other tables of integrals or have
been presented only for some special cases of
parameters or for integration only along the real axis
of the complex plane. Many of the integrals presented
here cannot be obtained using a computer (except via an
approximate numerical integration). Additionally, for
improper integrals, this book emphasizes the necessary
and sufficient conditions for the validity of the
presented formulas, including trajectory for going to
infinity on the complex plane; such conditions are
usually not given in computer-assisted analytical
integration and often not presented in the previously
published tables of integrals. Features The first book
in English language to present a comprehensive
collection of integrals related to the error function
Useful for researchers whose work involves the error
function (e.g., via probability integrals in
communication theory). Additionally, it can also be
used by broader audience.",
acknowledgement = ack-nhfb,
subject = "Integrals; Tables; Error functions",
tableofcontents = "Indefinite integrals \\
Definite integrals \\
Appendix: Some useful formulas for obtaining other
integrals.",
}
@Article{Muller:2020:EFA,
author = "Jean-Michel Muller",
title = "Elementary Functions and Approximate Computing",
journal = j-PROC-IEEE,
volume = "108",
number = "12",
pages = "2136--2149",
month = dec,
year = "2020",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1109/jproc.2020.2991885",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Tue Mar 1 06:07:02 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Naterop:2020:HRN,
author = "L. Naterop and A. Signer and Y. Ulrich",
title = "{handyG} --- Rapid numerical evaluation of generalised
polylogarithms in {Fortran}",
journal = j-COMP-PHYS-COMM,
volume = "253",
number = "??",
pages = "Article 107165",
month = aug,
year = "2020",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2020.107165",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 19 07:19:48 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465520300230",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@TechReport{Pornin:2020:OBG,
author = "Thomas Pornin",
title = "Optimized Binary {GCD} for Modular Inversion",
type = "Report",
number = "??",
institution = "International Association for Cryptologic Research",
address = "????",
pages = "16",
day = "23",
month = aug,
year = "2020",
bibdate = "Mon May 30 07:10:10 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://eprint.iacr.org/2020/972.pdf",
abstract = "In this short note, we describe a practical
optimization of the well-known extended binary GCD
algorithm, for the purpose of computing modular
inverses. The method is conceptually simple and is
applicable to all odd moduli (including non-prime
moduli). When implemented for inversion in the field of
integers modulo the prime $ 2^{255} - 19 $, on a recent
x86 CPU (Coffee Lake core), we compute the inverse in
6253 cycles, with a fully constant-time
implementation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Raveendran:2020:NPF,
author = "Aneesh Raveendran and Sandra Jean and J. Mervin and D.
Vivian and David Selvakumar",
editor = "{IEEE}",
booktitle = "{2020 33rd International Conference on VLSI Design and
2020 19th International Conference on Embedded Systems
(VLSID), Bengaluru, India, 4--8 January 2020}",
title = "A Novel Parametrized Fused Division and Square-Root
{POSIT} Arithmetic Architecture",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "207--212",
month = jan,
year = "2020",
DOI = "https://doi.org/10.1109/vlsid49098.2020.00053",
ISBN = "1-72815-701-3",
ISBN-13 = "978-1-72815-701-6",
ISSN = "1063-9667 (print), 2380-6923 (electronic)",
ISSN-L = "1063-9667",
bibdate = "Fri Dec 15 07:29:26 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Shibata:2020:SPV,
author = "Naoki Shibata and Francesco Petrogalli",
title = "{SLEEF}: A Portable Vectorized Library of {C} Standard
Mathematical Functions",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "31",
number = "6",
pages = "1316--1327",
month = jun,
year = "2020",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/TPDS.2019.2960333",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Thu Feb 20 10:08:58 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
keywords = "elementary functions; floating-point arithmetic;
Parallel and vector implementations; SIMD processors",
}
@Article{Wakhare:2020:TCJ,
author = "Tanay Wakhare and Christophe Vignat",
title = "{Taylor} coefficients of the {Jacobi} $ \theta_3 (q) $
function",
journal = j-J-NUMBER-THEORY,
volume = "216",
number = "??",
pages = "280--306",
month = nov,
year = "2020",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1016/j.jnt.2020.03.002",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Sat Aug 8 09:41:52 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X20300858",
acknowledgement = ack-nhfb,
ajournal = "J. Number Theory",
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
}
@Article{Xiao:2020:PAH,
author = "Feibao Xiao and Feng Liang and Bin Wu and Junzhe Liang
and Shuting Cheng and Guohe Zhang",
title = "Posit Arithmetic Hardware Implementations with The
Minimum Cost Divider and Square Root",
journal = j-ELECTRONICS,
volume = "9",
number = "10",
pages = "1622:1--1622:16",
month = oct,
year = "2020",
DOI = "https://doi.org/10.3390/electronics9101622",
ISSN = "2079-9292",
ISSN-L = "2079-9292",
bibdate = "Fri Dec 15 07:25:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@Article{Akram:2021:XFA,
author = "Riad Akram and Shantanu Mandal and Abdullah Muzahid",
title = "{XMeter}: Finding Approximable Functions and
Predicting Their Accuracy",
journal = j-IEEE-TRANS-COMPUT,
volume = "70",
number = "7",
pages = "1081--1093",
month = jul,
year = "2021",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2020.3005083",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jun 10 15:51:57 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Bailey:2021:PMN,
author = "David H. Bailey",
title = "\pkg{MPFUN2020}: a new thread-safe arbitrary precision
package",
howpublished = "Web document",
pages = "54",
day = "18",
month = may,
year = "2021",
bibdate = "Mon Dec 05 07:32:16 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.davidhbailey.com/dhbpapers/mpfun2020.pdf",
abstract = "Numerous research studies have arisen, particularly in
mathematical physics and experimental mathematics, that
require extremely high numeric precision. Such
precision greatly magnifies computer run times, so
software packages to support high-precision computing
must be designed for thread-based parallel
processing.
This paper describes a new arbitrary precision software
package (``MPFUN2020'') that features several
significant improvements over an earlier package. It
comes in two versions: a self-contained all-Fortran
version, and a version based on the MPFR package, which
is even faster. Both versions feature: (a) a completely
thread-safe design, so user codes can be converted for
parallel execution at the application level; (b) a
full-featured high-level Fortran interface, so that
most applications can be converted to multiprecision
with relatively minor changes to source code; (c) full
support for both real and complex datatypes; (d) a wide
variety of transcendental functions and special
functions; (e) run-time checking and other facilities
to overcome problems with converting double precision
constants and data; (f) a medium precision datatype,
which improves performance and reduces memory cost on
large variable precision applications; and (g)
interoperability --- with a simple restriction,
application codes written for one version can be run
with the other without change.",
acknowledgement = ack-nhfb,
}
@Article{Borges:2021:AIA,
author = "Carlos F. Borges",
title = "{Algorithm 1014}: an Improved Algorithm for {\tt
hypot(x,y)}",
journal = j-TOMS,
volume = "47",
number = "1",
pages = "9:1--9:12",
month = jan,
year = "2021",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3428446",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Jan 7 10:31:04 MST 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/julia.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3428446",
abstract = "We develop fast and accurate algorithms for evaluating
$ \sqrt {x^2 + y^2} $ for two floating-point numbers
$x$ and $y$. Library functions that perform this
computation are generally named {\tt hypot(x,y)}. We
compare five approaches that we will develop in this
article to the current resident library function that
is delivered with Julia 1.1 and to the code that has
been distributed with the C math library for decades.
We will investigate the accuracy of our algorithms by
simulation.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Borges:2021:CRN,
author = "Carlos F. Borges",
title = "A Correctly Rounded {Newton} Step for the Reciprocal
Square Root",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--8",
day = "28",
month = dec,
year = "2021",
bibdate = "Fri Sep 22 16:08:53 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2112.14321",
abstract = "The reciprocal square root is an important computation
for which many sophisticated algorithms exist (see for
example \cite{Moroz,863046,863031} and the references
therein). A common theme is the use of Newton's method
to refine the estimates. In this paper we develop a
correctly rounded Newton step that can be used to
improve the accuracy of a naive calculation (using
methods similar to those developed in \cite{borges})
The approach relies on the use of the fused
multiply-add (FMA) which is widely available in
hardware on a variety of modern computer architectures.
We then introduce the notion of {\em weak rounding} and
prove that our proposed algorithm meets this standard.
We then show how to leverage the exact Newton step to
get a Halley's method compensation which requires one
additional FMA and one additional multiplication. This
method appears to give correctly rounded results
experimentally and we show that it can be combined with
a square root free method for estimating the reciprocal
square root to get a method that is both very fast (in
computing environments with a slow square root) and,
experimentally, highly accurate.",
acknowledgement = ack-nhfb,
}
@Article{Borges:2021:FCA,
author = "Carlos F. Borges",
title = "Fast compensated algorithms for the reciprocal square
root, the reciprocal hypotenuse, and {Givens}
rotations",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--11",
day = "23",
month = feb,
year = "2021",
bibdate = "Fri Sep 22 16:05:47 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2103.08694",
abstract = "The reciprocal square root is an important computation
for which many very sophisticated algorithms exist (see
for example \cite{863046,863031} and the references
therein). In this paper we develop a simple
differential compensation (much like those developed in
\cite{borges}) that can be used to improve the accuracy
of a naive calculation. The approach relies on the use
of the fused multiply-add (FMA) which is widely
available in hardware on a variety of modern computer
architectures. We then demonstrate how to combine this
approach with a somewhat inaccurate but fast square
root free method for estimating the reciprocal square
root to get a method that is both fast (in computing
environments with a slow square root) and,
experimentally, highly accurate. Finally, we show how
this same approach can be extended to the reciprocal
hypotenuse calculation and, most importantly, to the
construction of Givens rotations.",
acknowledgement = ack-nhfb,
}
@Article{Iacono:2021:BEF,
author = "Roberto Iacono",
title = "Bounding the Error Function",
journal = j-COMPUT-SCI-ENG,
volume = "23",
number = "4",
pages = "65--68",
year = "2021",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCSE.2021.3083778",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Thu Jul 29 07:00:57 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Prompted by previous work published in this magazine,
in this article we focus on the derivation of global
analytical bounds for the error function of a real
argument. Using an integral representation of this
function, we obtain two simple and accurate lower
bounds, which complement a well-known upper bound given
long ago by P{\'o}lya.",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}
@Article{Johansson:2021:APC,
author = "Fredrik Johansson",
title = "Arbitrary-Precision Computation of the Gamma
Function",
journal = "arXiv.org",
pages = "1--51",
day = "17",
month = sep,
year = "2021",
DOI = "https://doi.org/10.48550/arXiv.2109.0839",
bibdate = "Sun Dec 04 11:01:23 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://arxiv.org/abs/2109.08392",
abstract = "We discuss the best methods available for computing
the gamma function $ \Gamma (z) $ in
arbitrary-precision arithmetic with rigorous error
bounds. We address different cases: rational,
algebraic, real or complex arguments; large or small
arguments; low or high precision; with or without
precomputation. The methods also cover the log-gamma
function $ \log \Gamma (z) $, the digamma function $
\psi (z) $, and derivatives $ \Gamma^{(n)}(z) $ and $
\psi^{(n)}(z) $. Besides attempting to summarize the
existing state of the art, we present some new
formulas, estimates, bounds and algorithmic
improvements and discuss implementation results.",
acknowledgement = ack-nhfb,
}
@Article{Kang:2021:NEE,
author = "Hongchao Kang and Hong Wang",
title = "Numerical evaluation and error analysis of many
different oscillatory {Bessel} transforms via confluent
hypergeometric function",
journal = j-APPL-NUM-MATH,
volume = "160",
number = "??",
pages = "23--41",
month = feb,
year = "2021",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Tue Dec 29 07:52:55 MST 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0168927420302932",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Langdon:2021:GID,
author = "William B. Langdon and Oliver Krauss",
title = "Genetic Improvement of Data for Maths Functions",
journal = j-TELO,
volume = "1",
number = "2",
pages = "7:1--7:30",
month = jun,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.1145/3461016",
ISSN = "2688-299X (print), 2688-3007 (electronic)",
ISSN-L = "2688-299X",
bibdate = "Sat Aug 21 15:11:10 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/telo.bib",
URL = "https://dl.acm.org/doi/10.1145/3461016",
abstract = "We use continuous optimisation and manual code changes
to evolve up to 1024 Newton--Raphson numerical values
embedded in an open source GNU C library glibc square
root sqrt to implement a double precision cube root
routine cbrt, binary logarithm log2 and reciprocal
square root function for C in seconds. The GI inverted
square root $ x{-1 / 2} $ is far more accurate than
Quake's InvSqrt, Quare root. GI shows potential for
automatically creating mobile or low resource mote
smart dust bespoke custom mathematical libraries with
new functionality.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Evolutionary Learning and
Optimization",
journal-URL = "https://dl.acm.org/loi/telo",
}
@InProceedings{Lim:2021:HPC,
author = "Jay P. Lim and Santosh Nagarakatte",
booktitle = "Proceedings of the {42nd ACM SIGPLAN International
Conference on Programming Language Design and
Implementation}",
title = "High performance correctly rounded math libraries for
32-bit floating point representations",
publisher = pub-ACM,
address = pub-ACM:adr,
month = jun,
year = "2021",
DOI = "https://doi.org/10.1145/3453483.3454049",
bibdate = "Tue Sep 24 15:06:44 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://github.com/rutgers-apl/rlibm-32",
abstract = "This paper proposes a set of techniques to develop
correctly rounded math libraries for 32-bit float and
posit types. It enhances our RLIBM approach that frames
the problem of generating correctly rounded libraries
as a linear programming problem in the context of
16-bit types to scale to 32-bit types. Specifically,
this paper proposes new algorithms to (1) generate
polynomials that produce correctly rounded outputs for
all inputs using counterexample guided polynomial
generation, (2) generate efficient piecewise
polynomials with bit-pattern based domain splitting,
and (3) deduce the amount of freedom available to
produce correct results when range reduction involves
multiple elementary functions. The resultant math
library for the 32-bit float type is faster than
state-of-the-art math libraries while producing the
correct output for all inputs. We have also developed a
set of correctly rounded elementary functions for
32-bit posits.",
acknowledgement = ack-nhfb,
description = "RLIBM-32 is both a math library that provides
correctly rounded result for all inputs and tools used
to generate the correct polynomials. The techniques
behind the tools will be appearing at PLDI 2021.
Currently, RLIBM-32 supports a number of elementary
functions for float and posit32
representations.\par
List of float functions supported by
RLIBM-32:\par
log(x), log2(x), log10(x) \\
exp(x), exp2(x), exp10(x) \\
sinh(x), cosh(x) \\
sinpi(x), cospi(x)\par
List of posit32 functions supported by
RLIBM-32:\par
log(x), log2(x), log10(x) \\
exp(x), exp2(x), exp10(x) \\
sinh(x), cosh(x)",
keywords = "binary32; correctly rounded functions; posit32",
remark-1 = "From page 360: ``Our RLibm approach [31, 32] generates
polynomials that approximate the correctly rounded
result rather than the real value of the elementary
function. \ldots{} Using the RLibm approach, we have
been successful in generating correctly rounded
libraries with 16-bit types such as bfloat16 and
posit16.''",
remark-2 = "From page 360: ``A naive use of the RLibm approach
with 32-bit types will generate more than a billion
constraints, which is beyond the capabilities of
current LP solvers.''",
remark-3 = "From page 361: ``Our elementary functions for floats
are faster than existing libraries: Intel's libm,
Glibc's libm, CR-LIBM [13], and Metalibm [25]. Unlike
existing libraries, our functions produce correctly
rounded results for all inputs. We have developed the
first correctly rounded implementations of functions
for 32-bit posits.''",
remark-4 = "From page 363: ``All internal computation such as
range reduction, polynomial evaluation, and output
compensation is performed in representation H where H
has higher precision than T. To attain good
performance, H is a representation that is supported in
hardware (e.g., double).''",
remark-5 = "From page 368: ``CR-LIBM has correctly rounded
functions for double precision. However, CR-LIBM does
not produce correctly rounded results for 32-bit floats
due to double rounding. There are no math libraries
available for posit32. All posit32 values can be
exactly represented in double.''",
remark-6 = "From page 370: ``All three re-purposed math libraries
produce wrong results for some inputs. RLibm-32
provides the first correctly rounded functions for the
posit32 type.''",
remark-7 = "From page 372: ``This paper extends our prior work on
RLibm [31, 32] and John Gustafson's Minefield method
[20], which advocate approximating the correctly
rounded value rather than real value of an elementary
function.''",
remark-8 = "From page 372: ``We have used RLibm to create
correctly rounded functions for 16-bit types: bfloat16
and posit16.''",
}
@Article{Lipovetsky:2021:BRI,
author = "Stan Lipovetsky",
title = "Book Review: {{\booktitle{Integrals Related to the
Error Function}}, by Nikolai E. Korotkov and Alexander
N. Korotkov. Boca Raton, FL: Chapman and Hall\slash CRC
Press, Taylor \& Francis Group, 2020, 228 pp., \$140.00
(hardback), \$46.36 (eBook), ISBN: 978-0-367-40820-6
(hardback)}",
journal = j-TECHNOMETRICS,
volume = "62",
number = "4",
pages = "560--560",
year = "2021",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.1080/00401706.2020.1825632",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Fri Feb 5 17:42:52 MST 2021",
bibsource = "http://www.tandf.co.uk/journals/titles/00401706.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics2020.bib",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.tandfonline.com/loi/utch20",
onlinedate = "23 Oct 2020",
}
@TechReport{MPFR:2021:MLA,
author = "{The MPFR Team}",
title = "The {MPFR} Library: Algorithms and Proofs",
type = "Report",
institution = "????",
address = "????",
pages = "69",
day = "5",
month = nov,
year = "2021",
bibdate = "Tue Mar 14 13:13:13 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.mpfr.org/algorithms.pdf",
acknowledgement = ack-nhfb,
}
@Article{Snyder:2021:CRA,
author = "W. Van Snyder",
title = "Corrigendum: {Remark on Algorithm 723: Fresnel
Integrals}",
journal = j-TOMS,
volume = "47",
number = "4",
pages = "37:1--37:1",
month = dec,
year = "2021",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3452336",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Sep 29 06:58:41 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Snyder:1993:AFI}.",
URL = "https://dl.acm.org/doi/10.1145/3452336",
abstract = "There are mistakes and typographical errors in Remark
on Algorithm 723: Fresnel Integrals, which appeared in
ACM Transactions on Mathematical Software 22, 4
(December 1996). This remark corrects those errors. The
software provided to Collected Algorithms of the ACM
was correct.",
acknowledgement = ack-nhfb,
articleno = "37",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Walczyk:2021:IAF,
author = "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
Cie{\'s}li{\'n}ski",
title = "Improving the Accuracy of the Fast Inverse Square Root
by Modifying {Newton--Raphson} Corrections",
journal = j-ENTROPY,
volume = "23",
number = "1",
pages = "86:1--86:20",
month = jan,
year = "2021",
CODEN = "ENTRFG",
DOI = "https://doi.org/10.3390/e23010086",
ISSN = "1099-4300",
ISSN-L = "1099-4300",
bibdate = "Wed Dec 20 07:52:39 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Entropy",
journal-URL = "https://www.mdpi.com/journal/entropy/",
}
@Misc{Anonymous:2022:DLM,
author = "Anonymous",
title = "Digital Library of Mathematical Functions: Date:
2010",
howpublished = "NIST Web site",
day = "14",
month = mar,
year = "2022",
bibdate = "Wed Oct 25 18:20:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://dlmf.nist.gov/;
https://www.nist.gov/mathematics-statistics/digital-library-mathematical-functions",
abstract = "In 2010, NIST released the Digital Library of
Mathematical Functions (DLMF), an online successor to
the classic Abramowitz and Stegun \booktitle{Handbook
of Mathematical Functions}.
[\cite{Abramowitz:1964:HMF}]",
acknowledgement = ack-nhfb,
remark = "From the site: ``By the late 1990s it [the 1964
Handbook] was still the most widely distributed and
cited publication of all time, regularly seeing more
than 2000 citations per year.''",
}
@InProceedings{Borges:2022:HLA,
author = "Carlos F. Borges and Claude-Pierre Jeannerod and
Jean-Michel Muller",
title = "High-level algorithms for correctly-rounded reciprocal
square roots",
crossref = "IEEE:2022:ISC",
pages = "18--25",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00013",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Bruguera:2022:LLH,
author = "Javier D. Bruguera",
title = "Low-Latency and High-Bandwidth Pipelined Radix-64
Division and Square Root Unit",
crossref = "IEEE:2022:ISC",
pages = "10--17",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00012",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Causley:2022:GFI,
author = "Matthew F. Causley",
title = "The gamma function via interpolation",
journal = j-NUMER-ALGORITHMS,
volume = "90",
number = "2",
pages = "687--707",
month = jun,
year = "2022",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-021-01204-8",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Sun May 8 06:36:19 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-021-01204-8",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Cojean:2022:GML,
author = "Terry Cojean and Yu-Hsiang Mike Tsai and Hartwig
Anzt",
title = "{Ginkgo} --- a math library designed for platform
portability",
journal = j-PARALLEL-COMPUTING,
volume = "111",
number = "??",
pages = "??--??",
month = jul,
year = "2022",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/j.parco.2022.102902",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Mon May 9 07:06:37 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167819122000096",
abstract = "In an era of increasing computer system diversity, the
portability of software from one system to another
plays a central role. Software portability is important
for the software developers as many software projects
have a lifetime longer than a specific system, e.g., a
supercomputer, and it is important for the domain
scientists that realize their scientific application in
a software framework and want to be able to run on one
or another system. On a high level, there exist two
approaches for realizing platform portability: (1)
implementing software using a portability layer
leveraging any technique which always generates
specific kernels from another language or through an
interface for running on different architectures; and
(2) providing backends for different hardware
architectures, with the backends typically differing in
how and in which programming language functionality is
realized due to using the language of choice for each
hardware (e.g., CUDA kernels for NVIDIA GPUs, SYCL
(DPC++) kernels to targeting Intel GPUs and other
supported hardware, \ldots). In practice, these two
approaches can be combined in applications to leverage
their respective strengths. In this paper, we present
how we realize portability across different hardware
architectures for the Ginkgo library by following the
second strategy and the goal to not only port to new
hardware architectures but also achieve good
performance. We present the Ginkgo library design,
separating algorithms from hardware-specific kernels
forming the distinct hardware executors, and report our
experience when adding execution backends for NVIDIA,
AMD, and Intel GPUs. We also present the performance we
achieve with this approach for distinct hardware
backends.",
acknowledgement = ack-nhfb,
articleno = "102902",
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@InProceedings{Gao:2022:TFI,
author = "Zhanyuan Gao and Laiping Zhao and Haonan Chen",
editor = "{IEEE}",
booktitle = "{2022 IEEE\slash ACIS 22nd International Conference on
Computer and Information Science (ICIS)}",
title = "A Trigonometric Function Instruction Set Extension
Method Based on {RISC-V}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "119--126",
year = "2022",
DOI = "https://doi.org/10.1109/ICIS54925.2022.9882453",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@Article{Hao:2022:DVP,
author = "Jiangwei Hao and Jinchen Xu and YuanYuan Xia",
title = "Design of variable precision transcendental function
automatic generator",
journal = j-J-SUPERCOMPUTING,
volume = "78",
number = "2",
pages = "2196--2218",
month = feb,
year = "2022",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-021-03937-8",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Mon Feb 28 16:44:34 MST 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
URL = "https://link.springer.com/article/10.1007/s11227-021-03937-8",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Howard:2022:AAA,
author = "Roy M. Howard",
title = "Arbitrarily Accurate Analytical Approximations for the
Error Function",
journal = j-MATH-COMPUT-APPL,
volume = "27",
number = "1",
pages = "14:1--14:44",
month = feb,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.3390/mca27010014",
ISSN = "2297-8747",
ISSN-L = "2297-8747",
bibdate = "Sun Feb 18 06:28:42 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
URL = "https://www.mdpi.com/2297-8747/27/1/14",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput. Appl.",
articleno = "14",
fjournal = "Mathematical and Computational Applications",
journal-URL = "https://www.mdpi.com/journal/mca",
}
@Article{Lim:2022:OPA,
author = "Jay P. Lim and Santosh Nagarakatte",
title = "One polynomial approximation to produce correctly
rounded results of an elementary function for multiple
representations and rounding modes",
journal = j-PACMPL,
volume = "6",
number = "POPL",
pages = "3:1--3:28",
month = jan,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1145/3498664",
ISSN = "2475-1421 (electronic)",
ISSN-L = "2475-1421",
bibdate = "Thu May 26 06:32:48 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
URL = "https://dl.acm.org/doi/10.1145/3498664",
abstract = "Mainstream math libraries for floating point (FP) do
not produce correctly rounded results for all inputs.
In contrast, CR-LIBM and RLIBM provide correctly
rounded implementations for a specific FP
representation with one rounding mode. Using such
libraries for a representation with a new rounding mode
or with different precision will result in wrong
results due to double rounding. This paper proposes a
novel method to generate a single polynomial
approximation that produces correctly rounded results
for all inputs for multiple rounding modes and multiple
precision configurations. To generate a correctly
rounded library for n-bits, our key idea is to generate
a polynomial approximation for a representation with
n+2-bits using the round-to-odd mode. We prove that the
resulting polynomial approximation will produce
correctly rounded results for all five rounding modes
in the standard and for multiple representations with
k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $
is the number of exponent bits in the representation.
Similar to our prior work in the RLIBM project, we
approximate the correctly rounded result when we
generate the library with n+2-bits using the
round-to-odd mode. We also generate polynomial
approximations by structuring it as a linear
programming problem but propose enhancements to
polynomial generation to handle the round-to-odd mode.
Our prototype is the first 32-bit float library that
produces correctly rounded results with all rounding
modes in the IEEE standard for all inputs with a single
polynomial approximation. It also produces correctly
rounded results for any FP configuration ranging from
10-bits to 32-bits while also being faster than
mainstream libraries.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "Proceedings of the ACM on Programming Languages
(PACMPL)",
journal-URL = "https://dl.acm.org/loi/pacmpl",
keywords = "correct rounding; elementary functions",
}
@InProceedings{Oh:2022:EPA,
author = "Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee",
editor = "{IEEE}",
booktitle = "{2022 19th International SoC Design Conference
(ISOCC)}",
title = "Evaluation of Posit Arithmetic on Machine Learning
based on Approximate Exponential Functions",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "358--359",
year = "2022",
DOI = "https://doi.org/10.1109/ISOCC56007.2022.10031524",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Takekawa:2022:FPC,
author = "Takashi Takekawa",
title = "Fast parallel calculation of modified {Bessel}
function of the second kind and its derivatives",
journal = j-SOFTWAREX,
volume = "17",
number = "??",
pages = "??--??",
month = jan,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.softx.2021.100923",
ISSN = "2352-7110",
ISSN-L = "2352-7110",
bibdate = "Mon Feb 28 10:41:25 MST 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/softwarex.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S2352711021001655",
acknowledgement = ack-nhfb,
articleno = "100923",
fjournal = "SoftwareX",
journal-URL = "https://www.sciencedirect.com/journal/softwarex/issues",
}
@Article{Ananthanarayan:2023:EAD,
author = "B. Ananthanarayan and Souvik Bera and S. Friot and O.
Marichev and Tanay Pathak",
title = "On the evaluation of the {Appell} {$ F_2 $} double
hypergeometric function",
journal = j-COMP-PHYS-COMM,
volume = "284",
number = "??",
pages = "Article 108589",
month = mar,
year = "2023",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2022.108589",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 06:01:54 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465522003083",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Bavier:2023:VNF,
author = "Eric Bavier and Nicholas Knight and Hugues de Lassus
Saint-Geni{\`e}s and Eric Love",
title = "Vectorized Nonlinear Functions with the {RISC-V}
Vector Extension",
crossref = "IEEE:2023:PIS",
pages = "127--130",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00032",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; floating point; Instruction sets; Libraries;
Pipelines; RISC-V vectors; scalable vectors; Software;
Software algorithms; vector mathematical functions;
Vectors; Writing",
}
@Article{Blanchard:2023:NMD,
author = "Jeffrey D. Blanchard and Marc Chamberland",
title = "{Newton}'s Method Without Division",
journal = j-AMER-MATH-MONTHLY,
volume = "130",
number = "7",
pages = "606--617",
year = "2023",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.1080/00029890.2022.2093573",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Fri Aug 25 08:24:37 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html;
https://www.tandfonline.com/loi/uamm20",
onlinedate = "04 Aug 2023",
}
@InProceedings{Brisebarre:2023:TME,
author = "Nicolas Brisebarre and Silviu-Ioan Filip",
title = "Towards Machine-Efficient Rational {$ L^\infty
$}-Approximations of Mathematical Functions",
crossref = "IEEE:2023:PIS",
pages = "119--126",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00029",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; ARITH-30; Behavioral
sciences; Digital arithmetic; Software",
}
@InProceedings{deLamarliere:2023:SFP,
author = "Paul Geneau de Lamarli{\`e}re and Guillaume Melquiond
and Florian Faissole",
title = "Slimmer Formal Proofs for Mathematical Libraries",
crossref = "IEEE:2023:PIS",
pages = "32--35",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00026",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Behavioral sciences; Codes; Coq proof
assistant; Costs; Digital arithmetic; Floating-point
arithmetic; Formal methods; Libraries; Mathematical
libraries; Writing",
}
@Article{Gil:2023:EGF,
author = "Amparo Gil and Andrzej Odrzywo{\l}ek and Javier Segura
and Nico M. Temme",
title = "Evaluation of the generalized {Fermi--Dirac} integral
and its derivatives for moderate\slash large values of
the parameters",
journal = j-COMP-PHYS-COMM,
volume = "283",
number = "??",
pages = "Article 108563",
month = feb,
year = "2023",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2022.108563",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Dec 5 09:16:39 MST 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S001046552200282X",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Graillat:2023:PCH,
author = "Stef Graillat and Youness Ibrahimy and Clothilde
Jeangoudoux and Christoph Lauter",
title = "A parallel compensated {Horner} scheme for {SIMD}
architecture",
crossref = "IEEE:2023:PIS",
pages = "131--138",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00010",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; AVX; compensated algorithms; Computer
architecture; Computers; Costs; Digital arithmetic;
error-free transformations; Horner scheme; Limiting;
parallel algorithms; polynomial evaluation; Registers;
rounding errors; Scalability; SIMD",
}
@TechReport{Hubrecht:2023:TCRa,
author = "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
Zimmermann",
title = "Towards a correctly-rounded and fast power function in
binary64 arithmetic",
type = "Report",
institution = "DI-ENS --- D{\'e}partement d'informatique --- ENS
Paris",
address = "Paris, France",
day = "12",
month = jul,
year = "2023",
bibdate = "Mon May 13 12:00:21 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-04159652v1/",
abstract = "We design algorithms for the correct rounding of the
power function $ x^y $ in the binary64 IEEE 754 format,
for all rounding modes, modulo the knowledge of
hardest-to-round cases. Our implementation of these
algorithms largely outperforms previous
correctly-rounded implementations and is not far from
the efficiency of current mathematical libraries, which
are not correctly-rounded. Still, we expect our
algorithms can be further improved for speed. The
proofs of correctness are fully detailed in an extended
version of this paper, with the goal to enable a formal
proof of these algorithms. We hope this work will
motivate the next IEEE 754 revision committee to
require correct rounding for mathematical functions.",
acknowledgement = ack-nhfb,
remark = "This is a longer version of \cite{Hubrecht:2023:TCRb}
with proofs.",
}
@InProceedings{Hubrecht:2023:TCRb,
author = "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
Zimmermann",
title = "Towards a correctly-rounded and fast power function in
binary64 arithmetic",
crossref = "IEEE:2023:PIS",
pages = "111--118",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00028",
bibdate = "Fri Dec 08 15:03:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arith2023.arithsymposium.org/slides/S6_PaulZimmermannS6P1.pdf;
https://inria.hal.science/hal-04159652v1/file/pow.pdf;
https://inria.hal.science/hal-04326201",
abstract = "We design algorithms for the correct rounding of the
power function $ x^y $ in the binary64 IEEE 754 format,
for all rounding modes, modulo the knowledge of
hardest-to-round cases. Our implementation of these
algorithms largely outperforms previous
correctly-rounded implementations and is not far from
the efficiency of current mathematical libraries, which
are not correctly-rounded. Still, we expect our
algorithms can be further improved for speed. The
proofs of correctness are fully detailed, with the goal
to enable a formal proof of these algorithms. We hope
this work will motivate the next IEEE 754 revision
committee to require correct rounding for mathematical
functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; binary64 format; correct rounding; Digital
arithmetic; double precision; efficiency; Error
analysis; IEEE 754; Libraries; power function;
Prediction algorithms; Software; Software algorithms;
Switches",
remark = "See also longer versions
\cite{Hubrecht:2023:TCRa,Hubrecht:2024:TCR}.",
}
@Article{Mansfield:2023:MSR,
author = "Daniel F. Mansfield",
title = "{Mesopotamian} square root approximation by a sequence
of rectangles",
journal = j-BRITISH-J-HIST-MATH,
volume = "38",
number = "3",
pages = "175--188",
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.1080/26375451.2023.2215652",
ISSN = "1749-8430 (print), 1749-8341 (electronic)",
ISSN-L = "1749-8341",
bibdate = "Thu Apr 25 11:06:30 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bshm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/26375451.2023.2215652",
acknowledgement = ack-nhfb,
ajournal = "BSHM Bull.",
fjournal = "BSHM Bulletin: Journal of the British Society for the
History of Mathematics",
journal-URL = "http://www.tandfonline.com/loi/tbsh20",
onlinedate = "09 Jun 2023",
}
@Article{Pradhan:2023:ETB,
author = "Chetana Pradhan and Martin Letras and J{\"u}rgen
Teich",
title = "Efficient Table-based Function Approximation on
{FPGAs} Using Interval Splitting and {BRAM}
Instantiation",
journal = j-TECS,
volume = "22",
number = "4",
pages = "73:1--73:??",
month = jul,
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.1145/3580737",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Aug 10 07:21:24 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
URL = "https://dl.acm.org/doi/10.1145/3580737",
abstract = "This article proposes a novel approach for the
generation of memory-efficient table-based function
approximation circuits for edge devices in general and
FPGAs in particular. Given a function $ f(x) $ to be
approximated in a given interval $ [x_0, x_0 + a) $ and
a maximum approximation error $ E_a $, the goal is to
determine a function table implementation with a
minimized memory footprint, i.e., number of entries
that need to be stored. Rather than state-of-the-art
work performing an equidistant sampling of the given
interval by so-called breakpoints and using linear
interpolation between two adjacent breakpoints to
determine $ f(x) $ at the maximum error bound, we
propose and compare three algorithms for splitting the
given interval into sub-intervals to reduce the
required memory footprint drastically based on the
observation that in sub-intervals of low gradient, a
coarser sampling grid may be assumed while guaranteeing
the maximum interpolation error bound $ E_a $.
Experiments on elementary mathematical functions show
that a large fraction in memory footprint may be saved.
Second, a hardware architecture implementing the
sub-interval selection, breakpoint lookup, and
interpolation at a latency of just 9 clock cycles is
introduced. Third, for each generated circuit design,
BRAMs are automatically instantiated rather than
synthesizing the reduced footprint function table using
LUT primitives, providing an additional degree of
resource efficiency. The approach presented here for
FPGAs can equally be applied to other circuit
technologies for fast and, at the same time,
memory-optimized function approximation at the edge.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Embed. Comput. Syst.",
articleno = "73",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "https://dl.acm.org/loi/tecs",
}
@Article{Slevinsky:2023:RAE,
author = "Richard M. Slevinsky and Hassan Safouhi",
title = "A recursive algorithm for an efficient and accurate
computation of incomplete {Bessel} functions",
journal = j-NUMER-ALGORITHMS,
volume = "92",
number = "1",
pages = "973--983",
month = jan,
year = "2023",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-022-01438-0",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Jan 30 12:22:09 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-022-01438-0",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Ananthanarayan:2024:OWR,
author = "B. Ananthanarayan and Souvik Bera and S. Friot and
Tanay Pathak",
title = "\pkg{Olsson.wl} and \pkg{ROC2.wl}: {Mathematica}
packages for transformations of multivariable
hypergeometric functions and regions of convergence for
their series representations in the two variables
case",
journal = j-COMP-PHYS-COMM,
volume = "300",
number = "??",
pages = "??--??",
month = jul,
year = "2024",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2024.109162",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon May 6 07:51:16 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465524000857",
acknowledgement = ack-nhfb,
articleno = "109162",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Briggs:2024:ISM,
author = "Ian Briggs and Yash Lad and Pavel Panchekha",
title = "Implementation and Synthesis of Math Library
Functions",
journal = j-PACMPL,
volume = "8",
number = "POPL",
pages = "32:1--32:??",
month = jan,
year = "2024",
CODEN = "????",
DOI = "https://doi.org/10.1145/3632874",
ISSN = "2475-1421 (electronic)",
ISSN-L = "2475-1421",
bibdate = "Fri May 10 10:23:39 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
URL = "https://dl.acm.org/doi/10.1145/3632874",
abstract = "Achieving speed and accuracy for math library
functions like exp, sin, and log is difficult. This is
because low-level implementation languages like C do
not help math library developers catch mathematical
errors, build implementations incrementally, or
separate high-level and low-level decision making. This
ultimately puts development of such functions out of
reach for all but the most experienced experts. To
address this, we introduce MegaLibm, a domain-specific
language for implementing, testing, and tuning math
library implementations. MegaLibm is safe, modular, and
tunable. Implementations in MegaLibm can automatically
detect mathematical mistakes like sign flips via
semantic wellformedness checks, and components like
range reductions can be implemented in a modular,
composable way, simplifying implementations. Once the
high-level algorithm is done, tuning parameters like
working precisions and evaluation schemes can be
adjusted through orthogonal tuning parameters to
achieve the desired speed and accuracy. MegaLibm also
enables math library developers to work interactively,
compiling, testing, and tuning their implementations
and invoking tools like Sollya and type-directed
synthesis to complete components and synthesize entire
implementations. MegaLibm can express 8
state-of-the-art math library implementations with
comparable speed and accuracy to the original C code,
and can synthesize 5 variations and 3 from-scratch
implementations with minimal guidance.",
acknowledgement = ack-nhfb,
ajournal = "Proc. ACM Program. Lang.",
articleno = "32",
fjournal = "Proceedings of the ACM on Programming Languages
(PACMPL)",
journal-URL = "https://dl.acm.org/loi/pacmpl",
}
@TechReport{Brisebarre:2024:CRE,
author = "Nicolas Brisebarre and Guillaume Hanrot and
Jean-Michel Muller and Paul Zimmermann",
title = "Correctly-rounded evaluation of a function: why, how,
and at what cost?",
type = "Report",
number = "hal-04474530",
institution = "CNRS --- Centre National de la Recherche Scientifique
and others",
address = "Paris, France",
pages = "29",
day = "23",
month = feb,
year = "2024",
bibdate = "Fri Feb 23 16:11:08 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.science/hal-04474530",
abstract = "The goal of this paper is to convince the reader that
a future standard for floating-point arithmetic should
require the availability of a correctly-rounded version
of a well-chosen core set of elementary functions. We
discuss the interest and feasibility of this
requirement. We also give answers to common objections
we have received over the last 10 years.",
acknowledgement = ack-nhfb,
keywords = "algorithmic number theory; approximation theory;
Computer arithmetic; elementary functions;
floating-point arithmetic; lattice basis reduction; LLL
algorithm; standardization",
}
@Article{Cameron:2024:AHM,
author = "Thomas R. Cameron and Stef Graillat",
title = "Accurate {Horner} methods in real and complex
floating-point arithmetic",
journal = j-BIT-NUM-MATH,
volume = "64",
number = "2",
pages = "??--??",
month = jun,
year = "2024",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-024-01017-w",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Tue May 28 15:02:24 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://link.springer.com/article/10.1007/s10543-024-01017-w",
acknowledgement = ack-nhfb,
ajournal = "Bit Num. Math.",
articleno = "17",
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Harris:2024:UDS,
author = "David Harris and James Stine and Milo Ercegovac and
Alberto Nannarelli and Katherine Parry and Cedar
Turek",
title = "Unified Digit Selection for Radix-4 Recurrence
Division and Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "73",
number = "1",
pages = "292--300",
month = jan,
year = "2024",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2023.3305760",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Dec 27 15:37:27 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "division; minimally-redundant radix-4; RISC-V; square
root; SRT",
}
@TechReport{Hubrecht:2024:TCR,
author = "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
Zimmermann and Laurence Rideau and Laurent Th{\'e}ry",
title = "Towards a correctly-rounded and fast power function in
binary64 arithmetic",
type = "Report",
institution = "DI-ENS --- D{\'e}partement d'informatique --- ENS
Paris",
address = "Paris, France",
day = "8",
month = feb,
year = "2024",
bibdate = "Mon May 13 12:00:21 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-04159652v2/",
abstract = "We design algorithms for the correct rounding of the
power function $ x^y $ in the binary64 IEEE 754 format,
for all rounding modes, modulo the knowledge of
hardest-to-round cases. Our implementation of these
algorithms largely outperforms previous
correctly-rounded implementations and is not far from
the efficiency of current mathematical libraries, which
are not correctly-rounded. Still, we expect our
algorithms can be further improved for speed. The
proofs of correctness are fully detailed and have been
formally verified. We hope this work will motivate the
next IEEE 754 revision committee to require correct
rounding for mathematical functions.",
acknowledgement = ack-nhfb,
remark = "This is a longer version of \cite{Hubrecht:2023:TCRb}
with proofs and remarks by the final two authors on the
formal verification.",
}
@Misc{Muller:2024:SNC,
author = "Jean-Michel Muller",
title = "Some notes on correct rounding of functions",
howpublished = "Attachment to STDS-754 mailing list",
pages = "31",
day = "18",
month = sep,
year = "2024",
bibdate = "Thu Sep 19 15:27:07 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Yoshida:2024:CIB,
author = "Toshio Yoshida and Yoshinori Adachi",
title = "Computation of incomplete beta function ratios {$
I_x(a, b) $} with {Deuflhard}'s algorithm",
journal = j-NUMER-ALGORITHMS,
volume = "97",
number = "1",
pages = "373--390",
month = sep,
year = "2024",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-023-01707-6",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Aug 7 06:17:56 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-023-01707-6",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Zaghloul:2024:CFI,
author = "Mofreh R. Zaghloul and Leen Alrawas",
title = "Calculation of {Fresnel} integrals of real and complex
arguments up to 28 significant digits",
journal = j-NUMER-ALGORITHMS,
volume = "96",
number = "2",
pages = "489--506",
month = jun,
year = "2024",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-023-01654-2",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Tue May 21 07:35:40 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-023-01654-2",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "complex cosine integral C(z); complex sine integral
S(z); Fresnel functions; real cosine integral C(x);
real sine integral S(x)",
}
@Article{Zaghloul:2024:EMP,
author = "Mofreh R. Zaghloul",
title = "Efficient multiple-precision computation of the scaled
complementary error function and the {Dawson}
integral",
journal = j-NUMER-ALGORITHMS,
volume = "95",
number = "3",
pages = "1291--1308",
month = mar,
year = "2024",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-023-01608-8",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Feb 14 08:54:32 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-023-01608-8",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Dawson(x); erf(x); erfc(x)",
}
@Article{Zaghloul:2024:ENA,
author = "Mofreh R. Zaghloul",
title = "Efficient numerical algorithms for multi-precision and
multi-accuracy calculation of the error functions and
{Dawson} integral with complex arguments",
journal = j-NUMER-ALGORITHMS,
volume = "95",
number = "??",
pages = "1--19",
month = "????",
year = "2024",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-023-01727-2",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Tue Feb 20 15:50:26 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Dawson(x); erf(x); erfc(x)",
remark = "[20-Feb-2024] Available at journal Web site, but not
yet assigned to a journal volume.",
}
@Proceedings{Anonymous:1998:TIC,
editor = "Anonymous",
booktitle = "{Tricomi's ideas and contemporary applied mathematics:
(Roma, 28--29 novembre --- Torino, 1--2 dicembre
1997)}",
title = "{Tricomi's ideas and contemporary applied mathematics:
(Roma, 28--29 novembre --- Torino, 1--2 dicembre
1997)}",
volume = "147",
publisher = "Accademia Nazionale dei Lincei",
address = "Roma, Italy",
pages = "322",
year = "1998",
ISSN = "0391-805X",
LCCN = "QA299.6",
bibdate = "Fri May 31 16:34:38 MDT 2024",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Atti dei convegni Lincei",
acknowledgement = ack-nhfb,
}
@Book{Knuth:1998:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Third",
pages = "xiii + 762",
year = "1998",
ISBN = "0-201-89684-2",
ISBN-13 = "978-0-201-89684-8",
LCCN = "QA76.6 .K64 1997",
bibdate = "Fri Jul 11 15:41:22 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/css.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$52.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
tableofcontents = "3: Random Numbers / 1 \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 10 \\
3.2.1. The Linear Congruential Method / 10 \\
3.2 1.1. Choice of modulus / 12 \\
3.2.1.2 Choice of multiplier / 16 \\
3.2.1.3. Potency / 23 \\
3.2.2. Other Methods / 26 \\
3.3. Statistical Tests / 41 \\
3.3.1. General Test Procedures for Studying Random Data
/ 41 \\
3.3.2. Empirical Tests / 61 \\
*3.3.3. Theoretical Tests / 80 \\
3.3.4. The Spectral Test / 93 \\
3.4. Other Types of Random Quantities / 119 \\
3.4 1. Numerical Distributions / 119 \\
3.4.2. Random Sampling and Shuffling / 142 \\
*3.5. What Is a Random Sequence? / 149 \\
3.6. Summary / 184 \\
4: Arithmetic / 194 \\
4.1. Positional Number Systems / 195 \\
4.2. Floating Point Arithmetic / 214 \\
4.2.1. Single-Precision Calculations / 214 \\
4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
*4.2.3. Double-Precision Calculations / 246 \\
4.2.4. Distribution of Floating Point Numbers / 253 \\
4.3 Multiple Precision Arithmetic / 265 \\
4.3.1. The Classical Algorithms / 265 \\
*4.3.2. Modular Arithmetic / 284 \\
*4.3.3. How Fast Can We Multiply? / 294 \\
4.4. Radix Conversion / 319 \\
4.5. Rational Arithmetic / 330 \\
4.5.1. Fractions / 330 \\
4.5.2. The Greatest Common Divisor / 333 \\
*4.5.3. Analysis of Euclid's Algorithm / 356 \\
4.5.4. Factoring into Primes / 379 \\
4.6. Polynomial Arithmetic / 418 \\
4.6.1. Division of Polynomials / 420 \\
*4.6.2. Factorization of Polynomials / 439 \\
4.6.3. Evaluation of Powers / 461 \\
4.6.4. Evaluation of Polynomials / 485 \\
*4.7. Manipulation of Power Series / 525 \\
Answers to Exercises / 538 \\
Appendix A: Tables of Numerical Quantities / 726 \\
1. Fundamental Constants (decimal) / 726 \\
2; Fundamental Constants ( octal) / 727 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 728 \\
Appendix B: Index to Notations / 730 \\
Index and Glossary / 735",
}
@Book{Borwein:2007:RHR,
editor = "Peter Borwein and Stephen Choi and Brendan Rooney and
Andrea Weirathmueller and others",
title = "The {Riemann Hypothesis}: a resource for the
afficionado and virtuoso alike",
volume = "27",
publisher = "Springer Science+Business Media, LLC",
address = "New York, NY, USA",
pages = "xiv + 533",
year = "2007",
DOI = "https://doi.org/10.1007/978-0-387-72126-2",
ISBN = "0-387-72125-8 (hardcover), 0-387-72126-6 (e-book)",
ISBN-13 = "978-0-387-72125-5 (hardcover), 978-0-387-72126-2
(e-book)",
LCCN = "QA246 .R53 2008",
bibdate = "Thu Sep 1 07:07:49 MDT 2022",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "CMS books in mathematics",
URL = "http://libanswers.liverpool.ac.uk/faq/182315",
abstract = "This book is an introduction to the theory surrounding
the Riemann Hypothesis. Part I serves as a compendium
of known results and as a primer for the material
presented in the 20 original papers contained in Part
II. The original papers place the material into
historical context and illustrate the motivations for
research on and around the Riemann Hypothesis. Several
of these papers focus on computation of the zeta
function, while others give proofs of the Prime Number
Theorem, since the Prime Number Theorem is so closely
connected to the Riemann Hypothesis. The text is
suitable for a graduate course or seminar or simply as
a reference for anyone interested in this extraordinary
conjecture.",
acknowledgement = ack-nhfb,
shorttableofcontents = "To the Riemann Hypothesis \\
Why This Book \\
Analytic Preliminaries \\
Algorithms for Calculating ?(s) \\
Empirical Evidence \\
Equivalent Statements \\
Extensions of the Riemann Hypothesis \\
Assuming the Riemann Hypothesis and Its Extensions
\ldots{} \\
Failed Attempts at Proof \\
Formulas \\
Timeline \\
Original Papers \\
Expert Witnesses \\
The Experts Speak for Themselves",
subject = "Mathematics; History; Number theory;
Math{\'e}matiques; Histoire; Th{\'e}orie des nombres;
Mathematics.; Number theory.",
tableofcontents = "Part 1: Introduction to the Riemann hypothesis \\
1: Why this book \\
1.1: The Holy Grail \\
1.2: Riemann's zeta and Liouville's lambda \\
1.3: The prime number theorem \\
2: Analytic preliminaries \\
2.1: The Riemann zeta function \\
2.2: Zero-free region \\
2.3: Counting the zeros of [cedilla](s) \\
2.4: Hardy's theorem \\
3: Algorithms for calculating [cedilla](s) \\
3.1: Euler--MacLaurin summation \\
3.2: Backlund \\
3.3: Hardy's function \\
3.4: The Riemann--Siegel formula \\
3.5: Gram's law \\
3.6: Turing \\
3.7: The Odlyzko--Sch{\"o}nhage algorithm \\
3.8: A simple algorithm for the zeta function \\
3.9: Further reading \\
4: Empirical evidence \\
4.1: Verification in an interval \\
4.2: A brief history of computational evidence \\
4.3: The Riemann hypothesis and random matrices \\
4.4: The Skewes number \\
5: Equivalent statements \\
5.1: Number-theoretic equivalences \\
5.2: Analytic equivalences \\
5.3: Other equivalences \\
6: Extensions of the Riemann hypothesis \\
6.1: The Riemann hypothesis \\
6.2: The generalized Riemann hypothesis \\
6.3: The extended Riemann hypothesis \\
6.4: An equivalent extended Riemann hypothesis \\
6.5: Another extended Riemann hypothesis \\
6.6: The Grand Riemann hypothesis \\
7: Assuming the Riemann hypothesis and its extensions
\\
7.1: Another proof of the prime number theorem \\
7.2: Goldbach's conjecture \\
7.3: More Goldbach \\
7.4: Primes in a given interval \\
7.5: The least prime in arithmetic progressions \\
7.6: Primality testing \\
7.7: Artin's primitive root conjecture \\
7.8: Bounds on Dirichlet $L$-series \\
7.9: The Lindel{\"o}f hypothesis \\
7.10: Titchmarsh's [delta](T) function \\
7.11: Mean values of [cedilla](s)8: Failed attempts at
proof \\
8.1: Stieltjes and Mertens' conjecture \\
8.2: Hans Rademacher and false hopes \\
8.3: Tur{\'a}n's condition \\
8.4: Louis de Branges's approach \\
8.5: No really good idea \\
9: Formulas \\
10: Timeline \\
pt. 2: Original papers \\
11: Expert witnesses \\
11. 1: E. Bombieri (2000--2001) \\
11.2: P. Sarnak (2004) \\
11.3: J.B. Conrey (2003) \\
11.4: A. Ivi{\'c} (2003) \\
12: The experts speak for themselves \\
12.1: P.L. Chebyshev (1852) \\
12.2: B. Riemann (1859) \\
12.3: J. Hadamard (1896) \\
12.4: C. de la Vall{\'e}e Poussin (1899) \\
12.5: G.H. Hardy (1914) \\
12.6: G.H. Hardy (1915) \\
12.7: G.H. Hardy and J.E. Littlewood (1915) \\
12.8: A. Weil (1941) \\
12.9: P. Tur{\'a}n (1948) \\
12.10: A. Selberg (1949) \\
12.11: P. Erdo$\cdot$s (1949) \\
12.12: S. Skewes (1955) \\
12.13: C.B. Haselgrove (1958) \\
12.14: H. Montgomery (1973) \\
12.15: D.J. Newman (1980) \\
12.16: J. Korevaar (1982) \\
12.17: H. Daboussi (1984) \\
12.18: A. Hildebrand (1986) \\
12.19: D. Goldston and H. Montgomery (1987) \\
12.20: M. Agrawal, N. Kayal, and N. Saxena (2004) \\
References \\
References \\
Index",
}
@Article{Dunster:2024:CPC,
author = "T. M. Dunster and A. Gil and J. Segura",
title = "Computation of parabolic cylinder functions having
complex argument",
journal = j-APPL-NUM-MATH,
volume = "197",
number = "??",
pages = "230--242",
month = mar,
year = "2024",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2023.11.017",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Mon Dec 18 15:47:31 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0168927423002969",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Proceedings{Bowden:1953:FTT,
editor = "{Baron} Bertram Vivian Bowden",
booktitle = "Faster Than Thought: a Symposium on Digital Computing
Machines",
title = "Faster Than Thought: a Symposium on Digital Computing
Machines",
publisher = "Sir Isaac Pitman and Sons, Ltd.",
address = "London, UK",
pages = "xix + 416 + 21",
year = "1953",
LCCN = "QA76.5 .B66",
bibdate = "Sun May 15 10:03:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "With a foreword by the Right Honourable the Earl of
Halsbury.",
URL = "https://archive.org/details/FasterThanThought",
acknowledgement = ack-nhfb,
listofcontributors = "Miss M. Audrey Bates, Ferranti Ltd., Moston,
Manchester (Chapter 25) \\
Dr. J. M. Bennett, Ferranti Ltd., Moston, Manchester
(Chapters 5, 17, 20) \\
Dr. A. D. Booth, Director of the Electronic Computation
Laboratory, Birkbeck College, London (Chapter 13) \\
Dr. B. V. Bowden, Ferranti Ltd., Moston, Manchester
(Chapters 1--4, 14, 22, 25, 26) \\
Mr. R. H. A. Carter, Telecommunications Research
Establishment, Malvern (M.O.S.) (Chapter 10) \\
Mr. E. H. Cooke-Yarborough, Atomic Energy Research
Establishment, Harwell (M.O.S.) (Chapter 9) \\
Mr. A. E. Glennie, Research Establishment, Fort
Halstead (M.O.S.) (Chapters 5, 19) \\
Dr. S. H. Hollingdale, Head of the Mathematical
Services Department, Royal Aircraft Establishment,
Farnborough (M.O.S.) \\
(Chapter 12) \\
Dr. T. Kilburn, Senior Lecturer, Electrical Engineering
Dept., Manchester University (Chapter 6) \\
Mr. S. Michaelson, Imperial College of Science and
Technology, London (Chapter 11) \\
Dr. G. Morton, Lecturer In Economics, London School of
Economics And Political Science (Chapter 23) \\
Mr. B. W. Pollard, Ferranti Ltd., Moston, Manchester
(Chapter 2) \\
Miss Cicely M. Popplewell, Staff Member of the Royal
Society Computing Laboratory, Manchester University
(Chapter 24) \\
Dr. D. G. Prinz, Ferranti Ltd., Moston, Manchester
(Chapter 15) \\
Dr. R. S. Scorer, Lecturer, Department of Meteorology,
Imperial College of Science and Technology, London
(Chapter 18) \\
Mr. J. B. Smith, Ferranti Ltd., Crewe Toll, Edinburgh
(Chapter 15) \\
Mr. R. Stuart-Williams, Sometime of Ferranti Ltd.,
Moston, Manchester, now at the R.C.A. Research
Laboratories, Princeton, New Jersey, U.S.A. (Chapter
16) \\
Mr. B. B. Swann, Ferranti Ltd., Moston, Manchester
(Chapter 21) \\
Mr. C. Strachey, National Research Development
Corporation (Chapter 25) \\
Dr. K. D. Tocher, Imperial College of Science and
Technology, London (Chapter 11) \\
Dr. A. M. Turing, F.R.S., Assistant Director of the
Royal Society Computing Laboratory, Manchester
University (Chapter 25) \\
Dr. A. M. Uttley, Telecommunications Research
Establishment, Malvern (M.O.S.) (Chapter 10) \\
Dr. M. V. Wilkes, Director of the University
Mathematical Laboratory, Cambridge (Chapter 17) \\
Professor F. C. Williams, O.B.E., F.R.S. (Professor of
Electrical Engineering) Director of the Royal Society
Computing Laboratory, Manchester University (Chapter 6)
\\
Chapter 8 is reprinted from \booktitle{Engineering} by
kind permission of the Publishers",
listofplates = "Ada Augusta, Countess of Lovelace / Frontispiece \\
I. Charles Babbage / 12 \\
II. Part of Babbage's Difference Engine / 28 \\
III. Two Hollerith Punch Cards of the Type Used in the
A.C.E. / 29 \\
IV. The Magnetic Drum of the Manchester Machine / 60
\\
V. The Photo-Electric Tape-Reader of the Manchester
Machine / 112 \\
VI. A Typical Stored Pattern on a Cathode-Ray-Tube
Screen / 120 \\
VII. The First Manchester University Computer / 121 \\
VIII. A General View of the Manchester University
Computer Without Covers / 124 \\
IX. A General View of the Manchester University
Computer and Control Desk / 126 \\
X. The Control Desk of the Manchester University
Computer, Showing the Console / 127 \\
XI. A General View of the E.D.S.A.C. / 132 \\
XII. One Unit of the A.C.E. / 136 \\
XIII. A View of the A.C.E. Showing Delay Units / 138
\\
XIV. A View of the A.C.E. Showing the Hollerith
Equipment Used for Input and Output / 139 \\
XV. A Cathode-Ray-Tube Store Pattern / 148 \\
XVI. The Ferranti (Edinburgh) Logical Computer and
Feedback Computer / 188 \\
XVII. ``Nimrod'' at the Science Exhibition, South
Kensington / 200 \\
XVIII. The $b$ Patterson Projection of Whale Myoglobin
Printed in Contour Form / 204",
remark-01 = "Portrait of Ada Augusta, Countess of Lovelace, faces
title page.",
remark-02 = "Chapter authors are credited only in the List of
Contributors on page xv; their names, and order, fail
to appear on chapter papers. No author is credited for
Chapters 7 and 8",
remark-03 = "From page ix: ``The principles on which all modern
computing machines are based were enunciated more than
a hundred years ago by a Cambridge mathematician named
Charles Babbage, who devoted his life and fortune to an
unsuccessful attempt to construct one. Modern
developments in electronics have made his dream come
true in the last decade, and there are now a dozen or
more machines in the world which do all and more than
he expected.",
remark-04 = "From page ix: ``A rough count showed that about 150
digital computers are being built at this moment, most
of them in universities and other research
establishments. It will be interesting to see if these
machines play in the next decade the part of the
cyclotrons and high voltage generators in the
`thirties'.''",
remark-05 = "From page x: ``It seems probable that we shall have a
second Industrial Revolution on our hands before long.
The first one replaced men's muscles by machines, and
eve1y worker in England now has an average of more than
3 horse power to help him. In the next revolution
machines may replace men's brains and relieve them of
much of the drudgery and boredom which is now the lot
of so many white collar workers.''",
remark-06 = "From page x: ``Nowadays many of these dedicated men
spend their time in computing prime numbers. The search
for the largest known prime is a hobby which is at
least as useful and interesting as playing bridge, and
computing machines have helped enormously. The reader
will not be surprised to hear that nowadays the biggest
primes are found in America. The largest which has been
discovered so far (January, 1953) consists of 2281
consecutive `ones,' when it is expressed in the binary
scale (see page 33).''",
remark-07 = "From page xi: ``The early history of these machines
and the story of poor Babbage's struggles is very
interesting. We owe our best account of Babbage's
`Engines' to the Countess of Lovelace, who was a
mathematician of great competence and one of the very
few people who understood what Babbage was trying to
do. Her ideas are so modern that they have become of
great topical interest once again, and since her paper
has long been out of print (it appeared more than a
hundred years ago) it has been reproduced as an
appendix to this book. Lady Lovelace's grand-daughter,
the Right Hon. Lady Wentworth, has very kindly allowed
me to read many of Lady Lovelace's most interesting
papers; I was so surprised by the connexion that I
found between digital computers and thoroughbred horses
that I have given a brief account of the story, for
further details of which the reader is referred to Lady
Wentworth's own books.''",
remark-08 = "From page xi: ``After I had finished the book, I saw a
microfilm of a life of Babbage which had been written
by his executor, the late Mr. L. H. D. Buxton. Mr.
Whitwell of the Powers Samas Company found the
manuscript in the Museum of the History of Science in
Oxford. It contains a more detailed account of the
construction of Babbage's Engines than any I have seen
elsewhere, and it is to be hoped that the material will
some day be published.''",
remark-09 = "From page xiii: ``Much of this book derives from the
work of those prolific authors `Anon' and `Ibid' who
have done so much to put our English platitudes on a
sound literary basis.''",
remark-10 = "From page xiii: ``I must express my thanks to all my
collaborators; to Lord Halsbury for writing the
foreword; to Lady Wentworth who gave me so much
information about Lady Lovelace, and who allowed me to
reproduce the portrait which has been used as a
frontispiece. I am also indebted to Miss Draper who
read all the Lovelace paper; and gave me a great deal
of help. I must thank Miss Dyke for preparing the flow
sheets which I used in Chapter 22. Dr. Gilles and Mr.
Whitewell told me the story of Dr. Comrie; Dr. Bullard
found some of Babbage's writing in the archives of the
National Physical Laboratory; and Professor Aitken, Mr.
W. Klein, Dr. van Wijngaarden, Dr. Stokvis, Mr. Seeber,
Mr. Ferris and Dr. Gabor gave me much of the
information on which Chapter 26 is based. The Portrait
of Babbage is included by courtesy of the Director of
the Science Museum, South Kensington.''",
remark-11 = "From glossary entry on page 411: ``{\em Computor}.
`Bad spelling of Computer' --- Oxford English
Dictionary.''",
remark-12 = "From glossary entry on page 411: ``{\em Cybernetics}.
A word invented by Professor Wiener to describe the
field of control and communication theory, whether in
the machine or in the animal. None of the authors quite
understands what the word means, so it has not been
used in this book.",
remark-13 = "From glossary entry on page 412: ``{\em Hartree
Constant}. The time which is expected to elapse before
a particular electronic computing machine is finished
and working. It was Professor Hartree who first pointed
out that this estimated time usually remains constant
at about six months for a period of several years
during the development of a machine. This phenomenon
was well known to Babbage. Few engineers are worried
unless the `constant' shows signs of increasing
monotonically as the years go by.''",
remark-14 = "From glossary entry on page 413: ``{\em Mill}.
Babbage's name for the arithmetic unit of his
machine.''",
remark-15 = "From glossary entry on page 414: ``{\em Programmer}.
One who prepares programmes for a machine, `a harmless
drudge'.''",
remark-16 = "From glossary entry on page 414: ``{\em T{\"u}ring
Machine}. In 1936 Dr. Turing wrote a paper on the
design and the limitations of computing machines. For
this reason they are sometimes known by his name. The
umlaut is an unearned and undesirable addition, due,
presumably, to an impression that anything so
incomprehensible must be Teutonic.''",
subject = "Electronic digital computers",
tableofcontents = "Foreword / v \\
Preface / vii \\
List of Contributors / xv \\
Part One: The History and Theory of Computing Machines
\\
1. A Brief History of Computation / B. V. Bowden / 3
\\
2. The Circuit Components of Digital Computers / B. V.
Bowden and B. W. Pollard / 32 \\
3. The Organization of a Typical Machine / B. V. Bowden
/ 67 \\
4. The Construction, Performance and Maintenance of
Digital Computers / B. V. Bowden / 78 \\
5. Programming For High-Speed Digital Calculating
Machines / J. M. Bennett and A. E. Glennie / 101 \\
Part Two: Electronic Computing Machines in Britain and
America / \\
6. The University of Manchester Computing Machine / T.
Kilburn and F. C. Williams / 117 \\
7. Calculating Machine Development at Cambridge / 130
\\
8. Automatic Computation at the National Physical
Laboratory / 135 \\
9. The Harwell Electronic Digital Computer / E. H.
Cooke-Yarborough / 140 \\
10. The Telecommunications Research Establishment
Parallel Electronic Digital Computer / R. H. A. Carter
and A. M. Uttley / 144 \\
11. The Imperial College Computing Engine / S.
Michaelson and K. D. Tocher / 161 \\
12. The Royal Aircraft Establishment
Sequence-Controlled Calculator / S. H. Hollingdale /
165 \\
13. Calculating Machines at the Birkbeck College
Computation Laboratory / A. D. Booth / 170 \\
14. Computers in America / B. V. Bowden / 173 \\
Part Three: Applications of Electronic Computing
Machines \\
15. Machines for the Solution of Logical Problems / D.
G. Prinz and J. B. Smith / 181 \\
16. Special-Purpose Automatic Computers / R.
Stuart-Williams / 199 \\
17. Digital Computation and the Crystallographer / J.
M. Bennett and M. V. Wilkes / 203 \\
18. The Use of High-Speed Computing Machines in
Meteorology / R. S. Scorer / 210 \\
19. An Application to Ballistics / A. E. Glennie / 216
\\
20. Digital Computers and the Engineer / J. M. Bennett
/ 223 \\
21. Machines in Government Calculations / B. B. Swann /
234 \\
22. The Application of Digital Computers to Business
and Commerce / B. V. Bowden / 246 \\
23. Electronic Machines and Economics / G. Morton / 272
\\
24. Problems of Dynamical Astronomy / Cicely M.
Popplewell / 282 \\
25. Digital Computers Applied to Games / M. Audrey
Bates, B. V. Bowden, C. Strachey, and A. M. Turing /
286 \\
26. Thought and Machine Processes / B. V. Bowden / 311
\\
Appendix 1: Extracts From \booktitle{Taylor's
Scientific Memoirs}, Vol. III / 341 \\
Appendix 2: Extracts From the \booktitle{Lovelace
Papers} / 409 \\
Glossary / 411 \\
Index / 415 \\
Insets \\
Flow Sheet For P.A.Y.E. Calculation / 254 \\
Computation of Bernoulli Numbers / 404",
}
@Book{Birkhoff:1954:SMM,
editor = "Garrett Birkhoff",
booktitle = "Studies in Mathematics and Mechanics Presented to
{Richard von Mises} by friends, colleagues, and
pupils",
title = "Studies in Mathematics and Mechanics Presented to
{Richard von Mises} by friends, colleagues, and
pupils",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 353",
year = "1954",
ISBN = "1-4832-6356-8",
ISBN-13 = "978-1-4832-6356-4",
LCCN = "QA3 .S853",
bibdate = "Fri Oct 20 10:13:10 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Studies in Mathematics and Mechanics is a collection
of studies presented to Professor Richard von Mises as
a token of reverence and appreciation on the occasion
of his seventieth birthday which occurred on April 19,
1953. von Mises' thought has been a stimulus in many
seemingly unconnected fields of mathematics, science,
and philosophy, to which he has contributed decisive
results and new formulations of fundamental concepts.
The book contains 42 chapters organized into five
parts. Part I contains papers on algebra, number theory
and geometry. These include a study of Poincar{\'e}'s
representation of a hyperbolic space on an Euclidean
half-space and elementary estimates for the least
primitive root. Part II on analysis includes papers on
a generalization of Green's Formula and its application
to the Cauchy problem for a hyperbolic equation, and
the fundamental solutions of a singular Beltrami
operator. Part III deals with theoretical mechanics and
covers topics such as turbulent flow, axially symmetric
flow, and oscillating wakes. The papers in Part IV
focus on applied mechanics. These include studies on
plastic flow under high stresses and the problem of
inelastic thermal stresses. Part V presents studies on
probability and statistics, including a finite
frequency theory of probability and the problem of
expansion of clusters of galaxies.",
acknowledgement = ack-nhfb,
subject-dates = "Richard von Mises (1883--1953)",
}
@Book{Langer:1959:NAP,
editor = "R. E. Langer",
booktitle = "On numerical approximation. {Proceedings of a
Symposium, Madison, April 21--23, 1958}",
title = "On numerical approximation. {Proceedings of a
Symposium, Madison, April 21--23, 1958}",
publisher = "The University of Wisconsin Press",
address = "Madison, WI, USA",
pages = "x + 462",
year = "1959",
LCCN = "QA3 .U45 no. 1",
bibdate = "Tue Jun 19 06:45:47 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Publication no. 1 of the Mathematics Research Center,
U.S. Army, the University of Wisconsin.",
acknowledgement = ack-nhfb,
subjects = "statistics",
tableofcontents = "1. On trends and problems in numerical
approximation / Ostrowski \\
2. Linear spaces and approximation theory / Buck \\
3. Operational methods in numerical analysis based on
rational approximations / Kopal \\
4. On the numerical integration of periodic analytic
functions / Davis \\
S. Some new divided difference algorithms in two
variables / Salzer \\
6. Numerical evaluation of multiple integrals / Hammer
\\
7. Optimal approximation and error bounds / Golomb and
Weinberger \\
8. The rationale of approximation / Sard \\
9. On extremal approximations / Walsh \\
10. Numerical methods of Tchebycheff approximation /
Stiefel \\
11. Minimax methods in table construction / Fox \\
12. Existence of essentially nonlinear families
suitable for oscillatory approximation / Motzkin \\
13. On variation diminishing approximation methods /
Schoenberg \\
14. Approximation by functions of fewer variables /
Golomb \\
15. Extremal approximations --- a summary / Miller \\
16. Survey of recent Russian literature on
approximation / Buck \\
17. The quotient--difference and epsilon algorithms /
Bauer \\
18. Some sufficient conditions for the existence of an
asymptotic formula or an asymptotic expansion / Rosser
\\
19. The estimation of (power) spectra and related
quantities / Tukey \\
20. Approximation in partial differential equations /
Collatz \\
21. Special polynomials in numerical analysis / Todd",
}
@Book{Ralston:1960:MMD,
editor = "Anthony Ralston and Herbert S. Wilf",
booktitle = "Mathematical methods for digital computers",
title = "Mathematical methods for digital computers",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "various",
year = "1960--1977",
ISBN = "0-471-70690-6",
ISBN-13 = "978-0-471-70690-8",
LCCN = "QA39 .R26",
bibdate = "Mon Jan 13 10:36:06 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Three volumes.",
acknowledgement = ack-nhfb,
}
@Book{Abramowitz:1964:HMF,
editor = "Milton Abramowitz and Irene A. Stegun",
key = "NBS",
booktitle = "Handbook of Mathematical Functions with Formulas,
Graphs, and Mathematical Tables",
title = "Handbook of Mathematical Functions with Formulas,
Graphs, and Mathematical Tables",
volume = "55",
publisher = "U. S. Department of Commerce",
address = "Washington, DC, USA",
pages = "xiv + 1046",
year = "1964",
LCCN = "QA47.A161 1972; QA 55 A16h 1972",
bibdate = "Thu Jan 27 07:58:12 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Tenth printing, with corrections (December 1972). This
book is also available online at
\path=http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP=
in bitmap image format.",
series = "Applied mathematics series",
abstract = "This book is a compendium of mathematical formulas,
tables, and graphs. It contains a table of analytical
integrals, differential equations, and numerical
series; and includes tables of trigonometric and
hyperbolic functions, tables for numerical integration,
rules for differentiation and integration, and
techniques for point interpolation and function
approximation. Additionally, it devotes a entire
section to mathematical and physical constants as
fractions and powers of Pi, e, and prime numbers; and
discusses statistics by presenting combinatorial
analysis and probability functions.",
acknowledgement = ack-nhfb,
tableofcontents = "Mathematical constants / David S. Liepman \\
Physical constants and conversion factors / A. G.
McNish \\
Elementary analytical methods / Milton Abramowitz \\
Elementary transcendental functions: logarithmic,
exponential, circular and hyperbolic functions / Ruth
Zucker \\
Exponential integral and related functions / Walter
Gautschi and William F. Cahill \\
Gamma function and related functions / Philip J. Davis
\\
Error function and Fresnel integrals / Walter Gautschi
\\
Legendre functions / Irene A. Stegun \\
Bessel functions of integer order / F. W. J. Olver \\
Bessell functions of fractional order / H. A.
Antosiewicz \\
Integrals of Bessel functions / Yudell L. Luke \\
Struve functions and related functions / Milton
Abramowitz \\
Confluent hypergeometric functions / Lucy Joan Slater
\\
Coulomb wave functions / Milton Abramowitz \\
Hypergeometric functions / Fritz Oberhettinger \\
Jacobian elliptic functions and theta functions;
Elliptic integrals / L. M. Milne-Thomson \\
Weierstrass elliptic and related functions / Thomas H.
Southard \\
Parabolic cylinder functions / J. C. P. Miller\ldots{}
Mathieu functions / Gertrude Blanch \\
Spheroidal wave functions / Arnold N. Lowan \\
Orthogonal polynomials / Urs W. Hochstrasser \\
Bernoulli and Euler polynomials, Riemann zeta function
/ Emilie V. Haynesworth and Karl Goldberg \\
Combinatorial analysis / K. Goldberg, M. Newman and E.
Haynesworth \\
Numerical interpolation, differentiation and
integration / Philip J. Davis and Ivan Polonsky \\
Probability functions / Marvin Zelen and Norman C.
Severo \\
Miscellaneous functions / Irene A. Stegun \\
Scales of notation / S. Peavy and A. Schopf \\
Laplace transforms",
}
@Book{Magnus:1966:FTS,
author = "Wilhelm Magnus and Fritz Oberhettinger and Raj Pal
Soni",
booktitle = "Formulas and theorems for the special functions of
mathematical physics",
title = "Formulas and theorems for the special functions of
mathematical physics",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Third",
pages = "viii + 508",
year = "1966",
LCCN = "QA1 G88 v. 52, 1966",
bibdate = "Sat Oct 30 18:23:25 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
note = "See errata
\cite{Cohl:2012:TEF,Szmytkowski:2013:EBT}.",
acknowledgement = ack-nhfb,
}
@Proceedings{AFIPS:1969:ACPb,
key = "AFIPS FJCC '69",
booktitle = "1969 Fall Joint Computer Conference, November 18--20,
1969, Las Vegas, Nevada",
title = "1969 Fall Joint Computer Conference, November 18--20,
1969, Las Vegas, Nevada",
volume = "35",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "807",
year = "1969",
LCCN = "TK7885.A1 J6 1969",
bibdate = "Sat Sep 24 01:06:00 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "AFIPS conference proceedings",
acknowledgement = ack-nhfb,
}
@Proceedings{AFIPS:1971:ACP,
key = "AFIPS SJCC '71",
booktitle = "1971 Spring Joint Computer Conference, May 18--20,
1971, Atlantic City, New Jersey",
title = "1971 Spring Joint Computer Conference, May 18--20,
1971, Atlantic City, New Jersey",
volume = "38",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "631",
year = "1971",
LCCN = "????",
bibdate = "Fri Sep 16 10:47:01 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "AFIPS conference proceedings",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Book{Rice:1971:MS,
author = "John R. Rice",
booktitle = "Mathematical Software",
title = "Mathematical Software",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 515",
year = "1971",
ISBN = "0-12-587250-X",
ISBN-13 = "978-0-12-587250-8",
LCCN = "QA1 .M26",
bibdate = "Thu Sep 15 18:56:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Based on the proceedings of the Mathematical Software
Symposium held at Purdue University, Lafayette,
Indiana, USA, April 1--3, 1970.",
acknowledgement = ack-nhfb,
}
@Proceedings{Askey:1975:TAS,
editor = "Richard Askey",
booktitle = "{Theory and application of special functions:
proceedings of an advanced seminar sponsored by the
Mathematics Research Center, the University of
Wisconsin-Madison, March 31--April 2, 1975}",
title = "{Theory and application of special functions:
proceedings of an advanced seminar sponsored by the
Mathematics Research Center, the University of
Wisconsin-Madison, March 31--April 2, 1975}",
number = "35",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xi + 560",
year = "1975",
ISBN = "0-12-064850-4",
ISBN-13 = "978-0-12-064850-4",
LCCN = "QA3 .U45 no. 35 QA351",
bibdate = "Sat Oct 30 07:41:32 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Publication of the Mathematics Research Center, the
University of Wisconsin",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
meetingname = "Advanced Seminar on Special Functions, Madison, Wis.,
1975.",
subject = "Functions, Special; Congresses",
}
@Proceedings{Miller:1975:TNA,
editor = "John J. H. Miller",
booktitle = "Topics in numerical analysis: proceedings of the Royal
Irish Academy Conference on Numerical Analysis, 1972,
1974, 1976",
title = "Topics in numerical analysis: proceedings of the Royal
Irish Academy Conference on Numerical Analysis, 1972,
1974, 1976",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "various",
year = "1975",
ISBN = "0-12-496950-X",
ISBN-13 = "978-0-12-496950-6",
LCCN = "QA297 .R69 1973",
bibdate = "Mon Jan 13 10:41:13 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Traub:1976:ACC,
editor = "J. F. (Joseph Frederick) Traub",
booktitle = "{Analytic computational complexity: Proceedings of the
Symposium on Analytic Computational Complexity, held by
the Computer Science Department, Carnegie-Mellon
University, Pittsburgh, Pennsylvania, on April 7--8,
1975}",
title = "{Analytic computational complexity: Proceedings of the
Symposium on Analytic Computational Complexity, held by
the Computer Science Department, Carnegie-Mellon
University, Pittsburgh, Pennsylvania, on April 7--8,
1975}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 239",
year = "1976",
ISBN = "0-12-697560-4",
ISBN-13 = "978-0-12-697560-4",
LCCN = "QA297.S9151 1975",
bibdate = "Mon Jan 13 10:18:33 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Cowell:1977:PMS,
editor = "Wayne Cowell",
booktitle = "{Portability of Numerical Software Workshop, Oak
Brook, Illinois, June 21--23, 1976}",
title = "{Portability of Numerical Software Workshop, Oak
Brook, Illinois, June 21--23, 1976}",
volume = "57",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 539",
year = "1977",
ISBN = "0-387-08446-0",
ISBN-13 = "978-0-387-08446-6",
LCCN = "QA297 .W65 1976",
bibdate = "Sat Sep 24 00:24:09 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Workshop organized by Argonne National Laboratory.",
}
@Proceedings{IEEE:1978:PSC,
editor = "{IEEE}",
booktitle = "Proceedings of the Symposium on Computer Arithmetic
{(4th: 1978: Santa Monica, CA)}",
title = "Proceedings of the Symposium on Computer Arithmetic
{(4th: 1978: Santa Monica, CA)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 274",
year = "1978",
ISSN = "1063-6889",
LCCN = "QA76.6 .S919a",
bibdate = "Mon May 19 15:22:15 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE catalog no. 78 CH1412-6C.",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic --- Congresses.; Electronic
digital computers --- Programming --- Congresses.;
Floating-point arithmetic --- Congresses.",
}
@Proceedings{Alefeld:1980:PSE,
editor = "G. Alefeld and R. D. Grigorieff and R. Albrecht and U.
Kulisch and F. Stummel",
booktitle = "{Fundamentals of numerical computation
(computer-oriented numerical analysis). Proceedings of
a conference held June 5--8, 1979, on the occasion of
the centennial of the Technical University of Berlin}",
title = "{Fundamentals of numerical computation
(computer-oriented numerical analysis). Proceedings of
a conference held June 5--8, 1979, on the occasion of
the centennial of the Technical University of Berlin}",
volume = "2",
publisher = pub-SV,
address = pub-SV:adr,
pages = "229",
year = "1980",
ISBN = "0-387-81566-X",
ISBN-13 = "978-0-387-81566-4",
ISSN = "0344-8029",
LCCN = "QA297 .F84",
bibdate = "Mon Jan 13 10:20:47 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Computing. Supplementum",
acknowledgement = ack-nhfb,
}
@Proceedings{Dieudonne:1980:SFL,
editor = "Jean Dieudonn{\'e}",
booktitle = "{Special functions and linear representations of Lie
groups}",
title = "{Special functions and linear representations of Lie
groups}",
volume = "42",
publisher = "Published for the Conference Board of the Mathematical
Sciences by the American Mathematical Society",
address = "Providence, RI, USA",
pages = "iii + 59",
year = "1980",
ISBN = "0-8218-1692-6",
ISBN-13 = "978-0-8218-1692-9",
LCCN = "????",
bibdate = "Sat Oct 30 17:14:47 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.bibsys.no:2100/BIBSYS",
series = "Regional conference series in mathematics",
acknowledgement = ack-nhfb,
remark = "Expository lectures from the CBMS regional conference
held at East Carolina University, March 5--9, 1979.",
}
@Proceedings{Lavington:1980:IPP,
editor = "Simon Hugh Lavington",
booktitle = "Information Processing 80: Proceedings of {IFIP}
Congress 80, Tokyo, Japan, October 6--9, 1980,
Melbourne, Australia, October 14--17, 1980",
title = "Information Processing 80: Proceedings of {IFIP}
Congress 80, Tokyo, Japan, October 6--9, 1980,
Melbourne, Australia, October 14--17, 1980",
publisher = pub-ENH,
address = pub-ENH:adr,
pages = "xiii + 1070",
year = "1980",
ISBN = "0-444-86034-7",
ISBN-13 = "978-0-444-86034-7",
LCCN = "QA 75.5 I57 1980",
bibdate = "Thu Sep 01 23:09:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1981:PIS,
editor = "{IEEE}",
booktitle = "Proceedings: 5th Symposium on Computer Arithmetic, May
18-19, 1981, University of Michigan, Ann Arbor,
Michigan",
title = "Proceedings: 5th Symposium on Computer Arithmetic, May
18-19, 1981, University of Michigan, Ann Arbor,
Michigan",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "vii + 278",
year = "1981",
LCCN = "QA76.9.C62 S95 1981",
bibdate = "Mon May 19 13:17:13 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE Catalog No. 81CH1630-3. Computer Society Order
No. 347.",
acknowledgement = ack-nhfb,
xxISBN = "none",
}
@Proceedings{IEEE:1981:PSC,
key = "IEEE CA5 '81",
booktitle = "Proceedings: 5th Symposium on Computer Arithmetic, May
18--19, 1981, University of Michigan, Ann Arbor,
Michigan",
title = "Proceedings: 5th Symposium on Computer Arithmetic: May
18--19, 1981, University of Michigan, Ann Arbor,
Michigan",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "vii + 278",
year = "1981",
LCCN = "QA 76.6 S985t 1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 81CH1630-C.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; Computer arithmetic and logic units ---
Congresses.; Electronic digital computers ---
Programming --- Congresses.; Floating-point arithmetic
Congresses.",
xxISBN = "(none)",
}
@Proceedings{Mulvey:1982:EMP,
editor = "J. M. Mulvey",
booktitle = "{Evaluating Mathematical Programming Techniques:
Proceedings of a Conference Held at the National Bureau
of Standards, Boulder, Colorado, January 5--6, 1981}",
title = "{Evaluating Mathematical Programming Techniques:
Proceedings of a Conference Held at the National Bureau
of Standards, Boulder, Colorado, January 5--6, 1981}",
volume = "199",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 379",
year = "1982",
ISBN = "0-387-11495-5",
ISBN-13 = "978-0-387-11495-8",
LCCN = "QA402.5 .E94 1982",
bibdate = "Thu Nov 17 06:36:49 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Lecture Notes in Economics and Mathematical Systems",
acknowledgement = ack-nhfb,
}
@Proceedings{Hwang:1985:PSC,
editor = "Kai Hwang",
booktitle = "Proceedings: 7th Symposium on Computer Arithmetic,
June 4--6, 1985, University of Illinois, Urbana,
Illinois",
title = "Proceedings: 7th Symposium on Computer Arithmetic,
June 4--6, 1985, University of Illinois, Urbana,
Illinois",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 343",
year = "1985",
ISBN = "0-8186-0632-0 (paperback), 0-8186-8632-4 (hard),
0-8186-4632-2 (microfiche)",
ISBN-13 = "978-0-8186-0632-8 (paperback), 978-0-8186-8632-0
(hard), 978-0-8186-4632-4 (microfiche)",
LCCN = "QA76.9.C62 S95 1985",
bibdate = "Thu Sep 08 00:11:41 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 85CH2146-9. IEEE Computer Society
order number 632.",
acknowledgement = ack-nj,
keywords = "ARITH-7",
}
@Proceedings{IEEE:1985:ERC,
key = "IEEE Region 5 '85",
booktitle = "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
Holiday Inn Civic Center, Lubbock, Texas",
title = "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
Holiday Inn Civic Center, Lubbock, Texas",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "vi + 71",
year = "1985",
LCCN = "TK 7801 N56 1985",
bibdate = "Thu Sep 15 18:50:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Proceedings{Marron:1985:FEP,
editor = "J. S. Marron",
booktitle = "{Function estimates: proceedings of a conference held
July 28--August 3, 1985}",
title = "{Function estimates: proceedings of a conference held
July 28--August 3, 1985}",
volume = "59",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "ix + 178",
year = "1985",
ISBN = "0-8218-5062-8",
ISBN-13 = "978-0-8218-5062-6",
ISSN = "0271-4132 (print), 1098-3627 (electronic)",
LCCN = "QA276.8 .C651 1985",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Held at Humboldt State University, Arcata,
California.",
series = "Contemporary mathematics (American Mathematical
Society)",
acknowledgement = ack-nhfb,
bibno = "18241",
catcode = "G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation",
genterm = "algorithms; theory",
guideno = "1986-12215",
procdate = "July 28--Aug. 3, 1985",
procloc = "Arcata, CA",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Proceedings{Miranker:1985:ASC,
editor = "Willard L. Miranker and Richard A. Toupin",
booktitle = "Accurate Scientific Computations: Symposium, Bad
Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
title = "Accurate Scientific Computations: Symposium, Bad
Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
volume = "235",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 205",
year = "1985",
DOI = "https://doi.org/10.1007/3-540-16798-6",
ISBN = "0-387-16798-6",
ISBN-13 = "978-0-387-16798-5",
LCCN = "QA76.95 .A231 1986",
bibdate = "Sat Sep 03 12:24:08 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Proceedings{Miranker:1986:ASC,
editor = "Willard L. Miranker and Richard A. Toupin",
booktitle = "Accurate scientific computations: symposium, Bad
Neuenahr, {FRG}, March 12--14, 1985: proceedings",
title = "Accurate scientific computations: symposium, Bad
Neuenahr, {FRG}, March 12--14, 1985: proceedings",
volume = "235",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 205",
year = "1986",
CODEN = "LNCSD9",
ISBN = "0-387-16798-6 (USA: paperback)",
ISBN-13 = "978-0-387-16798-5 (USA: paperback)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.95 .A231 1986",
bibdate = "Fri Apr 12 07:14:49 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Symposium sponsored by IBM Deutschland.",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "mathematics --- data processing --- congresses;
numerical calculations --- congresses",
}
@Proceedings{ACM:1987:UAA,
editor = "{ACM}",
booktitle = "Using Ada: {ACM} {SIGAda} international conference,
Boston, Massachusetts, December 8--11, 1987",
title = "Using Ada: {ACM} {SIGAda} international conference,
Boston, Massachusetts, December 8--11, 1987",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 240",
year = "1987",
ISBN = "0-89791-243-8",
ISBN-13 = "978-0-89791-243-3",
LCCN = "QA 76.73 A35 U85 1987",
bibdate = "Mon May 19 13:18:54 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Iserles:1987:SAN,
editor = "A. Iserles and M. J. D. Powell",
booktitle = "The State of the Art in Numerical Analysis:
Proceedings of the Joint {IMA}\slash {SIAM} Conference
on the State of the Art in Numerical Analysis held at
the University of Birmingham, 14--18 April 1986",
title = "The State of the Art in Numerical Analysis:
Proceedings of the Joint {IMA}\slash {SIAM} Conference
on the State of the Art in Numerical Analysis held at
the University of Birmingham, 14--18 April 1986",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xiv + 719",
year = "1987",
ISBN = "0-19-853614-3",
ISBN-13 = "978-0-19-853614-7",
LCCN = "QA297 .S781 1987",
bibdate = "Thu Sep 08 00:41:24 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "UK\pounds55.00, US\$77.50",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Proceedings{Mason:1987:AAB,
editor = "J. C. Mason and M. G. Cox",
booktitle = "{Algorithms for approximation: based on the
proceedings of the IMA Conference on Algorithms for the
Approximation of Functions and Data, held at the Royal
Military College of Science, Shrivenham, July 1985}",
title = "{Algorithms for approximation: based on the
proceedings of the IMA Conference on Algorithms for the
Approximation of Functions and Data, held at the Royal
Military College of Science, Shrivenham, July 1985}",
volume = "10",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xvi + 694 + 8",
year = "1987",
ISBN = "0-19-853612-7",
ISBN-13 = "978-0-19-853612-3",
LCCN = "QA221 .A5361 1987; QA221 .I47 1985",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$90",
series = "The Institute of Mathematics and Its Applications
conference series, new series",
acknowledgement = ack-nhfb,
bibno = "39820",
catcode = "G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "theory; algorithms",
guideno = "1987-16080",
meetingname = "IMA Conference on Algorithms for the Approximation of
Functions and Data (1985: Royal Military College of
Science, Shrivenham)",
procdate = "The Institute of mathematics and its applications
conference series; 10 July 1985",
procloc = "Shrivenham, UK",
sub = "Proceedings of the IMA Conference on Algorithms for
the approximation of functions",
subject = "Approximation theory; Data processing; Congresses; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
tableofcontents = "Preface / v \\
Contributors / xiii \\
\\
I Development of Algorithms \\
\\
1. Spline Approximation and Smoothing \\
\\
G. T. Anthony and M. G. Cox / The fitting of extremely
large data sets by bivariate splines / 5 \\
W. Dahmen / Subdivision algorithms --- recent results,
some extensions and further developments / 21 \\
P. Dierckx / Fast algorithms for smoothing data over a
disc or a sphere using tensor product splines / 51 \\
T. Lyche and K. M{\o}rken / A discrete approach to knot
removal and degree reduction algorithms for splines /
67 \\
R. H. J. Gmelig Meyling / On algorithms and
applications for bivariate B-splines / 83 \\
\\
2. Spline Interpolation and Shape Preservation \\
\\
R. E. Carlson / Shape preserving interpolation / 97 \\
M. G. Cox and H. M. Jones / Shape preserving spline
approximation in the $\ell_1$-norm / 115 \\
J. A. Gregory / A review of curve interpolation with
shape control / 131 \\
\\
3. Multivariate Interpolation \\
\\
M. J. D. Powell / Radial basis functions for
multivariable interpolation: a review / 143 \\
R. A. Lorentz / On the determinant of a bivariate
Birkhoff interpolation problem / 169 \\
A. Le Mehaute / Interpolation with piecewise
polynomials in more than one variable / 181 \\
\\
4. Least Square Methods \\
\\
R. Farwig / Multivariate interpolation of scattered
data by moving least squares methods / 193 \\
F. Yoshimoto / Least squares approximation by one-pass
methods with piecewise polynomials / 213 \\
\\
5. Rational Approximation \\
\\
L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable
Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227
\\
P. T. Breuer / A new method for real rational uniform
approximation / 265 \\
C. B. Dunham / Rationals with repeated poles / 285 \\
A. Iserles and S. P. N{\o}rsett / Error control of
rational approximation with a matrix argument / 293 \\
\\
6. Complex and Nonlinear Approximation \\
\\
K. Madsen / General algorithms for discrete non-linear
parameter estimation / 309 \\
G. Opfer / Complex rational approximation with
numerical experiments / 327 \\
G. A. Watson / Data fitting by positive sums of
exponentials / 337 \\
J. C. Mason and P. Owen / Some simple algorithms for
constrained complex and rational approximation / 357
\\
\\
7. Computer-Aided Design and Blending \\
\\
L. L. Schumaker / Numerical aspects of spaces of
piecewise polynomials on triangulations / 373 \\
M. V. Golitschek / The $H$-sets of the blending
functions / 407 \\
D. Levin / Multidimensional reconstruction by
set-valued approximations/ 421 \\
\\
II Applications \\
\\
8. Applications in Numerical Analysis \\
\\
H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the
behaviour of zeros of best approximating polynomials
and rational functions / 437 \\
J. Gilbert and W. A. Light / Multigrid methods and the
alternating algorithm / 447 \\
K. Jetter and J. St{\"o}ckler / On the computation of
Gauss--Birkhoff quadrature formulas / 459 \\
E. Schock / Error bounds for the solution of integral
equations by Galerkin-like methods / 471 \\
N. M. Temme / On the computation of the incomplete
gamma functions for large values of the parameters /
479 \\
\\
9. Applications in Partial Differential Equations \\
\\
J. R. Rice / Adaptive tensor product grids for singular
problems / 493 \\
W. Freeden / Harmonic splines for solving boundary
value problems of potential theory / 507 \\
D. C. Hanscomb / Recovery of fluid flow fields / 531
\\
L. Reichel / The selection of subspace and collocation
points in the boundary collocation method for some
plane elliptic boundary problems / 541 \\
\\
10. Applications in Other Disciplines \\
\\
L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex
formation constants --- a problem from solution
chemistry / 557 \\
D. E. Roberts and P. R. Graves-Morris / The application
of generalised inverse rational interpolants in the
model analysis of vibrating structures I / 573 \\
A. Daman and J. C. Mason / A generalised
cross-validation method for meteorological data with
gaps / 595 \\
K. P. Jackson and J. C. Mason / The approximation by
complex functions of stresses in cracked domains / 611
\\
J. H. McDonnell / Equally spaced cubic splines for
representing time histories / 623 \\
B. L. Rahimi and S. W. Ellacott / Dynamic phase
analysis of heart anomalies / 641 \\
\\
III Software \\
\\
J. G. Hayes / NAG algorithms for the approximation of
functions and data / 653 \\
G. T. Anthony and M. G. Cox / The National Physical
Laboratory's Data Approximation Subroutine Library /
669 \\
\\
M. G. Cox (editor) / Panel Discussion / 689",
}
@Proceedings{USENIX:1988:UPC,
editor = "{USENIX Association}",
booktitle = "{USENIX} proceedings: {C++} Conference, Denver, {CO},
October 17--21, 1988",
title = "{USENIX} proceedings: {C++} Conference, Denver, {CO},
October 17--21, 1988",
publisher = pub-USENIX,
address = pub-USENIX:adr,
pages = "362",
year = "1988",
bibdate = "Sun Feb 18 07:46:09 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "C++ (Computer program language) --- Congresses.",
}
@Proceedings{ACM:1989:PAI,
editor = "{ACM}",
booktitle = "Proceedings of the {ACM-SIGSAM 1989} International
Symposium on Symbolic and Algebraic Computation, {ISSAC
'89}",
title = "{Proceedings of the ACM--SIGSAM 1989 International
Symposium on Symbolic and Algebraic Computation, ISSAC
'89}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "399",
year = "1989",
ISBN = "0-89791-325-6",
ISBN-13 = "978-0-89791-325-6",
LCCN = "QA76.95.I59 1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
confdate = "17--19 July 1989",
conflocation = "Portland, OR, USA",
confsponsor = "ACM",
pubcountry = "USA",
}
@Book{Campbell-Kelly:1989:WCB-3,
editor = "Martin Campbell-Kelly",
booktitle = "The works of {Charles Babbage}, Vol. 3, The analytical
engine and mechanical notation",
title = "The works of {Charles Babbage}, Vol. 3, The analytical
engine and mechanical notation",
publisher = "William Pickering",
address = "London, UK",
pages = "253",
year = "1989",
ISBN = "1-85196-503-3, 1-85196-005-8 (set)",
ISBN-13 = "978-1-85196-503-8, 978-1-85196-005-7 (set)",
LCCN = "????",
MRclass = "01A75 (68-03)",
MRnumber = "998151 (90g:01064)",
MRreviewer = "A. D. Booth",
bibdate = "Sat Jan 12 22:42:35 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.libris.kb.se:210/libr",
acknowledgement = ack-nhfb,
subject = "Mathematics; Science; 1961; mathematics",
}
@Proceedings{Ercegovac:1989:PSC,
editor = "Milo{\v{s}} D. Ercegovac and Earl E. {Swartzlander,
Jr.}",
booktitle = "Proceedings: 9th Symposium on Computer Arithmetic:
September 6--8, 1989, Santa Monica, California, {USA}",
title = "Proceedings: 9th Symposium on Computer Arithmetic:
September 6--8, 1989, Santa Monica, California, {USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xv + 247",
year = "1989",
ISBN = "0-8186-8963-3 (case), 0-8186-5963-7 (microfiche)",
ISBN-13 = "978-0-8186-8963-5 (case), 978-0-8186-5963-8
(microfiche)",
LCCN = "QA 76.9 C62 S95 1989",
bibdate = "Thu Sep 01 22:36:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE catalog no. 89CH2757-3.",
acknowledgement = ack-nhfb,
confdate = "6-8 Sept. 1989",
conflocation = "Santa Monica, CA, USA",
confsponsor = "IEEE; IFIP; Univ. California",
pubcountry = "USA",
}
@Proceedings{IEE:1989:EEC,
editor = "{IEE}",
booktitle = "{ECCTD 89}: European Conference on Circuit Theory and
Design, 5--8 September 1989: venue, University of
Sussex, Brighton, United Kingdom",
title = "{ECCTD} 89: European Conference on Circuit Theory and
Design, 5--8 September 1989: venue, University of
Sussex, Brighton, United Kingdom",
publisher = pub-IEE,
address = pub-IEE:adr,
bookpages = "xviii + 680",
year = "1989",
ISBN = "0-85296-383-1",
ISBN-13 = "978-0-85296-383-8",
LCCN = "????",
bibdate = "Sat Nov 29 08:19:35 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Conference publication no. 308.",
acknowledgement = ack-nhfb,
confdate = "5-8 Sept. 1989",
conflocation = "Brighton, UK",
confsponsor = "IEE",
pubcountry = "UK",
}
@Proceedings{IEEE:1989:ASF,
editor = "{IEEE}",
booktitle = "30th annual Symposium on Foundations of Computer
Science, October 30--November 1, 1989, Research
Triangle Park, North Carolina",
title = "30th annual Symposium on Foundations of Computer
Science, October 30--November 1, 1989, Research
Triangle Park, North Carolina",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvii + 632",
year = "1989",
CODEN = "ASFPDV",
ISBN = "0-8186-1982-1 (casebound), 0-8186-5982-3
(microfiche)",
ISBN-13 = "978-0-8186-1982-3 (casebound), 978-0-8186-5982-9
(microfiche)",
ISSN = "0272-5428",
LCCN = "QA 76 S979 1989; TK7885.A1 S92 1989",
bibdate = "Thu Dec 3 07:11:18 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Formerly called the Annual Symposium on Switching and
Automata Theory. IEEE catalog no. 89CH2808-4. Computer
Society order no. 1982.",
acknowledgement = ack-nhfb,
keywords = "computational complexity --- congresses; electronic
data processing --- congresses; machine theory ---
congresses",
}
@Proceedings{IEEE:1989:PII,
key = "IEEE ICCD '89",
booktitle = "Proceedings: 1989 {IEEE} International Conference on
Computer Design: {VLSI} in Computer and Processors,
{ICCD} '89, Hyatt Regency Cambridge, Cambridge,
Massachusetts, October 2--4, 1989",
title = "Proceedings: 1989 {IEEE} International Conference on
Computer Design: {VLSI} in Computer and Processors,
{ICCD} '89, Hyatt Regency Cambridge, Cambridge,
Massachusetts, October 2--4, 1989",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvii + 587",
year = "1989",
ISBN = "0-8186-1971-6 (paper), 0-8186-5971-8 (microfiche),
0-8186-8971-4 (case)",
ISBN-13 = "978-0-8186-1971-7 (paper), 978-0-8186-5971-3
(microfiche), 978-0-8186-8971-0 (case)",
LCCN = "TK 7888.4 I23 1989",
bibdate = "Wed Dec 13 18:26:58 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 89CH2794-6.",
acknowledgement = ack-nj,
confdate = "2-4 Oct. 1989",
conflocation = "Cambridge, MA, USA",
confsponsor = "IEEE",
}
@Proceedings{MacNair:1989:WSC,
editor = "Edward A. MacNair and Kenneth J. Musselman and Philip
Heidelberger",
booktitle = "{1989 Winter Simulation Conference proceedings:
December 4--6, 1989, the Capital Hilton Hotel,
Washington, DC}",
title = "{1989 Winter Simulation Conference proceedings:
December 4--6, 1989, the Capital Hilton Hotel,
Washington, DC}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xx + 1139",
pages = "xx + 1139",
year = "1989",
ISBN = "0-911801-58-8",
ISBN-13 = "978-0-911801-58-3",
LCCN = "QA76.9.C65 W56 1989",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "IEEE order number 89CH2778-9.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5823",
acknowledgement = ack-nhfb,
bibno = "76750",
catcode = "I.6.3; G.1.6; G.3; G.1.2",
CRclass = "I.6.3 Applications; G.1.6 Optimization; G.1.2
Approximation; G.1.2 Elementary function
approximation",
descriptor = "Computing Methodologies, SIMULATION AND MODELING,
Applications; Mathematics of Computing, NUMERICAL
ANALYSIS, Optimization; Mathematics of Computing,
PROBABILITY AND STATISTICS; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
genterm = "algorithms; design; performance",
guideno = "1989-12012",
procdate = "December 4-6, 1989",
procloc = "Washington, D. C.",
subject = "I. Computing Methodologies; I.6 SIMULATION AND
MODELING; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY
AND STATISTICS; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Proceedings{Megiddo:1989:PMP,
editor = "N. Megiddo",
booktitle = "Progress in Mathematical Programming: Interior-Point
and Related Methods",
title = "Progress in Mathematical Programming: Interior-Point
and Related Methods",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 158",
year = "1989",
ISBN = "0-387-96847-4",
ISBN-13 = "978-0-387-96847-6",
LCCN = "QA402.5 .P7851 1989",
bibdate = "Sat Nov 09 07:07:37 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of the conference held at the Asilomar
conference center in Pacific Grove, California, March
1--4, 1987.",
acknowledgement = ack-nhfb,
}
@Book{Srivastava:1989:UFF,
editor = "H. M. Srivastava and Shigeyoshi Owa",
booktitle = "Univalent functions, fractional calculus, and their
applications (K{\=o}riyama, 1988)",
title = "Univalent functions, fractional calculus, and their
applications ({K}{\=o}riyama, 1988)",
publisher = pub-ELLIS-HORWOOD,
address = pub-ELLIS-HORWOOD:adr,
pages = "404",
year = "1989",
ISBN = "0-470-21630-1, 0-7458-0701-1",
ISBN-13 = "978-0-470-21630-9, 978-0-7458-0701-0",
LCCN = "QA331 .U55 1989",
bibdate = "Mon Jan 13 09:52:29 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
price = "UK\pounds 39.95",
acknowledgement = ack-nhfb,
}
@Proceedings{Cray:1990:PCU,
editor = "????",
key = "Cray UG '90",
booktitle = "Proceedings Cray User Group",
title = "Proceedings Cray User Group",
publisher = "????",
address = "????",
pages = "????",
month = "Spring",
year = "1990",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Sep 08 08:56:01 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Proceedings{Mason:1990:AAI,
editor = "J. C. Mason and M. G. Cox",
booktitle = "{Algorithms for approximation II: based on the
proceedings of the Second International Conference on
Algorithms for Approximation, held at Royal Military
College of Science, Shrivenham, July 1988}",
title = "{Algorithms for approximation II: based on the
proceedings of the Second International Conference on
Algorithms for Approximation, held at Royal Military
College of Science, Shrivenham, July 1988}",
publisher = pub-CHAPMAN-HALL,
address = pub-CHAPMAN-HALL:adr,
pages = "514",
year = "1990",
ISBN = "0-412-34580-3",
ISBN-13 = "978-0-412-34580-7",
LCCN = "QA221 .I54 1988",
bibdate = "Thu Sep 01 23:55:44 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Algorithms for
Approximation (2nd: 1988: Royal Military College of
Science, Shrivenham, England)",
subject = "Approximation theory; Data processing; Congresses",
tableofcontents = "Part One: Development of Algorithms / 1 \\
1. Spline Approximation / 3 \\
E. Arge, M. Dcehlen, T. Lyche and K. Morken /
Constrained spline approximation of functions and data
based on constrained knot removal / 4 \\
G. T. Anthony and M. G. Cox / Near real-time spline
fitting of long sequences of uniformly-spaced data / 21
\\
M. Bozzini and F. de Tisi / An algorithm for knot
location in bivariate least squares spline
approximation / 30 \\
M. G. Cox, P. M. Harris and H. M. Jones / A knot
placement strategy for least squares spline fitting
based on the use of local polynomial approximations /
37 \\
G. Opfer / An algorithm for nonlinear splines with
non-negativity constraints / 46 \\
C. Potier and C. Vercken / Spline curve fitting of
digitized contours / 54 \\
C. Rabut / A B-spline approximation algorithm for
quasi-interpolation or filtering / 62 \\
P. W. Smith / On knots and nodes for spline
interpolation / 72 \\
2. Polynomial and Piecewise Polynomial Approximation /
79 \\
W. Dahmen / A basis for certain spaces of multivariate
polynomials and exponentials / 80 \\
F. N. Fritschi / Monotone piecewise cubic data fitting
/ 99 \\
M. Heilmann and M. W. M{\"u}ller / Direct and converse
results on simultaneous approximation by the method of
Bernstein--Durrmeyer operators / 107 \\
A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M.
Sanz-Serna / Orthogonality and approximation in a
Sobolev space / 117 \\
M. A. Lachance / Piecewise polynomial approximation of
polynomial curves / 125 \\
E. Quak and L. L. Schumaker / Calculation of the energy
of a piecewise polynomial surface / 134 \\
3. Interpolation / 145 \\
M. D. Buhmann and M. J. D. Powell / Radial basis
function interpolation on an infinite regular grid /
146 \\
L. Brutman / The Fourier operator of even order and its
application to an extremum problem in interpolation /
170 \\
N. Dyn and A. Ron / On multivariate polynomial
interpolation / 177 \\
N. Dyn, D. Levin and S. Rippen / Algorithms for the
construction of data dependent triangulations / 185 \\
C. Rademacher and K. Scherer / Algorithms for computing
best parametric cubic interpolation / 193 \\
4. Smoothing and Constraint Methods / 209 \\
M. Von Golitschek and L. L. Schumaker / Data fitting by
penalized least squares / 210 \\
K. W. Bosworth / A semiinfinite programming algorithm
for constrained best approximation / 228 \\
M. Bozzini and L. Lenarduzzi / Inference region for a
method of local approximation by using the residuals /
236 \\
5. Complex Approximation / 245 \\
G. A. Watson / Numerical methods for Chebyshev
approximation of complex-valued functions / 246 \\
P. T. P. Tang / A fast algorithm for linear complex
Chebyshev approximation / 265 \\
Part Two: Applications / 275 \\
6. Computer Aided Design and Geometric Modelling / 277
\\
N. Dyn, J. A. Gregory and D. Levin / Uniform
subdivision algorithms for curves and surfaces / 278
\\
T. B. Boffey, M. G. Cox, L. M. Delves and C. J.
Pursglove / Approximation by spheres / 296 \\
T. A. Foley / Interpolation of scattered data on a
spherical domain / 303 \\
A. B. Forbes / Least squares best fit geometric
elements / 311 \\
W. Freeden and J. C. Mason / Uniform piecewise
approximation on the sphere / 320 \\
7. Applications in Numerical Analysis / 335 \\
L. N. Trefethen / Approximation theory and numerical
linear algebra / 336 \\
M. Frontini, G. Rodriguez and S. Seatzu / An algorithm
for computing minimum norm solutions of the finite
moment problem / 361 \\
R. H. J. Gmelig Meyling / Numerical solution of the
biharmonic equation using different types of bivariate
spline functions / 369 \\
G. O. Olaofe / Quadrature solution of integral
equations: a uniform treatment of Fredholm and Volterra
equations / 377 \\
G. Walz / Increasing the convergence modulus of an
asymptotic expansion: an algorithm for numerical
differentiation / 387 \\
J. Williams / Approximation and parameter estimation in
ordinary differential equations / 395 \\
8. Applications in Other Disciplines / 405 \\
C. Zala and I. Barrodale / Applications of discrete
$L_1$ methods in science and engineering / 406 \\
J. C. Mason, A. E. Trefethen and S. J. Wilde /
Constrained complex approximation algorithms in
communication engineering / 424 \\
R. W. Allen and J. G. Metcalfe / Integration of
absolute amplitude from a decibel B-spline fit / 449
\\
M. G. Cox and H. M. Jones / A nonlinear least squares
data fitting problem arising in microwave measurement /
458 \\
J. C. Mason and S. J. Wilde / A complex minimax
algorithm for phase-only adaptation in antenna arrays /
466 \\
Part Three: Catalogue of Algorithms / 477 \\
E. Grosse / A catalogue of algorithms for approximation
/ 479",
}
@Proceedings{Ullrich:1990:CCA,
editor = "Christian Ullrich",
booktitle = "Contributions to Computer Arithmetic and
Self-Validating Numerical Methods. (Proceedings of
{SCAN 89}, held in Basel, Oct. 2--6, 1989)",
title = "Contributions to Computer Arithmetic and
Self-Validating Numerical Methods. (Proceedings of
{SCAN} 89, held in Basel, Oct. 2--6, 1989)",
volume = "7",
publisher = pub-BALTZER,
address = pub-BALTZER:adr,
pages = "526",
year = "1990",
ISBN = "????",
ISBN-13 = "????",
LCCN = "QA76.9.C62 C664 1990",
bibdate = "Sat Nov 29 08:36:57 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
series = "IMACS annals on computing and applied mathematics",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic --- congresses; numerical analysis
--- congresses",
xxbooktitle = "SCAN-89, International Symposium on Scientific
Computing, Computer Arithmetic, and Numeric Validation
[October 1989, Basel, Switzerland]",
}
@Proceedings{Anonymous:1991:PIS,
editor = "Anonymous",
booktitle = "Proceedings of the International Symposium on
Supercomputing: Fukuoka, Japan, November 6--8, 1991",
title = "Proceedings of the International Symposium on
Supercomputing: Fukuoka, Japan, November 6--8, 1991",
publisher = "Kyushu University Press",
address = "Fukuoka, Japan",
pages = "iv + 261",
year = "1991",
ISBN = "4-87378-284-8",
ISBN-13 = "978-4-87378-284-3",
LCCN = "QA76.88.I 1991",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
searchkey = "ti:elementary function",
}
@Proceedings{Bowers:1991:CCI,
editor = "K. L. (Kenneth L.) Bowers and J. (John) Lund",
booktitle = "{Computation and control II: proceedings of the second
Bozeman conference, Bozeman, Montana, August 1--7,
1990}",
title = "{Computation and control II: proceedings of the second
Bozeman conference, Bozeman, Montana, August 1--7,
1990}",
volume = "11",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "369",
year = "1991",
ISBN = "0-8176-3611-0",
ISBN-13 = "978-0-8176-3611-1",
LCCN = "TA329 .C644 1991",
bibdate = "Wed May 9 08:56:08 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$65.00",
series = "Progress in systems and control theory",
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
subject = "Engineering mathematics; Congresses; Feedback control
systems",
}
@Proceedings{IEEE:1991:PSA,
editor = "{IEEE}",
booktitle = "Proceedings, Supercomputing '91: Albuquerque, New
Mexico, November 18--22, 1991",
title = "Proceedings, Supercomputing '91: Albuquerque, New
Mexico, November 18--22, 1991",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxiii + 917",
year = "1991",
ISBN = "0-8186-9158-1 (IEEE case), 0-8186-2158-3 (IEEE paper),
0-8186-6158-5 (IEEE microfiche), 0-89791-459-7 (ACM)",
ISBN-13 = "978-0-8186-9158-4 (IEEE case), 978-0-8186-2158-1 (IEEE
paper), 978-0-8186-6158-7 (IEEE microfiche),
978-0-89791-459-8 (ACM)",
LCCN = "QA76.5 .S894 1991",
bibdate = "Fri Aug 30 08:01:51 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
University of California MELVYL catalog.",
note = "ACM order number 415913. IEEE Computer Society Press
order number 2158. IEEE catalog number 91CH3058-5.",
acknowledgement = ack-nhfb,
classification = "C5440 (Multiprocessor systems and techniques); C5470
(Performance evaluation and testing); C6110P (Parallel
programming)",
keywords = "combinatorial algorithms; data dependence; distributed
memory code generation; high school environment;
latency tolerance; memory access; numerical algorithms;
parallel processing; parallel programming; performance
evaluation; performance tools; processor design;
program analysis; storage hierarchy optimization;
supercomputer benchmarks; supercomputer congresses;
supercomputing; system issues",
}
@Proceedings{Koopman:1991:PST,
editor = "Philip J. {Koopman, Jr.}",
booktitle = "{The proceedings of the second and third annual
workshops for the ACM Special Interest Group on Forth:
SIGForth '90, February 16--18, 1990, Dallas, Texas
\ldots{} SIGForth '91, March 7--9, 1991, San Antonio,
Texas}",
title = "{The proceedings of the second and third annual
workshops for the ACM Special Interest Group on Forth:
SIGForth '90, February 16--18, 1990, Dallas, Texas
\ldots{} SIGForth '91, March 7--9, 1991, San Antonio,
Texas}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ii + 134",
year = "1991",
ISBN = "0-89791-462-7",
ISBN-13 = "978-0-89791-462-8",
LCCN = "QA 76.73 F24 S53 1991",
bibdate = "Tue May 04 07:39:28 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 817911.",
acknowledgement = ack-nhfb,
}
@Proceedings{Kornerup:1991:PIS,
editor = "Peter Kornerup and David W. Matula",
booktitle = "Proceedings: 10th {IEEE} Symposium on Computer
Arithmetic: June 26--28, 1991, Grenoble, France",
title = "Proceedings: 10th {IEEE} Symposium on Computer
Arithmetic: June 26--28, 1991, Grenoble, France",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 282",
year = "1991",
ISBN = "0-8186-9151-4 (case), 0-8186-6151-8 (microfiche),
0-7803-0187-0 (library binding)",
ISBN-13 = "978-0-8186-9151-5 (case), 978-0-8186-6151-8
(microfiche), 978-0-7803-0187-0 (library binding)",
LCCN = "QA76.9.C62 S95 1991",
bibdate = "Thu Sep 01 23:18:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Lewin:1991:SPP,
editor = "Leonard Lewin",
booktitle = "Structural Properties of Polylogarithms",
title = "Structural Properties of Polylogarithms",
volume = "37",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xviii + 412",
year = "1991",
ISBN = "0-8218-1634-9, 1-4704-1264-0 (e-book)",
ISBN-13 = "978-0-8218-1634-9, 978-1-4704-1264-7 (e-book)",
ISSN = "0076-5376",
MRclass = "33E20, 00B15, 11-02, 11F67, 11R70, 11R42, 19F27,
33-02, 33-06, 33B99",
bibdate = "Fri Jun 16 14:03:50 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematical surveys and monographs",
acknowledgement = ack-nhfb,
editor-dates = "22-Jul-1919--13-Aug-2007",
editor-url = "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
subject = "Logarithmic functions; Fonctions logarithmes;
Mathematics; Algebra; Intermediate; Logarithmic
functions; Fonctions logarithmes",
tableofcontents = "Preface / xiii \\
Acknowledgments / xv \\
List of Contributors / xvii \\
\\
1: The Evolution of the Ladder Concept / L. Lewin / 1
\\
1.1 Early History / 1 \\
1.2 Functional Equations / 2 \\
1.3 More Recent Numerical Results / 4 \\
1.4 Current Developments / 6 \\
1.5 Base on the Unit Circle and Clausen Function
Ladders / 8 \\
References / 9 \\
\\
2: Dilogarithmic Ladders / L. Lewin / 11 \\
2.1 Derivation from Kummer's Functional Equation / 11
\\
2.2 Relation to Clausen's Function / 15 \\
2.3 A Three-Variable Dilogarithmic Functional Equation
/ 17 \\
2.4 Functional Equations in the Complex Plane / 18 \\
2.5 Cyclotomic Equations and Rogers' Function / 20 \\
2.6 Accessible and Analytic Ladders / 21 \\
2.7 Inaccessible Ladders / 23 \\
References / 25 \\
\\
3: Polylogarithmic Ladders / M. Abouzahra and L. Lewin
/ 27 \\
3.1 Kummer's Function and its Relation to the
Polylogarithm / 27 \\
3.2 Functional Equations for the Polylogarithm / 28 \\
3.3 A Generalization of Rogers' Function to the $n$th
Order / 31 \\
3.4 Ladder Order-Independence on Reduction of Order /
33 \\
3.5 Generic Ladders for the Base Equation $u^p + u^q =
1$ / 34 \\
3.6 Examples of Ladders for $n < 3$ / 40 \\
3.7 Examples of Ladders for $n < 4$ / 44 \\
3.8 Examples of Ladders for $n < 5$ / 45 \\
3.9 Polynomial Relations for Ladders / 46 \\
References / 47 \\
\\
4: Ladders in the Trans-Kummer Region / M. Abouzahra
and L. Lewin / 49 \\
4.1 Ladder Results to $n = 9$ for the Base p / 49 \\
4.2 Ladder Results to $n = 9$ for the Base co / 53 \\
4.3 Ladder Results to $n = 6$ for the Base 6 / 62 \\
4.4 The Nonexistence of Functional Equations at $n = 6$
with Arguments Limited to $\pm z^m (1 - z)^r (1 + z)^s$
/ 65 \\
References / 67 \\
\\
5: Supemumary Ladders / M. Abouzahra and L. Lewin / 69
\\
5.1 The Concept of Supemumary Results / 69 \\
5.2 Supemumary Results for $p = 4$ / 71 \\
5.3 Supemumary Results for $p = 5$ / 76 \\
5.4 Supemumary Results for $p = 6$ / 78 \\
5.5 Supemumary Results for the Equation-family $u^{6m +
1} u^{6r - 1}$ = 1 / 80 \\
5.6 Supemumary Results for an Irreducible Quintic / 82
\\
5.7 Supemumary Ladders from a 15-Term Functional
Equation / 84 \\
5.8 Supemumary Ladders on the Unit Circle / 90 \\
References \\
6: Functional Equations and Ladders / L. Lewin / 97 \\
6.1 New Categories of Functional Equations / 97 \\
6.2 The $\rho$-family of Equations / 100 \\
6.3 The $\omega$-family of Equations / 109 \\
6.4 The $\theta$-family of Equations / 115 \\
Acknowledgements / 121 \\
References / 121 \\
\\
7: Multivariable Polylogarithm Identities / G. A. Ray /
123 \\
7.0 Introduction / 123 \\
7.1 A General Identity for the Dilogarithm / 123 \\
7.2 A General Identity for the Bloch-Wigner Function /
135 \\
7.3 A General Identity for the Trilogarithm and
$D_3(z)$ / 141 \\
7.4 Linear Power Relations among Dilogarithms / 147 \\
7.5 Cyclotomic Equations and Bases for Polylogarithm
Relations / 154 \\
7.6 Mahler's Measure and Salem/Pisot Numbers / 160 \\
7.7 Recent Results for Supemumary Ladders / 165 \\
References / 168 \\
\\
8: Functional Equations of Hyperlogarithms / G.
Wechsung / 171 \\
8.1 Hyperlogarithms / 171 \\
8.2 Logarithmic Singularities / 172 \\
8.3 The Linear Spaces LI$_n$ and PLI$_n$ / 176 \\
8.4 Functional Equations of Hyperlogarithms / 177 \\
8.5 A Reduction Problem / 181 \\
References / 184 \\
\\
9: Kummer-Type Functional Equations of Polylogarithms /
G. Wechsung / 185 \\
9.1 Automorphic Functions / 185 \\
9.2 Kummer-Type Functional Equations / 186 \\
9.3 A Method to Construct Functional Equations / 191
\\
9.4 The Nonexistence of a Kummer-Type Functional
Equation for $\Li_6$ / 197 \\
References / 203 \\
\\
10: The Basic Structure of Polylogarithmic Equations /
Z. Wojtkowiak / 205 \\
10.1 Introduction / 205 \\
10.2 Canonical Unipotent Connection on
$P^1(\mathbb{C})\{a_1, \ldots{}, a_{n+1}\}$ / 211 \\
10.3 Horizontal Sections / 213 \\
10.4 Easy Lemmas about Monodromy / 215 \\
10.5 Functional Equations / 216 \\
10.6 Functional Equations of Polylogarithms / 218 \\
10.7 Functional Equations of Lower Degree
Polylogarithms / 223 \\
10.8 Generalized Bloch Groups / 228 \\
Acknowledgements / 231 \\
References / 231 \\
\\
11: $K$-Theory, Cyclotomic Equations and Clausen's
Function / J. Browkin / 233 \\
11.1 Algebraic Background / 233 \\
11.2 Analytic Background / 238 \\
11.3 $K$-theoretic Background / 248 \\
11.4 Examples / 251 \\
11.5 Problems and Conjectures / 270 \\
References / 272 \\
\\
12: Function Theory of Polylogarithms / S. Bloch / 275
\\
\\
13: Partition Identities and the Dilogarithm / J. H.
Loxton / 287 \\
13.1 Introduction / 287 \\
13.2 Cyclotomic Equations / 290 \\
13.3 Accessible Relations / 291 \\
13.4 Partition Identities / 292 \\
13.5 Generalisations and Extensions / 297 \\
References / 299 \\
\\
14: The Dilogarithm and Volumes of Hyperbolic Polytopes
/ R. Kellerhals / 301 \\
14.0 Introduction / 301 \\
14.1 A Particular Class of Hyperbolic Polytopes / 303
\\
14.2 The Volume of a rf-Truncated Orthoscheme / 309 \\
14.3 Applications / 321 \\
14.4 Further Aspects / 328 \\
References / 335 \\
\\
15: Introduction to Higher Logarithms / R. M. Hain and
R. MacPherson / 337 \\
15.1 The Problem of Generalizing the Logarithm and the
Dilogarithm / 337 \\
15.2 The Quest for Higher Logarithms / 340 \\
15.3 Higher Logarithms / 341 \\
15.4 The Higher Logarithm Bicomplex / 343 \\
15.5 Multivalued Deligne Cohomology / 346 \\
15.6 Higher Logarithms as Deligne Cohomology Classes /
350 \\
Acknowledgements 3 / 51 \\
References / 352 \\
\\
16: Some Miscellaneous Results / L. Lewin / 355 \\
16.1 Clausen's Function and the Di-Gamma Function for
Rational Arguments / 355 \\
16.2 An Infinite Integral of a Product of Two
Polylogarithms / 359 \\
16.3 Cyclotomic and Polylogarithmic Equations for a
Salem Number / 364 \\
16.4 New Functional Equations / 373 \\
References / 374 \\
\\
Appendix A. Special Values and Functional Equations of
Polylogarithms / D. Zagier / 377 \\
0. Introduction / 377 \\
1. The Basic Algebraic Relation and the Definition of
$\mathcal{A}_m(F)$ / 378 \\
2. Examples of Dilogarithm Relations / 383 \\
3. Examples for Higher Order Polylogarithms / 385 \\
4. Examples: Ladders / 387 \\
5. Existence of Relations among Polylogarithm Values of
Arbitrarily High Order / 390 \\
6. A Conjecture on Linear Independence / 391 \\
7. Functional Equations / 392 \\
References / 399 \\
\\
Appendix B. Summary of the Informal Polylogarithm
Workshop, November 17--18, 1990, MIT, Cambridge,
Massachusetts / 401 \\
R. MacPherson and H. Sah / List of Participants / 401
\\
Abbreviated Summary / 402 \\
Bibliography / 405 \\
Index / 409",
}
@Proceedings{EC2:1992:DJN,
key = "AEF'92",
booktitle = "{Deuxi{\`e}mes journ{\'e}es nationales: Les
applications des ensembles flous, en l'honneur du
Professeur A. Kaufmann, Nimes, 2--3 novembre 1992,
conference scientifique (English: Second national
conference: Application of Fuzzy Sets, in honor of
Professor A. Kaufman, Nimes, 2--3 November 1992,
scientific conference)}",
title = "{Deuxi{\`e}mes journ{\'e}es nationales: Les
applications des ensembles flous, en l'honneur du
Professeur A. Kaufmann, Nimes, 2--3 novembre 1992,
conference scientifique (English: Second national
conference: Application of Fuzzy Sets, in honor of
Professor A. Kaufman, Nimes, 2--3 November 1992,
scientific conference)}",
publisher = "EC2",
address = "Nanterre Cedex, France",
pages = "384",
year = "1992",
ISBN = "2-906899-78-X",
ISBN-13 = "978-2-906899-78-0",
LCCN = "????",
bibdate = "Wed Jan 10 07:40:53 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Richards:1992:HFD,
editor = "Donald St P. Richards",
booktitle = "{Hypergeometric functions on domains of positivity,
Jack polynomials, and applications: proceedings of an
AMS Special Session held March 22--23, 1991 in Tampa,
Florida}",
title = "{Hypergeometric functions on domains of positivity,
Jack polynomials, and applications: proceedings of an
AMS Special Session held March 22--23, 1991 in Tampa,
Florida}",
volume = "138",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "x + 259",
year = "1992",
ISBN = "0-8218-5159-4",
ISBN-13 = "978-0-8218-5159-3",
ISSN = "0271-4132 (print), 1098-3627 (electronic)",
LCCN = "QA353.H9 H97 1992",
bibdate = "Sat Oct 30 21:12:24 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Contemporary mathematics",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions; Congresses",
}
@Book{Adams:1993:ACA,
editor = "E. Adams and U. Kulisch",
booktitle = "Scientific Computing with Automatic Result
Verification",
title = "Scientific Computing with Automatic Result
Verification",
volume = "189",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 612",
year = "1993",
ISBN = "0-12-044210-8",
ISBN-13 = "978-0-12-044210-2",
LCCN = "QA76.S368 1993",
bibdate = "Mon Jan 13 09:58:58 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in science and engineering",
acknowledgement = ack-nhfb,
tableofcontents = "Contributors \\
Preface \\
Acknowledgements \\
Introduction \\
Part I. Language and Programming Support for Verified
Scientific Computation \\
1. PASCAL-XSC, New Concepts for Scientific Computation
and Numerical Data Processing \\
2. ACRITH-XSC, A Fortran-like Language for Verified
Scientific Computing \\
3. C-XSC, A Programming Environment for Verified
Scientific Computing and Numerical Data Processing \\
4. Proposal for Accurate Floating-Point Vector
Arithmetic",
}
@Proceedings{Albrecht:1993:VNT,
editor = "R. Albrecht and G. Alefeld and H. J. Stetter",
booktitle = "Validation numerics: theory and applications",
title = "Validation numerics: theory and applications",
volume = "9",
publisher = pub-SPRINGER-WIEN,
address = pub-SPRINGER-WIEN:adr,
pages = "291",
year = "1993",
CODEN = "COSPDM",
ISBN = "0-387-82451-0 (New York), 3-211-82451-0 (Vienna)",
ISBN-13 = "978-0-387-82451-2 (New York), 978-3-211-82451-1
(Vienna)",
ISSN = "0344-8029",
LCCN = "QA297 .V27 1993",
bibdate = "Wed Oct 13 18:45:11 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Dedicated to Ulrich Kulisch on the occasion of his
60th birthday.",
series = j-COMPUTING-SUPPLEMENTUM,
acknowledgement = ack-nhfb,
keywords = "convergence acceleration",
}
@Proceedings{Allasia:1993:PIJ,
editor = "G. Allasia and Luighi Gatteshi and Francesco Lerda",
booktitle = "Proceedings of the International Joint Symposium on
Special Functions and Artificial Intelligence, (1993:
Turin, Italy)",
title = "Proceedings of the International Joint Symposium on
Special Functions and Artificial Intelligence, (1993:
Turin, Italy)",
volume = "2(1/4)",
publisher = "Baltzer Science Publishers",
address = "Amsterdam, The Netherlands",
pages = "474",
year = "1993",
ISSN = "1021-2655",
LCCN = "QA297 A614 v. 2, no. 1/4",
bibdate = "Sat Oct 30 18:57:57 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Annals of numerical mathematics",
acknowledgement = ack-nhfb,
}
@Proceedings{Sincovec:1993:PSS,
editor = "Richard F. Sincovec and David E. Keyes and Michael R.
Leuze",
booktitle = "{Proceedings of the Sixth SIAM Conference on Parallel
Processing for Scientific Computing, held March 22--24,
1993, in Norfolk, VA, USA}",
title = "{Proceedings of the Sixth SIAM Conference on Parallel
Processing for Scientific Computing, held March 22--24,
1993, in Norfolk, VA, USA}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xix + 1041 + iv",
year = "1993",
ISBN = "0-89871-315-3",
ISBN-13 = "978-0-89871-315-2",
LCCN = "QA76.58 .S55 1993 v.1-2",
bibdate = "Tue Oct 11 12:21:40 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{Swartzlander:1993:SCA,
editor = "Earl {Swartzlander, Jr.} and Mary Jane Irwin and
Graham Jullien",
booktitle = "Proceedings: 11th Symposium on Computer Arithmetic,
June 29--July 2, 1993, Windsor, Ontario",
title = "Proceedings: 11th Symposium on Computer Arithmetic,
June 29--July 2, 1993, Windsor, Ontario",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 284",
year = "1993",
ISBN = "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound),
0-8186-3861-3 (microfiche)",
ISBN-13 = "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6
(casebound), 978-0-8186-3861-9 (microfiche)",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
LCCN = "QA 76.9 C62 S95 1993",
bibdate = "Thu Sep 01 22:58:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE Transactions on Computers {\bf 43(8)}, 1994",
acknowledgement = ack-nhfb,
}
@Proceedings{Brown:1994:PCL,
editor = "J. David Brown and Moody T. Chu and Donald C. Ellison
and Robert J. Plemmons",
booktitle = "{Proceedings of the Cornelius Lanczos International
Centenary Conference, Raleigh, North Carolina, December
12--17, 1993}",
title = "{Proceedings of the Cornelius Lanczos International
Centenary Conference, Raleigh, North Carolina, December
12--17, 1993}",
volume = "73",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "lxv + 644",
year = "1994",
ISBN = "0-89871-339-0",
ISBN-13 = "978-0-89871-339-8",
LCCN = "QC19.2 .C67 1993",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Proceedings in Applied Mathematics",
acknowledgement = ack-nhfb,
meetingname = "Cornelius Lanczos International Centenary Conference
(1993:Raleigh, NC)",
subject = "Mathematical physics; Congresses; Astrophysics;
Mathematics; Lanczos, Cornelius; Physicists; Hungary;
Biography; Mathematicians",
subject-dates = "1893--1974",
tableofcontents = "The Life and Works of Cornelius Lanczos \\
\\
A Photographic Essay / / xvii \\
Cornelius Lanczos: A Biographical Essay / Barbara
Gellai / xxi \\
Cornelius Lanczos (1893-1974), and the Hungarian
Phenomenon in Science and Mathematics / Peter D. Lax /
xlix \\
The Roots of Cornelius Lanczos / George Marx / liii \\
Reminiscences of Cornelius Lanczos / Jon Todd / lviii
\\
Published Papers and Books of Cornelius Lanczos / / lx
\\
\\
Plenary Presentations: Computational Mathematics \\
\\
Lanczos and the FFT: A Discovery Before its Time /
James W. Cooley / 3 \\
Lanczos Algorithms for Large Scale Symmetric and
Nonsymmetric Matrix Eigenvalue Problems / Jane K.
Cullum / 11 \\
The Look-Ahead Lanczos Process for Nonsymmetric
Matrices and its Applications / Roland W Freund / 33
\\
The Lanczos and Conjugate Gradient Algorithms in Finite
Precision Arithmetic / Anne Greenbaum / 49 \\
The Lanczos Process and Pade Approximation / Martin H.
Gutknecht / 61 \\
The Tau Method and the Numerical Solution of
Differential Equations: Past Research and Recent
Research / Eduardo L. Ortiz / 77 \\
Krylov Subspace Processes, Krylov Subspace Methods, and
Iteration Polynomials / C. C. Paige / 83 \\
Do We Fully Understand the Symmetric Lanczos Algorithm
Yet? / Beresford N. Parlett / 93 \\
On Generalized Band Matrices and Their Inverses /
P{\'a}l R{\'o}sa, Francesco Romani, and Roberto
Bevilacqua / 109 \\
Theoretical Error Bounds and General Analysis of a Few
Lanczos-Type Algorithms / Youcef Saad / 123 \\
Lanczos and Linear Systems / G. W. Stewart / 135 \\
\\
Plenary Presentations: Theoretical Physics and
Astrophysics \\
\\
Integration on the Space of Connections Modulo Gauge
Transformations / Abbay Ashtekar, Donald Marolf, and
Jose Mourdo / 143 \\
Quasiclassical Domains in a Quantum Universe / James B.
Hartle / 161 \\
Gauge Invariant Energy-Momentum Tensor in Spinar
Electrodynamics / D. Petiot and Y. Takahashi / 173 \\
$\gamma$-Ray Bursts and Neutron Star Mergers / Tsvi
Piran / 187 \\
Lanczos's Early Contributions to Relativity and His
Relationship with Einstein / John Stachel / 201 \\
Topological Roots of Black Hole Entropy / Claudio
Teitelboim / 223 \\
Variational Principles, Local Symmetries, and Black
Hole Entropy / Robert M. Wald / 231 \\
\\
Mathematics Minisymposia \\
\\
Eigenvalue Computations: Theory and Algorithms / / 241
\\
Eigenvalue Computations: Applications / / 249 \\
Moments in Numerical Analysis / / 265 \\
Iterative Methods for Linear Systems / / 277 \\
Least Squares / / 301 \\
Software for Lanczos-based Algorithms / / 311 \\
Tau Method / / 335 \\
Chebyshev Polynomials / / 357 \\
Lanczos Methods in Control and Signal Processing / /
375 \\
Development of the FFT / / 393 \\
The FFT in Signal Processing / / 399 \\
Wavelets / / 411 \\
\\
Physics Minisymposia \\
\\
Computational Magnetohydrodynamics in Astrophysics / /
431 \\
Numerical Simulations of Collisionless Space Plasmas /
/ 453 \\
Detection of Gravitational Radiation from Astrophysical
Sources / / 477 \\
Lanczos $H$-tensor / / 489 \\
Cosmic Censorship / / 513 \\
Cauchy Problem of General Relativity / / 527 \\
Black Hole Evaporation and Thermodynamics / / 543 \\
The Problem of Time in Quantum Gravity / / 555 \\
New Variables and Loop Quantization / / 571 \\
Decoherence and the Foundations of Quantum Mechanics /
/ 589 \\
Open Questions in Particle Theory / / 603 \\
Supercollider Physics / / 621 \\
Symplectic Methods in Physics / / 633",
}
@Proceedings{Cuyt:1994:NNM,
editor = "Annie Cuyt",
booktitle = "Nonlinear numerical methods and rational approximation
{II}",
title = "Nonlinear numerical methods and rational approximation
{II}",
volume = "296",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xviii + 446",
year = "1994",
ISBN = "0-7923-2967-8",
ISBN-13 = "978-0-7923-2967-1",
LCCN = "QA297 .N642 1994",
bibdate = "Wed Nov 3 09:30:14 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Proceedings of an international conference held at the
University of Antwerp, Belgium, Sept. 5--11, 1993.",
series = "Mathematics and its applications",
acknowledgement = ack-nhfb,
keywords = "approximation theory -- congresses; numerical analysis
-- congresses",
}
@Proceedings{Gautschi:1994:MCH,
editor = "Walter Gautschi",
booktitle = "{Mathematics of computation, 1943--1993: a
half-century of computational mathematics: Mathematics
of Computation 50th Anniversary Symposium, August
9--13, 1993, Vancouver, British Columbia}",
title = "{Mathematics of computation, 1943--1993: a
half-century of computational mathematics: Mathematics
of Computation 50th Anniversary Symposium, August
9--13, 1993, Vancouver, British Columbia}",
volume = "48",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xix + 643",
year = "1994",
ISBN = "0-8218-0291-7, 0-8218-0353-0 (pt. 1), 0-8218-0354-9
(pt. 2)",
ISBN-13 = "978-0-8218-0291-5, 978-0-8218-0353-0 (pt. 1),
978-0-8218-0354-7 (pt. 2)",
ISSN = "0160-7634",
LCCN = "QA1 .A56 v.48 1994; QA297.M385 1993",
MRclass = "00B25 (11-06 65-06)",
MRnumber = "95j:00014",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1940.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
note = "See also SIAM Review, September 1995, {\bf 37}(3), p.
483.",
series = "Proceedings of Symposia in Applied Mathematics",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
tableofcontents = "Preface / xi \\
Mathematics of Computation: A brief history / Eugene
Isaacson / xvii \\
\\
Part I. Symposium on Numerical Analysis \\
\\
Invited Papers \\
\\
On the development of multigrid methods and their
analysis / James H. Bramble / 5 \\
An introduction to inverse problems / Margaret Cheney /
21 \\
Algorithms for unconstrained optimization: A review of
recent developments / Donald Goldfarb / 33 \\
A survey of componentwise perturbation theory in
numerical linear algebra / Nicholas J. Higham / 49 \\
Numerical evaluation of special functions / D. W.
Lozier and F. W. J. Olver / 79 \\
A survey of numerical cubature over triangles / J. N.
Lyness and Ronald Cools / 127 \\
New trends in the use and analysis of integral
equations / J. C. Nedelec / 151 \\
Applications of multivariate splines / Larry L.
Schumaker / 177 \\
Initial value problems for ordinary differential
equations: Development of ideas, techniques, and
implementation / Hans J. Stetter / 205 \\
Multiresolution methods for partial differential
equations / Roger Temam / 225 \\
\\
Contributed Papers \\
\\
A comparison of techniques for solving ill-conditioned
problems arising from the immersed boundary method /
Loyce Adams and Zhiyun Yang / 243 \\
A mixed spectral-collocation and operator splitting
method for the Wigner-Poisson equation / Anton Arnold /
249 \\
Finite volume methods for irregular one-dimensional
grids / M. J. Berger, R. J. Leveque, and L. G. Stern /
255 \\
Linear rational interpolation of continuous functions
over an interval / Jean-Paul Berrut / 261 \\
A von Neumann reflection for the 2-D Burgers equation /
M. Brio and J. K. Hunter / 265 \\
Slow evolution from the boundary: A new stabilizing
constraint in ill-posed continuation problems / Alfred
S. Carasso / 269 \\
A finite element method for the 2D drift-diffusion
semiconductor model / Zhangxin Chen / 275 \\
Splitting functions and numerical analysis of WR-type
methods for evolutionary and stationary problems / S.
De Marchi, M. Vianello, and R. Zanovello / 281 \\
Error estimates for a quadrature rule for Cauchy
principal value integrals / Kai Diethelm / 287 \\
A numerical radius approach to stable difference
schemes for parabolic systems / Moshe Goldberg / 293
\\
An extension of the Olver-Sookne method for the
solution of second-order linear difference equations /
Takemitsu Hasegawa and Tatsuo Torii / 297 \\
The Faber polynomials for circular arcs / Matthew He /
301 \\
Finite element approximation for optimal control of
electrically conducting fluid flows / L. S. Hou and S.
S. Ravindran / 305 \\
ADI methods for heat equations with discontinuities
along an arbitrary interface / Zhilin Li and Anita Mayo
/ 311 \\
Eigenvalue approximation of Fredholm integral operators
/ E. B. Lin / 317 \\
Spectral methods for singular perturbation problems /
Wenbin Liu and Tao Tang / 323 \\
A quaternion-Jacobi method for symmetric matrices /
Niloufer Mackey / 327 \\
On constructing Chebyshev series solutions of
differential equations / Allan J. MacLeod / 333 \\
Multiquadric collocation methods in the numerical
solution of Volterra integral and integro-differential
equations / Athena Makroglou / 337 \\
Methods for solving large eigenvalue problems
associated with configuration interaction electronic
structure calculations / Kristyn J. Maschhoff / 343 \\
Computing limiting normals to real surfaces / Donal
O'Shea and Les Wilson / 349 \\
Orthogonal spline collocation solution of nonlinear
Schr{\"o}dinger equations / Mark P. Robinson / 355 \\
Who invented the computer? The debate from the
viewpoint of computer architecture / Ra{\'u}l Rojas /
361 \\
Locking and boundary layer effects in the finite
element approximation of the Reissner--Mindlin plate
model / Christoph Schwab and Manil Suri / 367 \\
Efficient spectral Galerkin methods for some elliptic
problems / Jie Shen / 373 \\
Periodic solutions of higher-order difference equations
in two independent variables / Qin Sheng and Ravi P.
Agarwal / 377 \\
Front tracking based on high-resolution wave
propagation methods / Keh-Ming Shyue / 383 \\
Time-splitting methods for nonhomogeneous conservation
laws / Tao Tang and Zhen-Huan Teng / 389 \\
Numerical aspects of uniform Airy-type asymptotic
expansions / N. M. Temme / 395 \\
Local dynamics and bifurcation consistencies of
continuous-time dynamical systems and their numerical
discretizations / Xin Wang, Edward K. Blum, and Qingnan
Li / 399 \\
Computing integrals of the complex error function / J.
A. C. Weideman / 403 \\
Quadratures for improper integrals and their
applications in integral equations / Yuesheng Xu and
Yunhe Zhao / 409 \\
Spline harmonic analysis and wavelet bases / Valery A.
Zheludev / 415 \\
\\
Part II. Minisymposium on Computational Number Theory
Dedicated to the memory of Derrick Henry Lehmer \\
\\
Invited Papers \\
\\
Algorithms for quadratic orders / Ingrid Biehl and
Johannes Buchmann / 425 \\
Analytic computations in number theory / Andrew M.
Odlyzko / 451 \\
The number field sieve / Carl Pomerance / 465 \\
Factoring integers before computers / H. C. Williams
and J. O. Shallit / 481 \\
\\
Contributed Papers \\
\\
Explicit bounds for primes in residue classes / Eric
Bach and Jonathan Sorenson / 535 \\
Ramanujan and Euler's constant / Richard P. Brent / 541
\\
Congruential sieves on FPGA computers / Nathan D.
Bronson and Duncan A. Buell / 547 \\
Lehmer pairs of zeros and the Riemann $\xi$-function /
George Csordas, Wayne Smith, and Richard S. Varga / 553
\\
A record Aliquot sequence / Andrew W. P. Guy and
Richard K. Guy / 557 \\
Implications of computational mathematics for the
philosophy of mathematics / Andrew J. Lazarus / 561 \\
Square roots of products of algebraic numbers / Peter
L. Montgomery / 567 \\
A locally parameterized version of Lehmer's problem /
Gary A. Ray / 573 \\
A new method for finding amicable pairs / H. J. J. te
Riele / 577 \\
Generalized Fermat numbers / Hans Riesel and Anders
Bj{\"o}rn / 583 \\
Evaluation of $\zeta_K(2)$ for some totally real
algebraic number fields K of degree 9 / Kisao Takeuchi
/ 589 \\
The period of the Bell exponential integers modulo a
prime / Samuel S. Wagstaff, Jr. / 595 \\
Computing invariant polynomials of $p$-adic reflection
groups / Changsheng Xu / 599 \\
Author Index / 603 \\
Subject Index / 619",
}
@Proceedings{Mudge:1994:PTS,
editor = "Trevor N. Mudge and Bruce D. Shriver",
booktitle = "{Proceedings of the Twenty-Seventh Hawaii
International Conference on System Sciences Vol. I:
Architecture}",
title = "{Proceedings of the Twenty-Seventh Hawaii
International Conference on System Sciences Vol. I:
Architecture}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1994",
ISBN = "0-8186-5050-8 (paper), 0-8186-5051-6 (microfiche)",
ISBN-13 = "978-0-8186-5050-5 (paper), 978-0-8186-5051-2
(microfiche)",
LCCN = "????",
bibdate = "Mon Jan 13 10:02:18 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "First of five volumes. IEEE Catalog No. 94TH0607-2.",
acknowledgement = ack-nhfb,
}
@Proceedings{Zahar:1994:ACF,
editor = "R. V. M. (Ramsay Vincent Michael) Zahar",
booktitle = "{Approximation and computation: a festschrift in honor
of Walter Gautschi: proceedings of the Purdue
conference, December 2--5, 1993}",
title = "{Approximation and computation: a festschrift in honor
of Walter Gautschi: proceedings of the Purdue
conference, December 2--5, 1993}",
volume = "119",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xlvi + 591",
year = "1994",
ISBN = "0-8176-3753-2",
ISBN-13 = "978-0-8176-3753-8",
LCCN = "QA221 .A634 1994",
bibdate = "Wed May 9 09:01:57 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "International series of numerical mathematics",
acknowledgement = ack-nhfb,
subject = "Approximation theory; Congresses; Orthogonal
polynomials; Numerical integration; Functions,
Special",
}
@Proceedings{Knowles:1995:PSC,
editor = "Simon Knowles and William H. McAllister",
booktitle = "Proceedings of the 12th Symposium on Computer
Arithmetic, July 19--21, 1995, Bath, England",
title = "Proceedings of the 12th Symposium on Computer
Arithmetic, July 19--21, 1995, Bath, England",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvi + 252",
year = "1995",
ISBN = "0-8186-7089-4 (paperback), 0-8186-7089-4 (case),
0-8186-7149-1 (microfiche), 0-8186-7089-4 (softbound),
0-7803-2949-X (casebound)",
ISBN-13 = "978-0-8186-7089-3 (paperback), 978-0-8186-7089-3
(case), 978-0-8186-7149-4 (microfiche),
978-0-8186-7089-3 (softbound), 978-0-7803-2949-2
(casebound)",
LCCN = "QA 76.9 C62 S95 1995",
bibdate = "Sun Mar 29 08:48:20 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Singh:1995:CRT,
editor = "Avtar Singh",
booktitle = "Conference record of the Twenty-Ninth Asilomar
Conference on Signals, Systems \& Computers: October
30--November 1, 1995 Pacific Grove, California",
title = "Conference record of the Twenty-Ninth Asilomar
Conference on Signals, Systems \& Computers: October
30--November 1, 1995 Pacific Grove, California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1995",
ISBN = "0-8186-7370-2",
ISBN-13 = "978-0-8186-7370-2",
LCCN = "TK7801 .A83 1995",
bibdate = "Sun Mar 29 08:51:26 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{LakshmanYN:1996:IPI,
editor = "{Lakshman Y.N.}",
booktitle = "{ISSAC '96: Proceedings of the 1996 International
Symposium on Symbolic and Algebraic Computation, July
24--26, 1996, Zurich, Switzerland}",
title = "{ISSAC '96: Proceedings of the 1996 International
Symposium on Symbolic and Algebraic Computation, July
24--26, 1996, Zurich, Switzerland}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xvii + 313",
year = "1996",
ISBN = "0-89791-796-0",
ISBN-13 = "978-0-89791-796-4",
LCCN = "QA 76.95 I59 1996",
bibdate = "Thu Mar 12 08:00:14 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
sponsor = "ACM; Special Interest Group in Symbolic and Algebraic
Manipulation (SIGSAM). ACM; Special Interest Group on
Numerical Mathematics (SIGNUM).",
}
@Book{Berggren:1997:PSB,
editor = "Lennart Berggren and Jonathan M. Borwein and Peter B.
Borwein",
booktitle = "Pi, a source book",
title = "Pi, a source book",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xix + 716",
year = "1997",
DOI = "https://doi.org/10.1007/978-1-4757-2736-4",
ISBN = "0-387-94924-0, 1-4757-2736-4 (e-book), 1-4757-2738-0
(print), 3-540-94924-0",
ISBN-13 = "978-0-387-94924-6, 978-1-4757-2736-4 (e-book),
978-1-4757-2738-8 (print), 978-3-540-94924-4",
LCCN = "QA484 .P5 1997",
bibdate = "Fri Sep 2 17:41:50 MDT 2022",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib;
z3950.loc.gov:7090/Voyager",
abstract = "The aim of this book is to provide a complete history
of pi from the dawn of mathematical time to the
present. The story of pi reflects the most seminal, the
most serious and sometimes the silliest aspects of
mathematics, and a surprising amount of the most
important mathematics and mathematicians have
contributed to its unfolding. Pi is one of the few
concepts in mathematics whose mention evokes a response
of recognition and interest in those not concerned
professionally with the subject. Yet, despite this, no
source book on pi has been published. One of the
beauties of the literature on pi is that it allows for
the inclusion of very modern, yet still accessible,
mathematics. Mathematicians and historians of
mathematics will find this book indispensable. Teachers
at every level from the seventh grade onward will find
here ample resources for anything from special topic
courses to individual talks and special student
projects. The literature on pi included in this source
book falls into three classes: first a selection of the
mathematical literature of four millennia, second a
variety of historical studies or writings on the
cultural meaning and significance of the number, and
third, a number of treatments on pi that are fanciful,
satirical and/or whimsical.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Pi; Pi (Le nombre); Pi.; Pi (le nombre)",
tableofcontents = "Preface / v \\
\\
Acknowledgments / ix \\
\\
Introduction / xvii \\
\\
1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
1650 B.C.) / A problem dealing with the area of a round
field of given diameter / 1 \\
\\
2. Engels. Quadrature of the Circle in Ancient Egypt
(1977) / A conjectural explanation of how the
mathematicians of ancient Egypt approximated the area
of a circle / 3 \\
\\
3. Archimedes. Measurement of a Circle ($\approx$ 250
BC) / The seminal work in which Archimedes presents the
first true algorithm for $\pi$ / 7 \\
\\
4. Phillips. Archimedes the Numerical Analyst (1981) /
A summary of Archimedes' work on the computation of
$\pi$ using modern notation / 15 \\
\\
5. Lam and Ang. Circle Measurements in Ancient China
(1986) / This paper discusses and contains a
translation of Liu Hui's (3rd century) method for
evaluating $\pi$ and also examines values for $\pi$
given by Zu Chongzhi (429--500) / 20 \\
\\
6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
and Solid Figures ($\approx$ 850) / This extract gives
an explicit statement and proof that the ratio of the
circumference to the diameter is constant / 36 \\
\\
7. M{\=a}dhava. The Power Series for Arctan and Pi
($\approx$ 1400) / These theorems by a fifteenth
century Indian mathematician give Gregory's series for
arctan with remainder terms and Leibniz's series for
$\pi$ / 45 \\
\\
8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
Ceulen (1938) / Correspondence about van Ceulen's
tombstone in reference to it containing some digits of
$\pi$ / 51 \\
\\
9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
Liber VII (1593) / Two excerpts. One containing the
first infinite expression of $\pi$, obtained by
relating the area of a regular $2n$-gon to that of a
regular $n$-gon / 53 \\
\\
10. Wallis. Computation of $\pi$ by Successive
Interpolations (1655) / How Wallis derived the infinite
product for $\pi$ that bears his name / 68 \\
\\
11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
including Prop. 189, 191 and an alternate form of the
result that gives Wm. Brounker's continued fraction
expression for $4/\pi$ / 78 \\
\\
12. Huygens. De Circuli Magnitudine Inventa (1724) /
Huygens's proof of W. Snell's discovery of improvements
in Archimedes' method of estimating the lengths of
circular arcs / 81 \\
\\
13. Gregory. Correspondence with John Collins (1671) /
A letter to Collins in which he gives his series for
arctangent, carried to the ninth power. / 87 \\
\\
14. Roy. The Discovery of the Series Formula for $\pi$
by Leibniz, Gregory, and Nilakantha (1990) / A
discussion of the discovery of the series $\pi/4 = 1 -
1/3 + 1/5, \cdots{}$ / 92 \\
\\
15. Jones. The First Use of $\pi$ for the Circle Ratio
(1706) / An excerpt from Jones' book, the Synopsis
Palmariorum Matheseos: or, a New Introduction to the
Mathematics, London, 1706 / 108 \\
\\
16. Newton. Of the Method of Fluxions and Infinite
Series (1737) / An excerpt giving Newton's calculation
of $\pi$ to 16 decimal places / 110 \\
\\
17. Euler. Chapter 10 of Introduction to Analysis of
the Infinite (On the Use of the Discovered Fractions to
Sum Infinite Series) (1748) / This includes many of
Euler's infinite series for $\pi$ and powers of $\pi$ /
112 \\
\\
18. Lambert. M{\'e}moire Sur Quelques
Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
Transcendentes Circulaires et Logarithmiques (1761) /
An excerpt from Lambert's original proof of the
irrationality of $\pi$ / 129 \\
\\
19. Lambert. Irrationality of $\pi$ (1969) / A
translation and Struik's discussion of Lambert's proof
of the irrationality of $\pi$ / 141 \\
\\
20. Shanks. Contributions to Mathematics Comprising
Chiefly of the Rectification of the Circle to 607
Places of Decimals (1853) / Pages from Shank's report
of his monumental hand calculation of $\pi$ / 147 \\
\\
21. Hermite. Sur La Fonction Exponentielle (1873) / The
first proof of the transcendence of $e$ / 162 \\
\\
22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
proof of the transcendence of $\pi$ / 194 \\
\\
23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
transcendence of $\pi$ / 207 \\
\\
24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
$\pi$ (1893) / Hilbert's short and elegant
simplification of the transcendence proofs for $e$ and
$\pi$ / 226 \\
\\
25. Goodwin. Quadrature of the Circle (1894) / The
dubious origin of the attempted legislation of the
value of $\pi$ in Indiana / 230 \\
\\
26. Edington. House Bill No. 246, Indiana State
Legislature, 1897 (1935) / A summary of the action
taken by the Indiana State Legislature to fix the value
of $\pi$ (including a copy of the actual bill that was
proposed) / 231 \\
\\
27. Singmaster. The Legal Values of Pi (1985) / A
history of the attempt by Indiana to legislate the
value of $\pi$ / 236 \\
\\
28. Ramanujan. Squaring the Circle (1913) / A geometric
approximation to $\pi$ / 240 \\
\\
29. Ramanujan. Modular Equations and Approximations to
$\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
includes a number of striking series and algebraic
approximations / 241 \\
\\
30. Watson. The Marquis and the Land Agent: A Tale of
the Eighteenth Century (1933) / A Presidential address
to the Mathematical Association in which the author
gives an account of ``some of the elementary work on
arcs and ellipses and other curves which led up to the
idea of inverting an elliptic integral, and so laying
the foundations of elliptic functions and doubly
periodic functions generally.'' / 258 \\
\\
31. Ballantine. The Best (?) Formula for Computing
$\pi$ to a Thousand Places (1939) / An early attempt to
orchestrate the calculation of $\pi$ more cleverly /
271 \\
\\
32. Birch. An Algorithm for Construction of Arctangent
Relations (1946) / The object of this note is to
express $\pi / 4 $ as a sum of arctan relations in
powers of 10 / 274 \\
\\
33. Niven. A Simple Proof that $\pi$ Is Irrational
(1947) / A very concise proof of the irrationality of
$\pi$ / 276 \\
\\
34. Reitwiesner. An ENIAC Determination of $\pi$ and
$e$ to 2000 Decimal Places (1950) / One of the first
computer-based computations / 277 \\
\\
35. Schepler. The Chronology of Pi (1950) / A fairly
reliable outline of the history of $\pi$ from 3000 BC
to 1949 / 282 \\
\\
36. Mahler. On the Approximation of $\pi$ (1953) /
``The aim of this paper is to determine an explicit
lower bound free of unknown constants for the distance
of $\pi$ from a given rational or algebraic number'' /
306 \\
\\
37. Wrench, Jr. The Evolution of Extended Decimal
Approximations to $\pi$ (1960) / A history of the
calculation of the digits of $\pi$ to 1960 \\
\\
38. Shanks and Wrench, Jr. Calculation of $\pi$ to
100,000 Decimals (1962) / A landmark computation of
$\pi$ to more than 100,000 places / 326 \\
\\
39. Sweeny. On the Computation of Euler's Constant
(1963) / The computation of Euler's constant to 3566
decimal places / 350 \\
\\
40. Baker. Approximations to the Logarithms of Certain
Rational Numbers (1964) / The main purpose of this deep
and fundamental paper is to ``deduce results concerning
the accuracy with which the natural logarithms of
certain rational numbers may be approximated by
rational numbers, or, more generally, by algebraic
numbers of bounded degree.'' / 359 \\
\\
41. Adams. Asymptotic Diophantine Approximations to $E$
(1966) / An asymptotic estimate for the rational
approximation to $e$ which disproves the conjecture
that $e$ behaves like almost all numbers in this
respect / 368 \\
\\
42. Mahler. Applications of Some Formulae by Hermite to
the Approximations of Exponentials of Logarithms (1967)
/ An important extension of Hilbert's approach to the
study of transcendence / 372 \\
\\
43. Eves. In Mathematical Circles; A Selection of
Mathematical Stories and Anecdotes (excerpt) (1969) / A
collection of mathematical stories and anecdotes about
$\pi$ / 400 \\
\\
44. Eves. Mathematical Circles Revisited; A Second
Collection of Mathematical Stories and Anecdotes
(excerpt) (1971) / A further collection of mathematical
stories and anecdotes about $\pi$ / 402 \\
\\
45. Todd. The Lemniscate Constants (1975) / A unifying
account of some of the methods used for computing the
lemniscate constants / 412 \\
\\
46. Salamin. Computation of r Using
Arithmetic-Geometric Mean (1976) / The first
quadratically converging algorithm for $\pi$ based on
Gauss's AGM and on Legendre's relation for elliptic
integrals / 418 \\
\\
47. Brent. Fast Multiple-Precision Evaluation of
Elementary Functions (1976) / ``This paper contains the
`Gauss-Legendre' method and some different algorithms
for log and exp (using Landen transformations).'' / 424
\\
\\
48. Beukers. A Note on the Irrationality of $\zeta(2)$
and $\zetq(3)$ (1979) / A short and elegant recasting
of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
(and $\zeta(2)$) / 434 \\
\\
49. van der Poorten. A Proof that Euler Missed \ldots{}
Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
(1979) / An illuminating account of Ap{\'e}ry's
astonishing proof of the irrationality of $\zeta(3)$ /
439 \\
\\
50. Brent and McMillan. Some New Algorithms for
High-Precision Computation of Euler's Constant (1980) /
Several new algorithms for high precision calculation
of Euler's constant, including one which was used to
compute 30,100 decimal places / 448 \\
\\
51. Apostol. A Proof that Euler Missed: Evaluating
$\zeta(2)$ the Easy Way (1983) / This note shows that
one of the double integrals considered by Beukers ([48]
in the table of contents) can be used to establish
directly that $\zeta(2) = \pi / 6$ / 456 \\
\\
52. O'Shaughnessy. Putting God Back in Math (1983) / An
article about the Institute of Pi Research, an
organization that ``pokes fun at creationists by
pointing out that even the Bible makes mistakes.'' /
458 \\
\\
53. Stern. A Remarkable Approximation to $\pi$ (1985) /
Justification of the value of $\pi$ in the Bible
through numerological interpretations / 460 \\
\\
54. Newman and Shanks. On a Sequence Arising in Series
for $\pi$ (1984) / More connections between $\pi$ and
modular equations / 462 \\
\\
55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
/ An extensive study of the complex analytic properties
of the AGM / 481 \\
\\
56. Borwein and Borwein. The Arithmetic-Geometric Mean
and Fast Computation of Elementary Functions (1984) /
The relationship between the AGM iteration and fast
computation of elementary functions (one of the
by-products is an algorithm for $\pi$) / 537 \\
\\
57. Newman. A Simplified Version of the Fast Algorithms
of Brent and Salamin (1984) / Elementary algorithms for
evaluating $e^x$ and $\pi$ using the Gauss AGM without
explicit elliptic function theory / 553 \\
\\
58. Wagon. Is Pi Normal? (1985) / A discussion of the
conjecture that $\pi$ has randomly distributed digits /
557 \\
\\
59. Keith. Circle Digits: A Self-Referential Story
(1986) / A mnemonic for the first 402 decimal places of
$\pi$ / 560 \\
\\
60. Bailey. The Computation of $\pi$ to 29,360,000
Decimal Digits Using Borweins' Quartically Convergent
Algorithm (1988) / The algorithms used, both for $\pi$
and for performing the required multiple-precision
arithmetic / 562 \\
\\
61. Kanada. Vectorization of Multiple-Precision
Arithmetic Program and 201,326,000 Decimal Digits of 1
Calculation (1988) / Details of the computation and
statistical tests of the first 200 million digits of
$\pi$ / 576 \\
\\
62. Borwein and Borwein. Ramanujan and Pi (1988) / This
article documents Ramanujan's life, his ingenious
approach to calculating $\pi$, and how his approach is
now incorporated into modern computer algorithms / 588
\\
\\
63. Chudnovsky and Chudnovsky. Approximations and
Complex Multiplication According to Ramanujan (1988) /
This excerpt describes ``Ramanujan's original quadratic
period--quasiperiod relations for elliptic curves with
complex multiplication and their applications to
representations of fractions of $\pi$ and other
logarithms in terms of rapidly convergent nearly
integral (hypergeometric) series.'' / 596 \\
\\
64. Borwein, Borwein and Bailey. Ramanujan, Modular
Equations, and Approximations to Pi or How to Compute
One Billion Digits of Pi (1989) / An exposition of the
computation of $\pi$ using mathematics rooted in
Ramanujan's work / 623 \\
\\
65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
and Asymptotic Expansions (1989) / An explanation as to
why the slowly convergent Gregory series for $\pi$,
truncated at 500,000 terms, gives $\pi$ to 40 places
with only the 6th, 17th, 18th, and 29th places being
incorrect / 642 \\
\\
66. Beukers, B{\'e}zivin, and Robba. An Alternative
Proof of the Lindemann--Weierstrass Theorem (1990) /
The Lindemann--Weierstrass theorem as a by-product of a
criterion for rationality of solutions of differential
equations / 649 \\
\\
67. Webster. The Tail of Pi (1991) / Various anecdotes
about $\pi$ from the 14th annual IMO Lecture to the
Royal Society / 654 \\
\\
68. Eco. An excerpt from Foucault's Pendulum (1993) /
``The unnumbered perfection of the circle itself.'' /
658 \\
\\
69. Keith. Pi Mnemonics and the Art of Constrained
Writing (1996) / A mnemonic for $\pi$ based on Edgar
Allen Poe's poem ``The Raven.'' / 659 \\
\\
70. Bailey, Borwein, and Plouffe. On the Rapid
Computation of Various Polylogarithmic Constants (1996)
/ A fast method for computing individual digits of
$\pi$ in base 2 / 663 \\
Appendix I --- On the Early History of Pi / 677 \\
\\
Appendix II --- A Computational Chronology of Pi / 683
\\
\\
Appendix III --- Selected Formulae for Pi / 686 \\
\\
Bibliography / 690 \\
\\
Credits / 697 \\
\\
Index / 701",
}
@Proceedings{Boisvert:1997:QNS,
editor = "Ronald F. Boisvert",
booktitle = "Quality of Numerical Software: Assessment and
Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working
Conference on the Quality of Numerical Software,
Assessment and Enhancement, Oxford, United Kingdom,
8--12 July 1996}",
title = "Quality of Numerical Software: Assessment and
Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working
Conference on the Quality of Numerical Software,
Assessment and Enhancement, Oxford, United Kingdom,
8--12 July 1996}",
publisher = pub-CHAPMAN-HALL,
address = pub-CHAPMAN-HALL:adr,
pages = "vii + 384",
year = "1997",
ISBN = "0-412-80530-8",
ISBN-13 = "978-0-412-80530-1",
LCCN = "QA297 .I35 1996",
bibdate = "Fri Jul 09 05:58:30 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Lang:1997:ISC,
editor = "Tomas Lang and Jean-Michel Muller and Naofumi Takagi",
booktitle = "13th {IEEE} Symposium on Computer Arithmetic:
proceedings, July 6--9, 1997, Asilomar, California,
{USA}",
title = "13th {IEEE} Symposium on Computer Arithmetic:
proceedings, July 6--9, 1997, Asilomar, California,
{USA}",
volume = "13",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 291",
year = "1997",
ISBN = "0-8186-7846-1, 0-8186-7847-X, 0-8186-7848-8",
ISBN-13 = "978-0-8186-7846-2, 978-0-8186-7847-9,
978-0-8186-7848-6",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 1997",
bibdate = "Fri Mar 27 09:56:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE Computer Society order number PR07846. IEEE Order
Plan catalog number 97CB36091.",
series = "Symposium on Computer Arithmetic",
acknowledgement = ack-nhfb,
sponsor = "IEEE.",
}
@Proceedings{Thiele:1997:IIC,
editor = "Lothar Thiele and others",
booktitle = "{IEEE International Conference on Application-Specific
Systems, Architectures and Processors: proceedings,
July 14--16, 1997, Z{\"u}rich, Switzerland}",
title = "{IEEE International Conference on Application-Specific
Systems, Architectures and Processors: proceedings,
July 14--16, 1997, Z{\"u}rich, Switzerland}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 540",
year = "1997",
ISBN = "0-8186-7959-X, 0-8186-7960-3, 0-8186-7958-1",
ISBN-13 = "978-0-8186-7959-9, 978-0-8186-7960-5,
978-0-8186-7958-2",
LCCN = "TK7874.6 .I57 1997eb; TK7874.6 .I57 1997; TK7874.6
.I58 1997",
bibdate = "Sun Mar 4 21:13:29 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Application-Specific
Systems, Architectures, and Processors (11th: 1997:
Z{\"u}rich, Switzerland)",
remark = "IEEE Computer Society Press order number PR07958. IEEE
catalog number 97TB100177",
subject = "Array processors; Congresses; Signal processing;
Digital techniques; Application-specific integrated
circuits",
}
@Proceedings{Rusev:1998:TMS,
editor = "Petur Rusev and I. Dimovski and Virginia Kiryakova",
booktitle = "{Transformation methods and special functions, Varna
'96: second international workshop: proceedings}",
title = "{Transformation methods and special functions, Varna
'96: second international workshop: proceedings}",
publisher = "Institute of Mathematics and Informatics, Bulgarian
Academy of Sciences",
address = "Sofia, Bulgaria",
pages = "vi + 613",
year = "1998",
ISBN = "954-8986-05-1",
ISBN-13 = "978-954-8986-05-2",
LCCN = "????",
bibdate = "Thu Dec 1 11:08:47 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
meetingname = "International Workshop ``Transform Methods and Special
Functions'' (2nd: 1996: Varna, Bulgaria)",
remark = "``This second edition of the Workshops 'TM and SF' has
been devoted to the 100th anniversary of the eminent
Bulgarian mathematician Nikola Obreshkoff
(1896-1963)''--T.p. verso.",
subject = "Transformations (Mathematics); Differential equations;
Integral equations",
tableofcontents = "On a generalization of the theorem on two constants
/ G. Adamczyk \\
On a construction of the solutions of some elliptic
equations with generalized coefficients / A. Antonevich
\\
Some non-metrizable spaces of harmonic functions / G.
Balikov, I. Dimitrov \\
Duhamel-type representations of the solutions of
non-local boundary value problems for the fractional
diffusion-wave equation / E. Bazhlekova \\
Pointwise convergence for Hankel transform / J.
Betancour, L. Rodr\'iguez-Mesa \\
On fractional order continuity, integrability and
derivability of real functions / B. Bonilla, J.
Trujillo, M. Rivero \\
On the root functions of a nonlocal Sturm--Liouville
problem / N. Bozhinov \\
Mellin transform theory and the role of its
differential and integral operators / P. Butzer, S.
Jansche \\
Exact solution of some systems of non-selfadjoint
partial differential equations / D. Callebaut \\
Numerical computation of Lame functions / H.-J. Dobner,
S. Ritter \\
Some extremal problems for $p$-valent alpha-convex
functions / J. Dziok \\
Extension of a result on the convolution product of
distributions / B. Fisher, A. Kilicman \\
Simple algorithms for approximations of generalized
elliptic-type integrals / M. A. El-Gabali, Shyam L.
Kalla \\
On Zernicke polynomials / H.-J. Glaeske \\
Tomato salad problem in spherical stereology / R.
Gorenflo \\
On existence of solutions of ordinary differential
equations of fractional order / N. Hayek \ldots{} [et
al.] \\
Tauberian theorem for distributions / J. Jel\'inek \\
Radiation field integrals and their evaluation
techniques / Shyam L. Kalla, H. G. Khajah \\
On the product of distributions / A. Kami\'nski \\
On isotopies of algebras and triple systems / N. Kamiya
\\
Univalence criteria connected with arithmetic and
geometric means: I / S. Kanas, A. Lecko \\
Global and causal solutions of fractional linear
differential equations / S. Kempfle, H. Beyer \\
On the applications of Mikusinski's operational
calculus to the controllability of dynamical systems /
W. Kierat, K. Sk\'ornik \\
Application of fractional calculus to solve
Abel--Volterra nonlinear and linear integral equations
/ A. Kilbas, M. Saigo \\
Note on linear operators and fractional calculus
operators in the univalent function theory / Yong Chan
Kim \\
Application of the generalized Mikhaylov criterion / S.
Krasinska \\
On some classes of holomorphic functions in the
half-plane / A. Lazi{\'n}ska \\
Expansions in series of Legendre functions / E. R.
Love, M. Hunter \\
Intersections with Gronwall methods / W. Luh \\
Applications of fractional calculus in mechanics / F.
Mainardi \\
Automorphisms in the commutant of the integration
operator in spaces of Lebesgue integrable functions /
S. Mincheva \\
Applications of fractional calculus operators to
univalent functions / S. Owa \\
Application of orthogonal polynomials to solution of
fractional integral equations / I. Podlubny \\
Remark on Watson transform / A. Prudnikov, U. Sk\'ornik
\\
Generalized operators of fractional
integro-differentiation in meaning of M. Saigo and
their applications / O. Repin \\
Fractional integrals and wavelet transformations / B.
Rubin, D. Ryabogin, E. Shamir \\
More generalization of fractional calculus / M. Saigo,
N. Maeda \\
On certain subclasses of analytic functions involving a
linear operator / H. Saitoh \\
On some sequence spaces / E. Savas \\
Class of integro-differential equations via fractional
calculus / N. Shawagfeh \\
On some extreme points of the unit ball / J. Sokol, W.
Szumny \\
Hyper-Bessel operators, differential equations,
functions, and integral transforms of 4th order / S.
Spirova \\
Some operational techniques in the theory of special
functions / H. M. Srivastava \\
Convolution in the theory of univalent functions / J.
Stankiewicz \\
Some extensions of the Rolle and Gauss--Lucas theorems
/ T. Stoyanov \\
On infinitely divisible probability distributions and
integral equations / K. Takano \\
Generating functions related to pairs of inverse
functions / R. Tremblay, B. J. Fug\`ere \\
Integral transforms connected with the group
representations / N. Tretyakova \\
On some integral operators in the clas of functions
with negative coefficients / L. Trojnar-Spelina \\
On a new generalized Taylor's formula / J. Trujillo, M.
Rivero, B. Bonilla \\
Some properties of the finite Laplace transform / M.
Valbuena, L. Galue, I. Ali \\
Airy integral transform and the Paley--Wiener theorem /
Vu Kim Tuan \\
On starlike functions related with hyperbolic regions /
A. Wi{\'s}niowska \\
Editorial: Nikola Obreshkoff (1896--1963): biographical
data and 100 selected papers of Acad. N. Obreshkoff \\
Obreshkoff's generalization of Descartes rule / P.
Rusev \\
Obrechkoff's generalization of the Laplace and Meijer
transformations: origins and recent developments / I.
Dimovski, V. Kiryakova \\
Longstanding conjecture failed? / V. Kiryakova \\
Afterthoughts on interpretation of fractional
derivatives and integrals / R. Gorenflo \\
Modelling viscous damped oscillations by fractional
differential operators / S. Kempfle \\
Considerations on fractional calculus: interpretations
and applications / F. Mainardi \\
Introduction to the fractional calculus and some
applications / K. Oldham",
}
@Book{Bultheel:1999:ORF,
editor = "Adhemar Bultheel and Pablo Gonzales-Vera and Erik
Hendriksen and Olav Njastad",
booktitle = "Orthogonal Rational Functions",
title = "Orthogonal Rational Functions",
volume = "5",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiv + 407",
year = "1999",
DOI = "https://doi.org/10.1017/CBO9780511530050",
ISBN = "0-521-65006-2 (hardcover)",
ISBN-13 = "978-0-521-65006-9 (hardcover)",
LCCN = "QA404.5 .O75 1999",
bibdate = "Tue Mar 24 21:04:21 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
series = "Cambridge monographs on applied and computational
mathematics",
URL = "http://www.loc.gov/catdir/description/cam029/98011646.html;
http://www.loc.gov/catdir/toc/cam024/98011646.html",
acknowledgement = ack-nhfb,
subject = "functions, orthogonal; functions of complex
variables",
tableofcontents = "1. Preliminaries / 15--41 \\
2. The fundamental spaces / 42--63 \\
3. The kernel functions / 64--73 \\
4. Recurrence and second kind functions / 74--105 \\
5. Para-orthogonality and quadrature / 106--120 \\
6. Interpolation / 121--148 \\
7. Density of the rational functions / 149--160 \\
8. Favard theorems / 161--172 \\
9. Convergence / 173--238 \\
10. Moment problems / 239--256 \\
11. The boundary case / 257--341 \\
12. Some applications / 342--388 \\
Conclusion / 389--392 \\
Bibliography/ 393--404 \\
Index / 405--407",
}
@Proceedings{IEEE:1999:PIF,
editor = "IEEE",
booktitle = "Proceedings of the {IEEE} Forum on Research and
Technology Advances in Digital Libraries, May 19--21,
1999, Baltimore, Maryland",
title = "Proceedings of the {IEEE} Forum on Research and
Technology Advances in Digital Libraries, May 19--21,
1999, Baltimore, Maryland",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 217",
year = "1999",
ISBN = "0-7695-0219-9",
ISBN-13 = "978-0-7695-0219-9",
LCCN = "ZA4080 .F67 1999",
bibdate = "Fri Jul 09 06:32:32 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
xxeditor = "Frances M. Titsworth",
}
@Proceedings{Koren:1999:ISC,
editor = "Israel Koren and Peter Kornerup",
booktitle = "14th {IEEE} Symposium on Computer Arithmetic:
proceedings: April 14--16, 1999, Adelaide, Australia",
title = "14th {IEEE} Symposium on Computer Arithmetic:
proceedings: April 14--16, 1999, Adelaide, Australia",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 274",
year = "1999",
ISBN = "0-7803-5609-8, 0-7695-0116-8, 0-7695-0118-4",
ISBN-13 = "978-0-7803-5609-2, 978-0-7695-0116-1,
978-0-7695-0118-5",
ISSN = "1063-6889",
LCCN = "QA76.6 .S887 1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "IEEE Computer Society Order Number PR00116. IEEE Order
Plan Catalog Number 99CB36336.",
URL = "http://computer.org/conferen/home/arith/;
http://www.ecs.umass.edu/ece/arith14/program.html",
acknowledgement = ack-nhfb,
annote = "Also known as ARITH-14.",
source = "Computer arithmetic",
sponsor = "IEEE.",
}
@Proceedings{Luk:1999:PSA,
editor = "Franklin T. Luk",
booktitle = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations IX:
19--21 July, 1999, Denver, Colorado}",
title = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations IX:
19--21 July, 1999, Denver, Colorado}",
volume = "3807",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "ix + 648",
year = "1999",
ISBN = "0-8194-3293-8",
ISBN-13 = "978-0-8194-3293-3",
LCCN = "TK5102.5 .A3325 1999; TK5102.5 .A3173 1999eb; TK5102.9
.A37 1999; TK5102.5; TS510 .S63",
bibdate = "Mon Mar 5 07:43:43 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
subject = "Signal processing; Digital techniques; Congresses;
Algorithms; Computer architecture",
}
@Book{Berggren:2000:PSB,
editor = "Lennart Berggren and Jonathan Borwein and Peter
Borwein",
booktitle = "Pi: a source book",
title = "Pi: a source book",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xx + 736",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-3240-5",
ISBN = "0-387-98946-3 (hardcover)",
ISBN-13 = "978-0-387-98946-4 (hardcover)",
LCCN = "QA484 .P5 2000",
MRclass = "11-00 (01A05 01A75 11-03)",
MRnumber = "1746004",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
libnote = "Not yet in my library.",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Pi (mathematical constant)",
tableofcontents = "Preface / v \\
\\
Preface to the Second Edition / viii \\
Acknowledgments / ix \\
\\
Introduction / xvii \\
\\
1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
1650 B.C.) / A problem dealing with the area of a round
field of given diameter / 1 \\
\\
2. Engels. Quadrature of the Circle in Ancient Egypt
(1977) / A conjectural explanation of how the
mathematicians of ancient Egypt approximated the area
of a circle / 3 \\
\\
3. Archimedes. Measurement of a Circle ($\approx$ 250
BC) / The seminal work in which Archimedes presents the
first true algorithm for $\pi$ / 7 \\
\\
4. Phillips. Archimedes the Numerical Analyst (1981) /
A summary of Archimedes' work on the computation of
$\pi$ using modern notation / 15 \\
\\
5. Lam and Ang. Circle Measurements in Ancient China
(1986) / This paper discusses and contains a
translation of Liu Hui's (3rd century) method for
evaluating $\pi$ and also examines values for $\pi$
given by Zu Chongzhi (429--500) / 20 \\
\\
6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
and Solid Figures ($\approx$ 850) / This extract gives
an explicit statement and proof that the ratio of the
circumference to the diameter is constant / 36 \\
\\
7. M{\=a}dhava. The Power Series for Arctan and Pi
($\approx$ 1400) / These theorems by a fifteenth
century Indian mathematician give Gregory's series for
arctan with remainder terms and Leibniz's series for
$\pi$ / 45 \\
\\
8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
Ceulen (1938) / Correspondence about van Ceulen's
tombstone in reference to it containing some digits of
$\pi$ / 51 \\
\\
9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
Liber VII (1593) / Two excerpts. One containing the
first infinite expression of $\pi$, obtained by
relating the area of a regular $2n$-gon to that of a
regular $n$-gon / 53 \\
\\
10. Wallis. Computation of $\pi$ by Successive
Interpolations (1655) / How Wallis derived the infinite
product for $\pi$ that bears his name / 68 \\
\\
11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
including Prop. 189, 191 and an alternate form of the
result that gives Wm. Brounker's continued fraction
expression for $4/\pi$ / 78 \\
\\
12. Huygens. De Circuli Magnitudine Inventa (1724) /
Huygens's proof of W. Snell's discovery of improvements
in Archimedes' method of estimating the lengths of
circular arcs / 81 \\
\\
13. Gregory. Correspondence with John Collins (1671) /
A letter to Collins in which he gives his series for
arctangent, carried to the ninth power. / 87 \\
\\
14. Roy. The Discovery of the Series Formula for $\pi$
by Leibniz, Gregory, and Nilakantha (1990) / A
discussion of the discovery of the series $\pi/4 = 1 -
1/3 + 1/5, \cdots{}$ / 92 \\
\\
15. Jones. The First Use of $\pi$ for the Circle Ratio
(1706) / An excerpt from Jones' book, the Synopsis
Palmariorum Matheseos: or, a New Introduction to the
Mathematics, London, 1706 / 108 \\
\\
16. Newton. Of the Method of Fluxions and Infinite
Series (1737) / An excerpt giving Newton's calculation
of $\pi$ to 16 decimal places / 110 \\
\\
17. Euler. Chapter 10 of Introduction to Analysis of
the Infinite (On the Use of the Discovered Fractions to
Sum Infinite Series) (1748) / This includes many of
Euler's infinite series for $\pi$ and powers of $\pi$ /
112 \\
\\
18. Lambert. M{\'e}moire Sur Quelques
Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
Transcendentes Circulaires et Logarithmiques (1761) /
An excerpt from Lambert's original proof of the
irrationality of $\pi$ / 129 \\
\\
19. Lambert. Irrationality of $\pi$ (1969) / A
translation and Struik's discussion of Lambert's proof
of the irrationality of $\pi$ / 141 \\
\\
20. Shanks. Contributions to Mathematics Comprising
Chiefly of the Rectification of the Circle to 607
Places of Decimals (1853) / Pages from Shank's report
of his monumental hand calculation of $\pi$ / 147 \\
\\
21. Hermite. Sur La Fonction Exponentielle (1873) / The
first proof of the transcendence of $e$ / 162 \\
\\
22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
proof of the transcendence of $\pi$ / 194 \\
\\
23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
transcendence of $\pi$ / 207 \\
\\
24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
$\pi$ (1893) / Hilbert's short and elegant
simplification of the transcendence proofs for $e$ and
$\pi$ / 226 \\
\\
25. Goodwin. Quadrature of the Circle (1894) / The
dubious origin of the attempted legislation of the
value of $\pi$ in Indiana / 230 \\
\\
26. Edington. House Bill No. 246, Indiana State
Legislature, 1897 (1935) / A summary of the action
taken by the Indiana State Legislature to fix the value
of $\pi$ (including a copy of the actual bill that was
proposed) / 231 \\
\\
27. Singmaster. The Legal Values of Pi (1985) / A
history of the attempt by Indiana to legislate the
value of $\pi$ / 236 \\
\\
28. Ramanujan. Squaring the Circle (1913) / A geometric
approximation to $\pi$ / 240 \\
\\
29. Ramanujan. Modular Equations and Approximations to
$\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
includes a number of striking series and algebraic
approximations / 241 \\
\\
30. Watson. The Marquis and the Land Agent: A Tale of
the Eighteenth Century (1933) / A Presidential address
to the Mathematical Association in which the author
gives an account of ``some of the elementary work on
arcs and ellipses and other curves which led up to the
idea of inverting an elliptic integral, and so laying
the foundations of elliptic functions and doubly
periodic functions generally.'' / 258 \\
\\
31. Ballantine. The Best (?) Formula for Computing
$\pi$ to a Thousand Places (1939) / An early attempt to
orchestrate the calculation of $\pi$ more cleverly /
271 \\
\\
32. Birch. An Algorithm for Construction of Arctangent
Relations (1946) / The object of this note is to
express $\pi / 4 $ as a sum of arctan relations in
powers of 10 / 274 \\
\\
33. Niven. A Simple Proof that $\pi$ Is Irrational
(1947) / A very concise proof of the irrationality of
$\pi$ / 276 \\
\\
34. Reitwiesner. An ENIAC Determination of $\pi$ and
$e$ to 2000 Decimal Places (1950) / One of the first
computer-based computations / 277 \\
\\
35. Schepler. The Chronology of Pi (1950) / A fairly
reliable outline of the history of $\pi$ from 3000 BC
to 1949 / 282 \\
\\
36. Mahler. On the Approximation of $\pi$ (1953) /
``The aim of this paper is to determine an explicit
lower bound free of unknown constants for the distance
of $\pi$ from a given rational or algebraic number'' /
306 \\
\\
37. Wrench, Jr. The Evolution of Extended Decimal
Approximations to $\pi$ (1960) / A history of the
calculation of the digits of $\pi$ to 1960 \\
\\
38. Shanks and Wrench, Jr. Calculation of $\pi$ to
100,000 Decimals (1962) / A landmark computation of
$\pi$ to more than 100,000 places / 326 \\
\\
39. Sweeny. On the Computation of Euler's Constant
(1963) / The computation of Euler's constant to 3566
decimal places / 350 \\
\\
40. Baker. Approximations to the Logarithms of Certain
Rational Numbers (1964) / The main purpose of this deep
and fundamental paper is to ``deduce results concerning
the accuracy with which the natural logarithms of
certain rational numbers may be approximated by
rational numbers, or, more generally, by algebraic
numbers of bounded degree.'' / 359 \\
\\
41. Adams. Asymptotic Diophantine Approximations to $E$
(1966) / An asymptotic estimate for the rational
approximation to $e$ which disproves the conjecture
that $e$ behaves like almost all numbers in this
respect / 368 \\
\\
42. Mahler. Applications of Some Formulae by Hermite to
the Approximations of Exponentials of Logarithms (1967)
/ An important extension of Hilbert's approach to the
study of transcendence / 372 \\
\\
43. Eves. In Mathematical Circles; A Selection of
Mathematical Stories and Anecdotes (excerpt) (1969) / A
collection of mathematical stories and anecdotes about
$\pi$ / 400 \\
\\
44. Eves. Mathematical Circles Revisited; A Second
Collection of Mathematical Stories and Anecdotes
(excerpt) (1971) / A further collection of mathematical
stories and anecdotes about $\pi$ / 402 \\
\\
45. Todd. The Lemniscate Constants (1975) / A unifying
account of some of the methods used for computing the
lemniscate constants / 412 \\
\\
46. Salamin. Computation of r Using
Arithmetic-Geometric Mean (1976) / The first
quadratically converging algorithm for $\pi$ based on
Gauss's AGM and on Legendre's relation for elliptic
integrals / 418 \\
\\
47. Brent. Fast Multiple-Precision Evaluation of
Elementary Functions (1976) / ``This paper contains the
`Gauss-Legendre' method and some different algorithms
for log and exp (using Landen transformations).'' / 424
\\
\\
48. Beukers. A Note on the Irrationality of $\zeta(2)$
and $\zetq(3)$ (1979) / A short and elegant recasting
of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
(and $\zeta(2)$) / 434 \\
\\
49. van der Poorten. A Proof that Euler Missed \ldots{}
Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
(1979) / An illuminating account of Ap{\'e}ry's
astonishing proof of the irrationality of $\zeta(3)$ /
439 \\
\\
50. Brent and McMillan. Some New Algorithms for
High-Precision Computation of Euler's Constant (1980) /
Several new algorithms for high precision calculation
of Euler's constant, including one which was used to
compute 30,100 decimal places / 448 \\
\\
51. Apostol. A Proof that Euler Missed: Evaluating
$\zeta(2)$ the Easy Way (1983) / This note shows that
one of the double integrals considered by Beukers ([48]
in the table of contents) can be used to establish
directly that $\zeta(2) = \pi / 6$ / 456 \\
\\
52. O'Shaughnessy. Putting God Back in Math (1983) / An
article about the Institute of Pi Research, an
organization that ``pokes fun at creationists by
pointing out that even the Bible makes mistakes.'' /
458 \\
\\
53. Stern. A Remarkable Approximation to $\pi$ (1985) /
Justification of the value of $\pi$ in the Bible
through numerological interpretations / 460 \\
\\
54. Newman and Shanks. On a Sequence Arising in Series
for $\pi$ (1984) / More connections between $\pi$ and
modular equations / 462 \\
\\
55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
/ An extensive study of the complex analytic properties
of the AGM / 481 \\
\\
56. Borwein and Borwein. The Arithmetic-Geometric Mean
and Fast Computation of Elementary Functions (1984) /
The relationship between the AGM iteration and fast
computation of elementary functions (one of the
by-products is an algorithm for $\pi$) / 537 \\
\\
57. Newman. A Simplified Version of the Fast Algorithms
of Brent and Salamin (1984) / Elementary algorithms for
evaluating $e^x$ and $\pi$ using the Gauss AGM without
explicit elliptic function theory / 553 \\
\\
58. Wagon. Is Pi Normal? (1985) / A discussion of the
conjecture that $\pi$ has randomly distributed digits /
557 \\
\\
59. Keith. Circle Digits: A Self-Referential Story
(1986) / A mnemonic for the first 402 decimal places of
$\pi$ / 560 \\
\\
60. Bailey. The Computation of $\pi$ to 29,360,000
Decimal Digits Using Borweins' Quartically Convergent
Algorithm (1988) / The algorithms used, both for $\pi$
and for performing the required multiple-precision
arithmetic / 562 \\
\\
61. Kanada. Vectorization of Multiple-Precision
Arithmetic Program and 201,326,000 Decimal Digits of 1
Calculation (1988) / Details of the computation and
statistical tests of the first 200 million digits of
$\pi$ / 576 \\
\\
62. Borwein and Borwein. Ramanujan and Pi (1988) / This
article documents Ramanujan's life, his ingenious
approach to calculating $\pi$, and how his approach is
now incorporated into modern computer algorithms / 588
\\
\\
63. Chudnovsky and Chudnovsky. Approximations and
Complex Multiplication According to Ramanujan (1988) /
This excerpt describes ``Ramanujan's original quadratic
period--quasiperiod relations for elliptic curves with
complex multiplication and their applications to
representations of fractions of $\pi$ and other
logarithms in terms of rapidly convergent nearly
integral (hypergeometric) series.'' / 596 \\
\\
64. Borwein, Borwein and Bailey. Ramanujan, Modular
Equations, and Approximations to Pi or How to Compute
One Billion Digits of Pi (1989) / An exposition of the
computation of $\pi$ using mathematics rooted in
Ramanujan's work / 623 \\
\\
65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
and Asymptotic Expansions (1989) / An explanation as to
why the slowly convergent Gregory series for $\pi$,
truncated at 500,000 terms, gives $\pi$ to 40 places
with only the 6th, 17th, 18th, and 29th places being
incorrect / 642 \\
\\
66. Beukers, B{\'e}zivin, and Robba. An Alternative
Proof of the Lindemann--Weierstrass Theorem (1990) /
The Lindemann--Weierstrass theorem as a by-product of a
criterion for rationality of solutions of differential
equations / 649 \\
\\
67. Webster. The Tail of Pi (1991) / Various anecdotes
about $\pi$ from the 14th annual IMO Lecture to the
Royal Society / 654 \\
\\
68. Eco. An excerpt from Foucault's Pendulum (1993) /
``The unnumbered perfection of the circle itself.'' /
658 \\
\\
69. Keith. Pi Mnemonics and the Art of Constrained
Writing (1996) / A mnemonic for $\pi$ based on Edgar
Allen Poe's poem ``The Raven.'' / 659 \\
\\
70. Bailey, Borwein, and Plouffe. On the Rapid
Computation of Various Polylogarithmic Constants (1996)
/ A fast method for computing individual digits of
$\pi$ in base 2 / 663 \\
Appendix I --- On the Early History of Pi / 677 \\
\\
Appendix II --- A Computational Chronology of Pi / 683
\\
\\
Appendix III --- Selected Formulae for Pi / 686 \\
\\
Appendix IV --- Translations of Vi{\`e}te and Huygens /
690 \\
Bibliography / 711 \\
\\
Credits / 717 \\
\\
Index / 721",
}
@Proceedings{Cocolicchio:2000:ASF,
editor = "Decio Cocolicchio and G. Dattoli and H. M.
Srivastava",
booktitle = "{Advanced special functions and applications:
proceedings of the workshop: Melfi (PZ), Italy, 9--12
May 1999}",
title = "{Advanced special functions and applications:
proceedings of the workshop: Melfi (PZ), Italy, 9--12
May 1999}",
volume = "1",
publisher = "Aracne",
address = "Roma, Italy",
edition = "1.",
pages = "336",
year = "2000",
ISBN = "88-7999-265-X",
ISBN-13 = "978-88-7999-265-7",
LCCN = "QA351 .A38 2000",
bibdate = "Sat Oct 30 19:16:34 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Proceedings of the Melfi school on advanced topics in
mathematics and physics",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Congresses",
}
@Proceedings{Dunkl:2000:PIW,
editor = "Charles Dunkl and Mourad Ismail and Roderick Wong",
booktitle = "{Proceedings of the international workshop, special
functions: Hong Kong, 21--25 June 1999}",
title = "{Proceedings of the international workshop, special
functions: Hong Kong, 21--25 June 1999}",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xi + 438",
year = "2000",
ISBN = "981-02-4393-6",
ISBN-13 = "978-981-02-4393-7",
LCCN = "QA351 .P76 2000",
bibdate = "Fri Jul 09 06:30:25 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Sprague:2000:PAH,
editor = "Ralph H. Sprague",
booktitle = "{Proceedings of the 33rd Annual Hawaii International
Conference on System Sciences: abstracts and CD-ROM of
full papers: January 4--7, 2000, Maui, Hawaii}",
title = "{Proceedings of the 33rd Annual Hawaii International
Conference on System Sciences: abstracts and CD-ROM of
full papers: January 4--7, 2000, Maui, Hawaii}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "liv + 259",
year = "2000",
ISBN = "0-7695-0493-0, 0-7695-0494-9, 0-7695-0495-7",
ISBN-13 = "978-0-7695-0493-3, 978-0-7695-0494-0,
978-0-7695-0495-7",
LCCN = "TA168 .H37 2000; TA168 .H37 2000xeb; TA168",
bibdate = "Sun Mar 4 21:23:42 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "Hawaii International Conference on System Sciences
(33rd: 2000: Maui, Hawaii)",
remark = "IEEE Computer Society Order Number: PR00493",
subject = "Systems engineering; Congresses; Information theory;
Electronic data processing; System design",
}
@Proceedings{Banerji:2001:SFS,
editor = "P. K. Banerji",
booktitle = "{Special functions: selected articles: proceedings of
the First National Conference of the Society for
Special Functions and their Applications, March 3--4,
2000, Jodhpur, India}",
title = "{Special functions: selected articles: proceedings of
the First National Conference of the Society for
Special Functions and their Applications, March 3--4,
2000, Jodhpur, India}",
publisher = "Published by Scientific Publishers (India) for the
Society for Special Functions and their Applications",
address = "Jodhpur, India",
pages = "258",
year = "2001",
ISBN = "81-7233-267-X",
ISBN-13 = "978-81-7233-267-9",
LCCN = "QA351 .S665 2001",
bibdate = "Sat Oct 30 19:13:10 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Congresses",
}
@Proceedings{Burgess:2001:ISC,
editor = "N. Burgess and L. Ciminiera",
booktitle = "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
title = "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 285",
year = "2001",
ISBN = "0-7695-1150-3; 0-7695-1152-X",
ISBN-13 = "978-0-7695-1150-4; 978-0-7695-1152-8",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2001",
bibdate = "Fri May 03 14:20:49 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE order no. PR01150.",
price = "US\$145",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
xxnote = "Check dates: 11--13 or 11--17??",
xxtitle = "Computer Arithmetic: Papers presented at the {15th
IEEE Symposium on Computer Arithmetic (Arith-15 2001),
11--17 June, 2001, Vail, CO}",
}
@Book{Garvan:2001:SCN,
editor = "Frank (Frank G.) Garvan and Mourad Ismail",
booktitle = "Symbolic Computation, Number Theory, Special
Functions, Physics, and Combinatorics",
title = "Symbolic Computation, Number Theory, Special
Functions, Physics, and Combinatorics",
volume = "4",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "x + 283",
year = "2001",
ISBN = "1-4020-0101-0",
ISBN-13 = "978-1-4020-0101-7",
LCCN = "QA295 .S86 2001",
bibdate = "Sat Oct 30 17:31:50 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
series = "Developments in mathematics",
acknowledgement = ack-nhfb,
subject = "q-series; Congresses; Algebra; Data processing; Number
theory; Functions, Special; Mathematical physics;
Combinatorial analysis",
tableofcontents = "Preface \\
Participants \\
Gaussian hypergeometric series and combinatorial
congruences / Scott Ahlgren / 1--12 \\
A double bounded key identity for Gollnitz's (BIG)
partition theorem / Krishnaswami Alladi and Alexander
Berkovich / 13--32 \\
Engel expansions of q-series by computer algebra /
George E. Andrews, Arnold Knopfmacher and Peter Paule /
[and others] / 33--57 \\
Sums of squares and the preservation of modularity
under congruence restrictions / Paul T. Bateman, Boris
A. Datskovsky and Marvin I. Knopp / 59--71 \\
On the transformation formula for the Dedekind
eta-function / Bruce C. Berndt and K. Venkatachaliengar
/ 73--77 \\
Experiments and discoveries in q-trigonometry / R. Wm.
Gosper / 79--105 \\
Algebraic consequences of Jacobi's two- and four-square
theorems / Michael D. Hirschhorn and James A. McGowan /
107--132 \\
The Borweins' Cubic Theta Functions and q-Elliptic
Functions / Richard Lewis, Zhi-Guo Liu / 133--145 \\
Some Eisenstein Series Identities Associated with the
Borwein Functions / Zhi-Guo Liu / 147--169 \\
Hankel Determinants of Eisenstein Series / Stephen C.
Milne / 171--188 \\
Jacobi's Identity and Two K3-Surfaces / Maki Murata /
189--198 \\
$q$-Random Matrix Ensembles / K. A. Muttalib, Y. Chen,
M. E. H. Ismail / 199--221 \\
Differential Endomorphisms for Modular Forms On
$\Gamma_0(4)$ / Ken Ono / 223--229 \\
On the Asymptotics of Takeuchi Numbers / Thomas
Prellberg / 231--242 \\
Fine-Tuning Zeilberger's Algorithm / Axel Riese /
243--254 \\
Gaussian Integrals and the Rogers--Ramanujan Identities
/ D. Stanton / 255--265 \\
Some Remarks on a Product Expansion / M. V. Subbarao,
A. Verma / 267--283 \\
Back Matter / 285--285",
}
@Book{Lide:2001:CEM,
editor = "David R. Lide",
booktitle = "A Century of Excellence in Measurements, Standards,
and Technology",
title = "A Century of Excellence in Measurements, Standards,
and Technology",
volume = "958",
publisher = pub-NIST,
address = pub-NIST:adr,
pages = "ix + 386",
year = "2001",
bibdate = "Fri Jul 09 06:29:11 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "NIST special publication",
acknowledgement = ack-nhfb,
}
@Proceedings{Siafarikas:2001:PFI,
editor = "Panayiotis D. Siafarikas and Theodore Seio Chihara",
booktitle = "{Proceedings of the Fifth International Symposium on
Orthogonal Polynomials, Special Functions and their
Applications: Patras, Greece, 20--24 September 1999}",
title = "{Proceedings of the Fifth International Symposium on
Orthogonal Polynomials, Special Functions and their
Applications: Patras, Greece, 20--24 September 1999}",
volume = "133(1/2)",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "xxvii + 705",
year = "2001",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
LCCN = "QA76 J86 v. 133, no. 1/2",
bibdate = "Sat Oct 30 19:08:06 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Journal of computational and applied mathematics",
acknowledgement = ack-nhfb,
}
@Proceedings{Borrione:2002:TIW,
editor = "Dominique Borrione",
booktitle = "{Third International Workshop on the ACL2 Theorem
Prover and its Applications (ACL2-2002), April 8--9,
2002, in Grenoble, France. Presentations, affiliated
with ETAPS 2002}",
title = "{Third International Workshop on the ACL2 Theorem
Prover and its Applications (ACL2-2002), April 8--9,
2002, in Grenoble, France. Presentations, affiliated
with ETAPS 2002}",
publisher = "????",
address = "????",
pages = "????",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Jun 25 12:28:18 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.utexas.edu/users/moore/acl2/workshop-2002/",
acknowledgement = ack-nhfb,
}
@Book{Lide:2002:CEM,
editor = "David R. Lide",
booktitle = "A Century of Excellence in Measurements, Standards,
and Technology",
title = "A Century of Excellence in Measurements, Standards,
and Technology",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "ix + 386",
year = "2002",
ISBN = "0-8493-1247-7",
ISBN-13 = "978-0-8493-1247-2",
LCCN = "QC100.U6 .C46 2002",
bibdate = "Fri Jul 09 06:29:11 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Republication of \cite{Lide:2001:CEM}.",
URL = "http://www.loc.gov/catdir/toc/fy031/2002283707.html",
acknowledgement = ack-nhfb,
tableofcontents = "Introduction / 1 \\
1901--1930 \\
The Absolute Measurement of Inductance / 5 \\
Determination of the Constants of Total Radiation From
a Black Body / 7 \\
The Testing of Thermal Insulators / 10 \\
Precipitation Hardening of Metal Alloys / 14 \\
Construction and Operation of a Simple Homemade Radio
Receiving Outfit / 16 \\
Methods for Standardizing and Testing Precision Gage
Blocks / 19 \\
Recommended Minimum Requirements for Small Dwelling
Construction / 22 \\
Visibility of Radiant Energy / 25 \\
Test of the Severity of Building Fires / 28 \\
Calculation of Compounds in Portland Cements / 33 \\
Development of the Visual-Type Airway Radio-Beacon
System / 38 \\
1931--1950 \\
A Hydrogen Isotope of Mass 2 / 43 \\
Air Flow and Turbulence in Boundary Layers / 46 \\
Thermodynamic Properties of Water and Steam for Power
Generation / 49 \\
Absolute Pressure Calibrations of Microphones / 53 \\
Absolute Determination of the Ampere / 56 \\
Radio Proximity Fuzes / 59 \\
Stability of Double-Walled Manganin Resistors / 63 \\
Manufacture of Paper for War Maps and Other
Applications / 66 \\
Transmission of Sound Waves in Gases at Low Pressures /
69 \\
Atomic Energy Levels and Other Spectroscopic Data / 73
\\
Iteration Method for the Solution of the Eigenvalue
Problem of Linear Differential and Integral Operators /
77 \\
1951--1960 \\
Methods of Conjugate Gradients for Solving Linear
Systems / 81 \\
Computer Development at the National Bureau of
Standards / 86 \\
Thermal Converters as AC-DC Transfer Standards for
Current and Voltage Measurements at Audio Frequencies /
90 \\
Selected Values of Chemical Thermodynamic Properties /
93 \\
Applied Inorganic Analysis / 97 \\
The Diamond Anvil Pressure Cell / 100 \\
Polymer Crystallization With Folded Chains / 104 \\
Cryogenic Engineering / 107 \\
Reversal of the Parity Conservation Law in Nuclear
Physics / 111 \\
1961--1970 \\
Effects of Configuration Interaction on Intensities and
Phase Shifts / 116 \\
Electromagnetic Waves in Stratified Media / 120 \\
``Second Breakdown'' in Transistors / 123 \\
Stress Relaxation With Finite Strain / 126 \\
Realistic Evaluation of the Precision and Accuracy of
Instrument Calibration Systems / 129 \\
Experimental Statistics / 132 \\
Handbook of Mathematical Functions / 135 \\
Paths, Trees, and Flowers / 140 \\
Concepts, Terminology, and Notation for Optical
Modulation / 145 \\
Theory of Light Scattering in Fluids / 149 \\
Scaling Analysis of Thermodynamic Properties in the
Critical Region of Fluids / 152 \\
Resonance Tunneling of Field Emitted Electrons Through
Adsorbates on Metal Surfaces / 155 \\
Quantitative Electron Probe Microanalysis / 160 \\
Limits for Qualitative Detection and Quantitative
Determination / 164 \\
Traceability: An Evolving Concept / 167 \\
Code for Information Interchange --- ASCII / 172 \\
Consumer Information Series / 174 \\
Theory of Isoperibol Calorimetry for Laser Power and
Energy Measurement / 178 \\
Influence of Water on Crack Growth in Glass / 181 \\
Phase Equilibria Diagrams / 184 \\
Determination of Reduced Cells in Crystallography / 188
\\
1971--1980 \\
Speed of Light From Direct Frequency and Wavelength
Measurements / 191 \\
Connecting Visible Wavelength Standards With X Rays and
$\gamma$ Rays / 194 \\
Laser Cooling of Atoms / 200 \\
Spin-Polarized Electrons / 203 \\
Needs for Radioactivity Standards and Measurements in
Different Fields / 209 \\
The Topografiner: An Instrument for Measuring Surface
Microtopography / 214 \\
Electron-Stimulated Desorption / 219 \\
Photochemistry of Small Molecules / 224 \\
Role of Standard Reference Materials in Measurement
Systems / 227 \\
Metrology and Standardization to Assist Industrializing
Economies / 230 \\
Publications Taking Us Toward a Metric America / 234
\\
A New Approach to Manipulator Control: The Cerebellar
Model Articulation Controller / 237 \\
Three Dimensional Metrology / 241 \\
Initial Graphics Exchange Specifications / 246 \\
Data Encryption Standard / 250 \\
OMNIDATA and the Computerization of Scientific Data /
254 \\
FORTRAN Test Programs / 258 \\
Design and Evaluation Criteria for Energy Conservation
in New Buildings / 260 \\
Computer Program for Heating and Cooling Loads in
Buildings / 266 \\
Methods for Testing and Rating the Performance of
Heating and Air Conditioning Systems / 270 \\
System for Fire Safety Evaluation of Health Care
Facilities / 275 \\
Estimation of Rate of Heat Release by Means of Oxygen
Consumption Measurements / 280 \\
Probability-Based Load Criteria for Structural Design /
283 \\
Resistivity--Dopant Density Relationship for
Phosphorus-Doped Silicon / 289 \\
1981--1990 \\
Critical Data for Critical Needs / 291 \\
Materials at Low Temperatures / 294 \\
Optical Fiber Characterization / 297 \\
Quasicrystals / 300 \\
Protein Crystallography by Joint X-Ray and Neutron
Diffraction / 303 \\
Strain Effects in Superconducting Compounds / 306 \\
Dental Research at the National Bureau of Standards /
309 \\
Handbook for Standard Reference Materials Users / 313
\\
A Practical Josephson Voltage Standard at One Volt /
315 \\
Plane-Wave Scattering-Matrix Theory of Antennas and
Antenna--Antenna Interactions / 319 \\
The Automated Manufacturing Research Facility / 322 \\
Submicrometer Linewidth Metrology / 328 \\
Observation of Atoms Laser-Cooled Below the Doppler
Limit / 331 \\
Laser-Excited Hot-Electron Induced Desorption / 334 \\
Measurement of the Universal Gas Constant Using an
Acoustic Resonator / 339 \\
Thermal and Oxidative Degradation of Polymers / 344 \\
HAZARD I: Software for Fire Hazard Assessment / 347 \\
Analysis of the Catastrophic Rupture of a Pressure
Vessel / 350 \\
Curing Those Uncontrollable Fits of Interaction / 353
\\
Baldrige Criteria for Performance Excellence / 357 \\
1991--2000 \\
The Advanced Technology Program / 359 \\
NIST Manufacturing Extension Partnership / 363 \\
Questions and Answers on Quality / 366 \\
Uniformity in Weights and Measures Laws and Regulations
/ 368 \\
Certification of 10 $\mu$m Diameter Polystyrene Spheres
(``Space Beads') / 371 \\
Bose--Einstein Condensation in a Dilute Atomic Vapor /
375 \\
Index / 379",
}
@Proceedings{Anonymous:2003:CRN,
editor = "Anonymous",
booktitle = "5th Conference on Real Numbers and Computers 2003 ---
{RNC5}, Lyon, France, September 2003",
title = "5th Conference on Real Numbers and Computers 2003 ---
{RNC5}, Lyon, France, September 2003",
publisher = "????",
address = "????",
pages = "????",
year = "2003",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Jun 25 14:57:33 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Koelink:2003:OPS,
editor = "Erik Koelink and Walter {Van Assche}",
booktitle = "Orthogonal polynomials and special functions: {Leuven
2002}",
title = "Orthogonal polynomials and special functions: {Leuven
2002}",
volume = "1817",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 249",
year = "2003",
ISBN = "3-540-40375-2",
ISBN-13 = "978-3-540-40375-3",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
LCCN = "33 33-06 33C 68W",
bibdate = "Sat Oct 30 17:00:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.bibsys.no:2100/BIBSYS",
series = "Lecture notes in mathematics",
acknowledgement = ack-nhfb,
subject = "functions, special; orthogonal polynomials",
}
@Book{Berggren:2004:PSB,
editor = "Lennart Berggren and Jonathan Borwein and Peter
Borwein",
booktitle = "Pi: a source book",
title = "Pi: a source book",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Third",
pages = "xx + 797",
year = "2004",
DOI = "https://doi.org/10.1007/978-1-4757-4217-6",
ISBN = "0-387-20571-3",
ISBN-13 = "978-0-387-20571-7",
MRclass = "11-00 (01A05 01A75 11-03)",
MRnumber = "2065455",
MRreviewer = "F. Beukers",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 2003:210.",
tableofcontents = "Preface to the Third Edition / v \\
Preface to the Second Edition / vi \\
Preface / vii \\
Acknowledgments / x \\
Introduction / xvii \\
1. The Rhind Mathematical Papyrus --- Problem 50
($\approx$1650 B.C.) / A problem dealing with the area
of a round field of given diameter / 1 \\
2. Engels / Quadrature of the Circle in Ancient Egypt
(1977) / A conjectural explanation of how the
mathematicians of ancient Egypt approximated the area
of a circle / 3 \\
3. Archimedes / Measurement of a Circle --- (-250 B.C.)
/ The seminal work in which Archimedes presents the
first true algorithm for $ \pi $ / 7 \\
4. Phillips / Archimedes the Numerical --- Analyst
(1981) / A summary of Archimedes' work on the
computation of $ \pi $ using modem notation / 15 \\
5. Lam and Ang / Circle Measurements in Ancient China
(1986) / This paper discusses and contains a
translation of Liu Hui's (3rd century) method for
evaluating $ \pi $ and also examines values for $ \pi $
given by Zu Chongzhi (429--500) / 20 \\
6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
and Solid Figures (--850) / This extract gives an
explicit statement and proof that the ratio of the
circumference to the diameter is constant / 36 \\
7. M{\=a}dhava / The Power Series for Arctan and Pi
(-1400) / These theorems by a fifteenth century Indian
mathematician give Gregory's series for arctan with
remainder terms and Leibniz's series for $ \pi $ / 45
\\
8. Hope-Jones / Ludolph (or Ludolff or Lucius) van
Ceulen (1938) / Correspondence about van Ceulen's
tombstone in reference to it containing some digits of
$ \pi $ / 51 \\
9. Vi{\`e}te / \booktitle{Variorum de Rebus
Mathematicis Reponsorum Liber VII} (1593) / Two
excerpts. One containing the first infinite expression
of $ \pi $, obtained by relating the area of a regular
$2n$-gon to that of a regular $n$-gon / 53 \\
10. Wallis. Computation of $ \pi $ by Successive
Interpolations (1655) / How Wallis derived the infinite
product for $ \pi $ that bears his name / 68 \\
11. Wallis / \booktitle{Arithmetica Infinitorum} (1655)
/ An excerpt including Prop. 189, 191 and an alternate
form of the result that gives Wm. Brounker's continued
fraction expression for $ 4 / \pi$ / ?? \\
12. Huygens / \booktitle{De Circuli Magnitudine
Inventa} (1654) / Huygens's demonstration of how to
triple the number of correct decimals over those in
Archimedes' estimate of $ \pi $ / 81 13. Gregory /
Correspondence with John Collins (1671) / A letter to
Collins in which he gives his series for arctangent,
carried to the ninth power / 87 \\
14. Roy / The Discovery of the Series Formula for $ \pi
$ by Leibniz, Gregory, and Nilakantha (1990) / A
discussion of the discovery of the series $ \pi / 4 = 1
- 1/3 + 1/5 - \cdots{} $ / 92 \\
15. Jones / The First Use of $ \pi $ for the Circle
Ratio (1706) / An excerpt from Jones' book, the
\booktitle{Synopsis Palmariorum Matheseos: or, a New
Introduction to the Mathematics}, London, 1706 / 108
\\
16. Newton / Of the Method of Fluxions and Infinite
Series (1737) / An excerpt giving Newton's calculation
of $ \pi $ to 16 decimal places / 110 \\
17. Euler / Chapter 10 of \booktitle{Introduction to
Analysis of the Infinite (On the Use of the Discovered
Fractions to Sum Infinite Series)} (1748) / This
includes many of Euler's infinite series for $ \pi $
and powers of $ \pi $ / 112 \\
18. Lambert / \booktitle{M{\'e}moire Sur Quelques
Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
Transcendentes Circulaires et Logarithmiques} (1761) /
An excerpt from Lambert's original proof of the
irrationality of $ \pi $ / 129 19. Lambert /
Irrationality of $ \pi $ (1969) / A translation and
Struik's discussion of Lambert's proof of the
irrationality of $ \pi $ / 141 \\
20. Shanks / Contributions to Mathematics Comprising
Chiefly of the Rectification of the Circle to 607
Places of Decimals (1853) / Pages from Shanks's report
of his monumental hand calculation of $ \pi $ / 147 \\
21. Hermite / \booktitle{Sur La Fonction Exponentielle}
(1873) / The first proof of the transcendence of $ e $
/ 162 \\
22. Lindemann / \booktitle{Ueber die Zahl $ \pi $}
(1882) / The first proof of the transcendence of $ \pi
$ / 194 23. Weierstrass / \booktitle{Zu Lindemann's
Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) /
Weierstrass' proof of the transcendence of $ \pi $ /
207 24. Hilbert / \booktitle{Ueber die Transzendenz der
Zahlen $ e $ und $ \pi $} (1893) / Hilbert's short and
elegant simplification of the transcendence proofs for
$ e $ and $ \pi $ / 226 25. Goodwin / Quadrature of the
Circle (1894) / The dubious origin of the attempted
legislation of the value of $ \pi $ in Indiana / 230
\\
26. Edington / House Bill No. 246, Indiana State
Legislature, 1897 (1935) / A summary of the action
taken by the Indiana State Legislature to fix the value
of $ \pi $ (including a copy of the actual bill that
was proposed) / 231 \\
27. Singmaster / The Legal Values of Pi (1985) / A
history of the attempt by Indiana to legislate the
value of $ \pi $ / 236 \\
28. Ramanujan / Squaring the Circle (1913) / A
geometric approximation to $ \pi $ / 240 \\
29. Ramanujan / Modular Equations and Approximations to
$ \pi $ (1914) / Ramanujan's seminal paper on pi that
includes a number of striking series and algebraic
approximations / 241 \\
30. Watson / The Marquis and the Land Agent: A Tale of
the Eighteenth Century (1933) / A Presidential address
to the Mathematical Association in which the author
gives an account of ``some of the elementary work on
arcs and ellipses and other curves which led up to the
idea of inverting an elliptic integral, and so laying
the foundations of elliptic functions and doubly
periodic functions generally.'' / ?? \\
31. Ballantine / The Best (?) Formula for Computing $
\pi $ to a Thousand Places (1939) / An early attempt to
orchestrate the calculation of $ \pi $ more cleverly /
271 \\
32. Birch / An Algorithm for Construction of Arctangent
Relations (1946) / The object of this note is to
express $ \pi / 4$ as a sum of arctan relations in
powers of 10 / 274 \\
33. Niven / A Simple Proof that $ \pi $ is Irrational
(1947) / A very concise proof of the irrationality of $
\pi $ / 276 \\
34. Reitwiesner / An ENIAC Determination of $ \pi $ and
$ e $ to 2000 Decimal Places (1950) / One of the first
computer-based computations / 277 \\
35. Schepler / The Chronology of Pi (1950) / A fairly
reliable outline of the history of $ \pi $ from 3000
B.C. to 1949 / 282 \\
36. Mahler / On the Approximation of $ \pi $ (1953) /
``The aim of this paper is to determine an explicit
lower bound free of unknown constants for the distance
of $ \pi $ from a given rational or algebraic number.''
/ 306 \\
37. Wrench, Jr. / The Evolution of Extended Decimal
Approximations to $ \pi $ (1960) / A history of the
calculation of the digits of $ \pi $ to 1960 / 319 \\
38. Shanks and Wrench, Jr. / Calculation of $ \pi $ to
100,000 Decimals (1962) / A landmark computation of $
\pi $ to more than 100,000 places / 326 39. Sweeny / On
the Computation of Euler's Constant (1963) / The
computation of Euler's constant to 3566 decimal places
/ 350 40. Baker / Approximations to the Logarithms of
Certain Rational Numbers (1964) / The main purpose of
this deep and fundamental paper is to ``deduce results
concerning the accuracy with which the natural
logarithms of certain rational numbers may be
approximated by rational numbers, or, more generally,
by algebraic numbers of bounded degree.'' / 359 \\
41. Adams / Asymptotic Diophantine Approximations to e
(1966) / An asymptotic estimate for the rational
approximation to $ e $ which disproves the conjecture
that $ e $ behaves like almost all numbers in this
respect / 368 \\
42. Mahler / Applications of Some Formulae by Hermite
to the Approximations of Exponentials of Logarithms
(1967) / An important extension of Hilbert's approach
to the study of transcendence / 372 43. Eves / In
Mathematical Circles; A Selection of Mathematical
Stories and Anecdotes (excerpt) (1969) / A collection
of mathematical stories and anecdotes about $ \pi $ /
456 \\
44. Eves / Mathematical Circles Revisited; A Second
Collection of Mathematical Stories and Anecdotes
(excerpt) (1971) / A further collection of mathematical
stories and anecdotes about $ \pi $ / 402 45. Todd /
The Lemniscate Constants (1975) / A unifying account of
some of the methods used for computing the lemniscate
constants / 412 \\
46. Salamin / Computation of $ \pi $ Using
Arithmetic--Geometric Mean (1976) / The first
quadratically converging algorithm for $ \pi $ based on
Gauss's AGM and on Legendre's relation for elliptic
integrals / 418 \\
47. Brent / Fast Multiple-Precision Evaluation of
Elementary Functions (1976) / ``This paper contains the
`Gauss--Legendre' method and some different algorithms
for $\log$ and $\exp$ (using Landen transformations).''
/ 424 \\
48. Beukers / A Note on the Irrationality of $ \zeta(2)
$ and $ \zeta(3) $ (1979) / A short and elegant
recasting of Apery's proof of the irrationality of
$\zeta(3)$ (and $\zeta(2)$) / 434 \\
49. van der Poorten / A Proof that Euler Missed
\ldots{} Apery's Proof of the Irrationality of $\zeta
(3)$ (1979) / An illuminating account of Apery's
astonishing proof of the irrationality of $\zeta (3)$ /
439 \\
50. Brent and McMillan / Some New Algorithms for
High-Precision Computation of Euler's Constant (1980) /
Several new algorithms for high-precision calculation
of Euler's constant, including one which was used to
compute 30,100 decimal places / 448 \\
51. Apostol / A Proof that Euler Missed: Evaluating
$\zeta(2)$ the Easy Way (1983) / This note shows that
one of the double integrals considered by Beukers ([48]
in the table of contents) can be used to establish
directly that $\zeta(2) = \pi^2 / 6$ / 456 \\
52. O'Shaughnessy / Putting God Back in Math (1983) /
An article about the Institute of Pi Research, an
organization that ``pokes fun at creationists by
pointing out that even the Bible makes mistakes.'' /
458 \\
53. Stern / A Remarkable Approximation to $ \pi $
(1985) / Justification of the value of $ \pi $ in the
Bible through numerological interpretations / 460 \\
54. Newman and Shanks / On a Sequence Arising in Series
for $ \pi $ (1984) / More connections between $ \pi $
and modular equations / 462 \\
55. Cox / The Arithmetic--Geometric Mean of Gauss
(1984) / An extensive study of the complex analytic
properties of the AGM / 481 \\
56. Borwein and Borwein / The Arithmetic--Geometric
Mean and Fast Computation of Elementary Functions
(1984) / The relationship between the AGM iteration and
fast computation of elementary functions (one of the
by-products is an algorithm for $ \pi $) / 537 57.
Newman / A Simplified Version of the Fast Algorithms of
Brent and Salamin (1984) / Elementary algorithms for
evaluating $ e^x $ and $ \pi $ using the Gauss AGM
without explicit elliptic function theory / 553 \\
58. Wagon / Is Pi Normal? (1985) / A discussion of the
conjecture that $ \pi $ has randomly distributed digits
/ 557 \\
59. Keith / Circle Digits: A Self-Referential Story
(1986) / A mnemonic for the first 402 decimal places of
$ \pi $ / 560 \\
60. Bailey / The Computation of $ \pi $ to 29,360,000
Decimal Digits Using Borwein's Quartically Convergent
Algorithm (1988) / The algorithms used, both for $ \pi
$ and for performing the required multiple-precision
arithmetic / 562 \\
61. Kanada / Vectorization of Multiple-Precision
Arithmetic Program and 201,326,000 Decimal Digits of $
\pi $ Calculation (1988) / Details of the computation
and statistical tests of the first 200 million digits
of $ \pi $ / 576 \\
62. Borwein and Borwein / Ramanujan and Pi (1988) /
This article documents Ramanujan's life, his ingenious
approach to calculating $ \pi $, and how his approach
is now incorporated into modern computer algorithms /
588 \\
63. Chudnovsky and Chudnovsky / Approximations and
Complex Multiplication According to Ramanujan (1988) /
This excerpt describes ``Ramanujan's original quadratic
period--quasiperiod relations for elliptic curves with
complex multiplication and their applications to
representations of fractions of $ \pi $ and other
logarithms in terms of rapidly convergent nearly
integral (hypergeometric) series.'' / 596 \\
64. Borwein, Borwein and Bailey / Ramanujan, Modular
Equations, and Approximations to Pi or How to Compute
One Billion Digits of Pi (1989) / An exposition of the
computation of $ \pi $ using mathematics rooted in
Ramanujan's work / 623 \\
65. Borwein, Borwein and Dilcher / Pi, Euler Numbers,
and Asymptotic Expansions (1989) / An explanation as to
why the slowly convergent Gregory series for $ \pi $,
truncated at 500,000 terms, gives $ \pi $ to 40 places
with only the 6th, 17th, 18th, and 29th places being
incorrect / 642 \\
66. Beukers, Bezivin, and Robba / An Alternative Proof
of the Lindemann--Weierstrass Theorem (1990) / The
Lindemann--Weierstrass theorem as a by-product of a
criterion for rationality of solutions of differential
equations / 649 \\
67. Webster / The Tale of Pi (1991) / Various anecdotes
about $ \pi $ from the 14th annual IMO Lecture to the
Royal Society / 654 \\
68. Eco / An excerpt from Foucault's Pendulum (1993) /
``The unnumbered perfection of the circle itself.'' /
658 \\
69. Keith / Pi Mnemonics and the Art of Constrained
Writing (1996) / A mnemonic for $ \pi $ based on Edgar
Allen Poe's poem ``The Raven.'' / 659 \\
70. Bailey, Borwein, and Plouffe / On the Rapid
Computation of Various Polylogarithmic Constants (1997)
/ A fast method for computing individual digits of $
\pi $ in base 2 / 663 \\
Appendix I --- On the Early History of Pi / 677 \\
Appendix II --- A Computational Chronology of Pi / 683
\\
Appendix III --- Selected Formulae for Pi / 686 \\
Appendix IV --- Translations of Viele and Huygens / 690
\\
Bibliography / 710 \\
Credits / 717 \\
A Pamphlet on Pi / 721 \\
Contents / 723 \\
1. Pi and Its Friends / 725 \\
2. Normality of Numbers / 741 \\
3. Historia Cyclometrica / 753 \\
4. Demotica Cyclometrica / 771 \\
References / 779 \\
Index / 783",
}
@Proceedings{Frougny:2004:RCR,
editor = "Christiane Frougny and Vasco Brattka and Norbert
M{\"u}ller",
booktitle = "{RNC'6, 6th Conference on Real Numbers and Computers:
Nov 15--17, 2004, Dagstuhl, Germany}",
title = "{RNC'6, 6th Conference on Real Numbers and Computers:
Nov 15--17, 2004, Dagstuhl, Germany}",
publisher = "Universita{\"a}t Trier, Fachbereich IV, Mathematik,
Informatik",
address = "Trier, Germany",
bookpages = "216 + i",
pages = "216 + i",
year = "2004",
ISSN = "0944-0488",
ISSN-L = "0944-0488",
bibdate = "Thu Apr 28 05:55:01 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Forschungsbericht Nr. 04-8.",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004;
http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6-complete.pdf",
acknowledgement = ack-nhfb,
keywords = "base conversion; decimal floating-point arithmetic",
tableofcontents = "Introduction / Christiane Frougny / 1--4 \\
Invited Lecture: New ideas and results for solving
Differential equations symbolically [abstract only] /
Benno Fuchssteiner / 5--5 \\
Invited Lecture: A survey of Integer Relations
algorithms and rational numbers [abstract only] / Simon
Plouffe / 6--6 \\
Invited Lecture: Real Numbers and Robustness in
Computational Geometry / Stefan Schirra / 7--21 \\
Bridging the gap between formal specification and
bit-level floating-point arithmetic / Sylvie Boldo /
22--36 \\
Automata, Borel functions and real numbers in Pisot
base / B. Cagnard, P. Simonnet / 37--54 \\
Generating formally certified bounds on values and
round-off errors / Marc Daumas, Guillaume Melquiond /
55--70 \\
A proven correctly rounded logarithm in
double-precision / Florent de Dinechin, Catherine
Loirat, Jean-Michel Muller / 71--85 \\
A comparison of polynomial evaluation schemes / L.
Fousse, S. Schmitt / 86--102 \\
A comparison of real and complex pseudozero sets for
polynomials with real coefficients / Stef Graillat,
Philippe Langlois / 103--112 \\
On Intermediate Precision Required for
Correctly-Rounding Decimal-to-Binary Floating-Point
Conversion / Michel Hack / 113--134 \\
The Generic Multiple-Precision Floating-Point Addition
With Exact Rounding (as in the MPFR Library) / Vincent
Lef{\`e}vre / 135--145 \\
Software Division and Square Root Using Goldschmidt's
Algorithms / Peter Markstein / 146--157 \\
A Fast Algorithm for Julia Sets of Hyperbolic Rational
Functions / R. Rettinger / 158--171 \\
An extension of Chaitin's halting probability $\Omega$
to measurement operator in infinite dimensional quantum
system / Kohtaro Tadaki / 172--191 \\
On the Hierarchy of $\Delta_2^0$-Real Numbers / Xizhong
Zheng / 192--215 \\
Trierer Forschungsberichte Mathematik / Informatik [one
page list of reports] / 1--1 (216--216)",
}
@Proceedings{Wahdan:2004:IHE,
editor = "Abdel-Moniem Wahdan",
booktitle = "{ICEEC'04: 2004 International Conference on
Electrical, Electronic and Computer Engineering:
proceedings: 5--7 September, 2004, Cairo, Egypt}",
title = "{ICEEC'04: 2004 International Conference on
Electrical, Electronic and Computer Engineering:
proceedings: 5--7 September, 2004, Cairo, Egypt}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xlv + 954",
year = "2004",
ISBN = "0-7803-8575-6",
ISBN-13 = "978-0-7803-8575-7",
LCCN = "TK7801 .I5125 2004",
bibdate = "Tue Jul 19 08:01:02 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
note = "IEEE catalog number 04EX893.",
acknowledgement = ack-nhfb,
subject = "Electric engineering; Congresses; Electronics;
Congresses; Computer engineering; Congresses",
}
@Proceedings{IEEE:2005:PIS,
editor = "{IEEE}",
booktitle = "{Proceedings of the 17th IEEE Symposium on Computer
Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
Massachusetts, USA}",
title = "{Proceedings of the 17th IEEE Symposium on Computer
Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
Massachusetts, USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2005",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Jun 21 19:02:16 2005",
bibsource = "http://arith17.polito.it/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
xxnote = "Not yet published: check editor??",
}
@Book{Ismail:2005:TAS,
editor = "Mourad E. H. Ismail and Erik Koelink",
booktitle = "Theory and Applications of Special Functions: a Volume
Dedicated to {Mizan Rahman}",
title = "Theory and Applications of Special Functions: a Volume
Dedicated to {Mizan Rahman}",
volume = "13",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 491",
year = "2005",
ISBN = "0-387-24231-7 (hardcover), 0-387-24233-3 (e-book)",
ISBN-13 = "978-0-387-24231-6 (hardcover),
978-0-387-24233-0(e-book)",
LCCN = "QA351 .T44 2005",
bibdate = "Sat Oct 30 07:35:31 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Developments in mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0663/2005275626-d.html;
http://www.loc.gov/catdir/toc/fy0605/2005275626.html",
abstract = "This book, dedicated to Mizan Rahman, is made up of a
collection of articles on various aspects of q-series
and special functions. It also includes an article by
Askey, Ismail, and Koelink on Rahman's mathematical
contributions and how they influenced the recent
upsurge in the subject. Theory and Applications of
Special Functions is intended for researchers and
graduate students in special functions, algebraic
combinatorics, quantum groups, and integrable
systems.",
acknowledgement = ack-nhfb,
subject = "Mathematics; Special Functions; Functions, special;
Integral Transforms; Approximations and Expansions;
Integral Transforms, Operational Calculus",
tableofcontents = "Mizan Rahman, his mathematics and literary writings
/ Richard Askey, Mourad E. H. Ismail and Erik Koelink
\\
On the completeness of sets of $q$-Bessel function
$J\nu^{(3)}(x; q)$ / L. D. Abreu and J. Bustoz \\
$\alpha$-Gaussian polynomials and finite
Rogers-Ramanujan identities / George E. Andrews \\
On a generalized gamma convolution related to the
$q$-calculus / Christian Berg \\
Ramanujan and cranks / Bruce C. Berndt, Heng Huat Chan,
Song Heng Chan and Wen-Chin Liaw \\
Saalschutz chain reactions and multiple $q$-series
transformations / Chu Wenchang \\
Painleve equations and associated polynomials / Peter
A. Clarkson \\
Zeta functions of Heisenberg graphs over finite rings /
Michelle DeDeo, Maria Martinez, Archie Medrano, Marvin
Minei, Harold Stark and Audrey Terras \\
$q$-Analogues of some multivariable biorthogonal
polynomials / George Gasper and Mizan Rahman \\
^?? : Some systems of multivariable orthogonal
Askey-Wilson polynomials / George Gasper and Mizan
Rahman \\
Continuous Hahn functions as Clebsch--Gordan
coefficients / Wolter Groenevelt, Erik Koelink and
Hjalmar Rosengren \\
New proofs of some $q$-series results / Mourad E. H.
Ismail and Ruiming Zhang \\
Little $q$-Jacobi functions of complex order / Kevin W.
J. Kadell \\
Second addition formula for continuous
$q$-ultraspherical polynomials / Tom H. Koornwinder \\
Bilateral series involving basic hypergeometric
functions / Hjalmar Rosengren \\
Hilbert space asymptotics of a class of orthonormal
polynomials on a bounded interval / S. N. M.
Ruijsenaars \\
Abel--Rothe type generalizations of Jacobi's triple
product identity / Michael Schlosser \\
Summable sums of hypergeometric series / D. Stanton \\
Askey--Wilson functions and quantum groups / Jasper V.
Stokman \\
Analog of the Cauchy--Hadamard formula for expansions
in $q$-polynomials /Remarks on some basic
hypergeometric series / Changgui Zhang",
}
@Proceedings{Vassiliadis:2005:IIC,
editor = "Stamatis Vassiliadis and Nikitas J. Dimopoulos and
Sanjay Vishnu Rajopadhye",
booktitle = "{16th IEEE International Conference on
Application-Specific Systems, Architectures, and
Processors: ASAP 2005: 23--25 July 2005, Samos,
Greece}",
title = "{16th IEEE International Conference on
Application-Specific Systems, Architectures, and
Processors: ASAP 2005: 23--25 July 2005, Samos,
Greece}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 419",
year = "2005",
ISBN = "0-7695-2407-9",
ISBN-13 = "978-0-7695-2407-8",
LCCN = "TK7874.6 .I58 2005",
bibdate = "Sun Mar 4 21:53:56 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Application-Specific
Systems, Architectures, and Processors (16th: 2005:
Samos, Greece)",
subject = "Array processors; Congresses; Signal processing;
Digital techniques; Application specific integrated
circuits",
}
@Proceedings{zuCastell:2005:ILO,
editor = "Wolfgang zu Castell and Frank Filbir and Brigitte
Forster",
booktitle = "{Inzell lectures on orthogonal polynomials}",
title = "{Inzell lectures on orthogonal polynomials}",
publisher = "Nova Science",
address = "Hauppauge, NY, USA",
pages = "x + 199",
year = "2005",
ISBN = "1-59454-108-6",
ISBN-13 = "978-1-59454-108-7",
LCCN = "QA404.5 .I595 2005",
bibdate = "Sat Oct 30 17:16:08 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
prodorbis.library.yale.edu:7090/voyager",
note = "Lectures from the Inzell Summer School on Orthogonal
Polynomials, Harmonic Analysis, Approximation, and
Applications, held in Inzell, Germany, September
17--21, 2001.",
series = "Advances in the theory of special functions and
orthogonal polynomials",
acknowledgement = ack-nhfb,
remark = "Canonical moments, orthogonal polynomials with
applications to statistics / Holger Dette \\
Discrete commutative hypergroups / Rupert Lasser \\
Orthogonal polynomials and Banach algebras / Ryszard
Szwarc \\
Lecture notes on orthogonal polynomials of several
variables / Yuan Xu",
subject = "Orthogonal polynomials",
}
@Proceedings{Anonymous:2006:PCR,
editor = "Anonymous",
booktitle = "{Proceedings of the 7th Conference on Real Numbers and
Computers (RNC 7) LORIA, Nancy, France, July 10--12,
2006}",
title = "{Proceedings of the 7th Conference on Real Numbers and
Computers (RNC 7) LORIA, Nancy, France, July 10--12,
2006}",
publisher = "????",
address = "????",
pages = "????",
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Jun 27 10:26:43 2006",
bibsource = "http://rnc7.loria.fr/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Menezes:2006:PAS,
editor = "Ronaldo Menezes",
booktitle = "{Proceedings of the 44th annual Southeast Regional
Conference 2006: Melbourne, Florida, March 10--12,
2006}",
title = "{Proceedings of the 44th annual Southeast Regional
Conference 2006: Melbourne, Florida, March 10--12,
2006}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "823",
year = "2006",
ISBN = "1-59593-315-8 (print)",
ISBN-13 = "978-1-59593-315-7 (print)",
LCCN = "QA75.5 A184 2006 E",
bibdate = "Sat Oct 9 15:04:24 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "Computer-assisted instruction; Congresses; Database
management; Electronic data processing",
}
@Proceedings{Brown:2007:PIS,
editor = "C. W. Brown",
booktitle = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
title = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2007",
ISBN = "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
ISBN-13 = "978-1-59593-743-8 (print), 978-1-59593-742-1
(CD-ROM)",
LCCN = "QA76.5 S98 2007",
bibdate = "Fri Jun 20 08:53:37 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
note = "ACM order number 505070.",
acknowledgement = ack-nhfb,
}
@Proceedings{Holzapfel:2007:AGA,
editor = "Rolf-Peter Holzapfel and A. Muhammed Uludag and
Masaaki Yoshida",
booktitle = "{Arithmetic and geometry around hypergeometric
functions: lecture notes of a CIMPA Summer School held
at Galatasaray University, Istanbul, Turkey, June
13--25, 2005}",
title = "{Arithmetic and geometry around hypergeometric
functions: lecture notes of a CIMPA Summer School held
at Galatasaray University, Istanbul, Turkey, June
13--25, 2005}",
volume = "235",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "viii + 437",
year = "2007",
ISBN = "3-7643-8283-X",
ISBN-13 = "978-3-7643-8283-4",
LCCN = "QA245 .S86 2005",
bibdate = "Sat Oct 30 21:12:24 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Progress in mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0913/2006939568-d.html;
http://www.loc.gov/catdir/enhancements/fy0913/2006939568-t.html",
acknowledgement = ack-nhfb,
subject = "Algebra; Congresses.; Geometry, Algebraic; Congresses;
Number theory",
}
@Proceedings{Iske:2007:AAP,
editor = "Armin Iske and Jeremy Levesley",
booktitle = "{Algorithms for Approximation: Proceedings of the 5th
International Conference, Chester, July 2005}",
title = "{Algorithms for Approximation: Proceedings of the 5th
International Conference, Chester, July 2005}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "300",
year = "2007",
DOI = "https://doi.org/10.1007/978-3-540-46551-5",
ISBN = "3-540-46551-0, 3-540-33283-9",
ISBN-13 = "978-3-540-46551-5, 978-3-540-33283-1",
LCCN = "QA221 .A44 2007",
bibdate = "Thu Dec 1 09:41:19 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.bibsys.no:2100/BIBSYS",
acknowledgement = ack-nhfb,
subject = "Mathematics; Special Functions; Functions, special;
Engineering mathematics; Mathematics of Computing;
Approximations and Expansions; Computer science;
Computational Mathematics and Numerical Analysis; Appl.
Mathematics / Computational Methods of Engineering",
}
@Proceedings{Kornerup:2007:PIS,
editor = "Peter Kornerup and Jean-Michel Muller",
booktitle = "{Proceedings of the 18th IEEE Symposium on Computer
Arithmetic, June 25--27, 2007, Montpellier, France}",
title = "{Proceedings of the 18th IEEE Symposium on Computer
Arithmetic, June 25--27, 2007, Montpellier, France}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 269",
year = "2007",
ISBN = "0-7695-2854-6",
ISBN-13 = "978-0-7695-2854-0",
ISSN = "1063-6889",
LCCN = "QA76.9.C62",
bibdate = "Tue Jun 27 10:26:43 2006",
bibsource = "http://www.lirmm.fr/arith18/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
odin2.bib.sdu.dk:210/Horizon",
URL = "http://www.lirmm.fr/arith18/",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Book{Cerone:2008:AIS,
editor = "Pietro Cerone and Sever Silvestru Dragomir",
booktitle = "Advances in Inequalities for Special Functions",
title = "Advances in Inequalities for Special Functions",
publisher = "Nova Science Publishers",
address = "New York, NY, USA",
pages = "170",
year = "2008",
ISBN = "1-60021-919-5 (hardcover), 1-60692-621-7 (e-book)",
ISBN-13 = "978-1-60021-919-1 (hardcover), 978-1-60692-621-5
(e-book)",
LCCN = "QA351 .A375 2008",
bibdate = "Fri Oct 18 16:18:25 MDT 2024",
bibsource = "fsz3950.oclc.org:210/WorldCat",
series = "Advances in mathematical inequalities",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/159822357.html",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Inequalities (Mathematics);
Fonctions sp{\'e}ciales; In{\'e}galit{\'e}s
(Math{\'e}matiques); MATHEMATICS; Calculus;
Mathematical Analysis; Functions, Special;
Inequalities (Mathematics)",
tableofcontents = "Special functions approximations and bounds via
integral representation / P. Cerone / 1 \\
Inequalities for positive Dirichlet series / P. Cerone
and S. S. Dragomir / 37 \\
Monotonicity of the mean value function of normalized
Bessel functions of first kind / Stamatis Koumandos /
67 \\
Sturm theory for some classes of Sturm--Liouville
equations and inequalities and monotonicity properties
for the zeros of Bessel functions / Andrea Laforgia and
Pierpaolo Natalini / 73 \\
Inequalities for the Gamma function via convexity /
Milan Merkle / 81 \\
Some inequalities for hyperharmonic series / Istv{\'a}n
Mez{\H{o}} / 101 \\
The Hermite--Hadamard inequalities for double Dirichlet
averages and their applications to special functions /
Edward Neuman / 107 \\
On new inequalities involving convex functions / B. G.
Pachpatte / 119 \\
On growth rates of Weierstrass $\wp'(z)$ and $\wp(z)$ /
Tibor K. Pog{\'a}ny / 125 \\
On certain special functions of number theory and
mathematical analysis / J{\'o}zsef S{\'a}ndor / 133 \\
On the operator $\oplus^k_B$ related to the Bessel-wave
equation and Laplacian--Bessel / Mehmet Zeki Sarikaya
and H{\"u}seyin Yildirim / 149 \\
Inequalities for Walsh polynomials with semi-monotone
coefficients of higher order / {\v{Z}}ivorad Tomovski /
161 \\
Index / 169",
}
@Proceedings{Dominici:2008:SFO,
editor = "Diego Dominici and Robert S. Maier",
booktitle = "{Special functions and orthogonal polynomials: AMS
Special Session on Special Functions and Orthogonal
Polynomials, April 21--22, 2007, Tucson, Arizona}",
title = "{Special functions and orthogonal polynomials: AMS
Special Session on Special Functions and Orthogonal
Polynomials, April 21--22, 2007, Tucson, Arizona}",
volume = "471",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "v + 218",
year = "2008",
ISBN = "0-8218-4650-7",
ISBN-13 = "978-0-8218-4650-6",
LCCN = "????",
bibdate = "Sat Oct 30 17:30:10 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.bibsys.no:2100/BIBSYS",
series = "Contemporary mathematics",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2008:ICA,
editor = "{IEEE}",
booktitle = "{2008 International Conference on Application-Specific
Systems, Architectures and Processors: Leuven, Belgium,
2--4 July 2008}",
title = "{2008 International Conference on Application-Specific
Systems, Architectures and Processors: Leuven, Belgium,
2--4 July 2008}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 309 + 12",
year = "2008",
ISBN = "1-4244-1897-6 (paperback), 1-4244-1898-4",
ISBN-13 = "978-1-4244-1897-8 (paperback), 978-1-4244-1898-5",
LCCN = "????",
bibdate = "Mon Feb 10 07:31:38 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "IEEE catalog number CFP08063-PRT.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4569858;
http://www.gbv.de/dms/tib-ub-hannover/631855815.pdf",
acknowledgement = ack-nhfb,
remark = "Kongress auch zitiert als: ASAP 08. Parallel als
Online-Ausg. erschienen. ASAP 08.",
tableofcontents = "ASAP08 Conference proceedings / c1--c1 / doi:
10.1109/ASAP.2008.4580199 \\
ASAP08 Conference proceedings / c2--c2 / doi:
10.1109/ASAP.2008.4580200 \\
Frontmatter and table of contents / c1--xiii / doi:
10.1109/ASAP.2008.4580202 \\
ASAP Organizing and Steering Committees / ix \\
ASAP Technical Technical Program Committee / x \\
Keynote 1: Security and Opportunities for
Application-Specific Processors / Ruby B. Lee / xii \\
Keynote 2: Art of of Application-Specific Processor
Design: Great Artists use Good Tools / Gert Goossens /
xiv \\
Session 1: Application-Specific Processor Instruction
Sets / 1 \\
Copyright notice / i--i / doi:
10.1109/ASAP.2008.4580197 \\
Copyright notice / ii--ii / doi:
10.1109/ASAP.2008.4580198 \\
K. Atasu, O. Mencer, W. Luk, C. Ozturan and G. Dundar /
Fast custom instruction identification by convex
subgraph enumeration / 1--6 / doi:
10.1109/ASAP.2008.4580145 \\
Y. Hilewitz, C. Lauradoux and R. B. Lee / Bit matrix
multiplication in commodity processors / 7--12 / doi:
10.1109/ASAP.2008.4580146 \\
M. Alle et al. / Synthesis of application accelerators
on Runtime Reconfigurable Hardware / 13--18 / doi:
10.1109/ASAP.2008.4580147 \\
A. Amaricai, M. Vladutiu, M. Udrescu, L. Prodan and O.
Boncalo / Floating point multiplication rounding
schemes for interval arithmetic / 19--24 / doi:
10.1109/ASAP.2008.4580148 \\
S. Balasubramanian, H. W. Carter, A. Bogdanov, A. Rupp
and Jintai Ding / Fast multivariate signature
generation in hardware: The case of rainbow / 25--30 /
doi: 10.1109/ASAP.2008.4580149 \\
M. Hosseinabady and J. Nunez-Yanez / Fault-tolerant
dynamically reconfigurable NoC-based SoC / 31--36 /
doi: 10.1109/ASAP.2008.4580150 \\
T. Lorunser et al. / Security Processor with Quantum
Key Distribution / 37--42 / doi:
10.1109/ASAP.2008.4580151 \\
P. K. Meher and J. C. Patra / Fully-pipelined efficient
architectures for FPGA realization of discrete Hadamard
transform / 43--48 / doi: 10.1109/ASAP.2008.4580152 \\
R. Rajore, G. Garga, H. S. Jamadagni and S. K. Nandy /
Reconfigurable Viterbi decoder on mesh connected
multiprocessor architecture / 49--54 / doi:
10.1109/ASAP.2008.4580153 \\
T. Ramdas, G. K. Egan, D. Abramson and K. K. Baldridge
/ Run-time thread sorting to expose data-level
parallelism / 55--60 / doi: 10.1109/ASAP.2008.4580154
\\
S. Jovanovic, C. Tanougast and S. Weber / A New
High-Performance Scalable Dynamic Interconnection for
FPGA-based Reconfigurable Systems / 61--66 / doi:
10.1109/ASAP.2008.4580155 \\
D. Dickin and L. Shannon / Extending the SIMPPL SoC
architectural framework to support application-specific
architectures on multi-FPGA platforms / 67--72 / doi:
10.1109/ASAP.2008.4580156 \\
A. E. Kiasari, S. Hessabi and H. Sarbazi-Azad / PERMAP:
A performance-aware mapping for application-specific
SoCs / 73--78 / doi: 10.1109/ASAP.2008.4580157 \\
A. C. Atici, L. Batina, Junfeng Fan, I. Verbauwhede and
S. Berna Ors Yalcin / Low-cost implementations of NTRU
for pervasive security / 79--84 / doi:
10.1109/ASAP.2008.4580158 \\
M. Knezzevic, K. Sakiyama, Y. K. Lee and I. Verbauwhede
/ On the high-throughput implementation of RIPEMD-160
hash algorithm / 85--90 / doi:
10.1109/ASAP.2008.4580159 \\
Wang Haixin, Bai Guoqiang and Chen Hongyi / Zodiac:
System architecture implementation for a
high-performance Network Security Processor / 91--96 /
doi: 10.1109/ASAP.2008.4580160 \\
P. K. Meher / Efficient systolization of cyclic
convolution for systolic implementation of sinusoidal
transforms / 97--101 / doi: 10.1109/ASAP.2008.4580161
\\
D. B. Thomas and W. Luk / Resource efficient generators
for the floating-point uniform and exponential
distributions / 102--107 / doi:
10.1109/ASAP.2008.4580162 \\
I. L. Dalal, D. Stefan and J. Harwayne-Gidansky / Low
discrepancy sequences for Monte Carlo simulations on
reconfigurable platforms / 108--113 / doi:
10.1109/ASAP.2008.4580163 \\
Y. Vanderperren and W. Dehaene / A subsampling pulsed
UWB demodulator based on a flexible complex SVD /
114--119 / doi: 10.1109/ASAP.2008.4580164 \\
J. Divyasree, H. Rajashekar and K. Varghese /
Dynamically reconfigurable regular expression matching
architecture / 120--125 / doi:
10.1109/ASAP.2008.4580165 \\
J. Khan, S. Niar, A. Menhaj, Y. Elhillali and J. L.
Dekeyser / An MPSoC architecture for the Multiple
Target Tracking application in driver assistant system
/ 126--131 / doi: 10.1109/ASAP.2008.4580166 \\
Wangyuan Zhang and Tao Li / Managing multi-core
soft-error reliability through utility-driven cross
domain optimization / 132--137 / doi:
10.1109/ASAP.2008.4580167 \\
S. Braganza and M. Leeser / An efficient implementation
of a phase unwrapping kernel on reconfigurable hardware
/ 138--143 / doi: 10.1109/ASAP.2008.4580168 \\
H. Flatt, S. Blume, S. Hesselbarth, T. Schunemann and
P. Pirsch / A parallel hardware architecture for
connected component labeling based on fast label
merging / 144--149 / doi: 10.1109/ASAP.2008.4580169 \\
Yuki Kobayashi, M. Jayapala, P. Raghavan, F. Catthoor
and Masaharu Imai / Operation shuffling over cycle
boundaries for low energy L0 clustering / 150--155 /
doi: 10.1109/ASAP.2008.4580170 \\
V. Kundeti, Yunsi Fei and S. Rajasekaran / An efficient
digital circuit for implementing Sequence Alignment
algorithm in an extended processor / 156--161 / doi:
10.1109/ASAP.2008.4580171 \\
B. K. Mohanty and P. K. Meher / Concurrent systolic
architecture for high-throughput implementation of
3-dimensional discrete wavelet transform / 162--166 /
doi: 10.1109/ASAP.2008.4580172 \\
S. Mirzaei, A. Irturk, R. Kastner, B. T. Weals and R.
E. Cagley / Design space exploration of a cooperative
MIMO receiver for reconfigurable architectures /
167--172 / doi: 10.1109/ASAP.2008.4580173 \\
Mao Nakajima and Minoru Watanabe / Dynamic holographic
reconfiguration on a four-context ODRGA / 173--178 /
doi: 10.1109/ASAP.2008.4580174 \\
F. Pardo, P. Lopez and D. Cabello / FPGA-based hardware
accelerator of the heat equation with applications on
infrared thermography / 179--184 / doi:
10.1109/ASAP.2008.4580175 \\
M. Rahmati, M. S. Sadri and M. A. Naeini / FPGA based
singular value decomposition for image processing
applications / 185--190 / doi:
10.1109/ASAP.2008.4580176 \\
A. Jacob, J. Buhler and R. D. Chamberlain /
Accelerating Nussinov RNA secondary structure
prediction with systolic arrays on FPGAs / 191--196 /
doi: 10.1109/ASAP.2008.4580177 \\
J. Lee, L. Shannon, M. J. Yedlin and G. F. Margrave / A
multi-FPGA application-specific architecture for
accelerating a floating point Fourier Integral Operator
/ 197--202 / doi: 10.1109/ASAP.2008.4580178 \\
K. F. C. Yiu, Chun Hok Ho, N. Grbric, Yao Lu, Xiaoxiang
Shi and W. Luk / Reconfigurable acceleration of
microphone array algorithms for speech enhancement /
203--208 / doi: 10.1109/ASAP.2008.4580179 \\
Yang Sun, Yuming Zhu, M. Goel and J. R. Cavallaro /
Configurable and scalable high throughput turbo decoder
architecture for multiple 4G wireless standards /
209--214 / doi: 10.1109/ASAP.2008.4580180 \\
M. B. S. Tavares, S. Kunze, E. Matus and G. P. Fettweis
/ Architecture and VLSI realization of a high-speed
programmable decoder for LDPC convolutional codes /
215--220 / doi: 10.1109/ASAP.2008.4580181 \\
D. Llorente, K. Karras, T. Wild and A. Herkersdorf /
Buffer allocation for advanced packet segmentation in
Network Processors / 221--226 / doi:
10.1109/ASAP.2008.4580182 \\
A. Vazquez and E. Antelo / New insights on Ling adders
/ 227--232 / doi: 10.1109/ASAP.2008.4580183 \\
N. Brisebarre, F. de Dinechin and J. Muller / Integer
and floating-point constant multipliers for FPGAs /
239--244 / doi: 10.1109/ASAP.2008.4580184 \\
N. Brisebarre, S. Chevillard, M. D. Ercegovac, J.
Muller and S. Torres / An efficient method for
evaluating polynomial and rational function
approximations / 233--238 / doi:
10.1109/ASAP.2008.4580185 \\
A. Garcia, M. Berekovic and T. Vander Aa / Mapping of
the AES cryptographic algorithm on a Coarse-Grain
reconfigurable array processor / 245--250 / doi:
10.1109/ASAP.2008.4580186 \\
J. Nimmy et al. / RECONNECT: A NoC for polymorphic
ASICs using a low overhead single cycle router /
251--256 / doi: 10.1109/ASAP.2008.4580187 \\
M. Mbaye, N. Belanger, Y. Savaria and S. Pierre /
Loop-oriented metrics for exploring an
application-specific architecture design-space /
257--262 / doi: 10.1109/ASAP.2008.4580188 \\
S. K. Dash and T. Srikanthan / Rapid estimation of
instruction cache hit rates using loop profiling /
263--268 / doi: 10.1109/ASAP.2008.4580189 \\
Xuan Guan and Yunsi Fei / Reducing power consumption of
embedded processors through register file partitioning
and compiler support / 269--274 / doi:
10.1109/ASAP.2008.4580190 \\
A. Tumeo, M. Monchiero, G. Palermo, F. Ferrandi and D.
Sciuto / Lightweight DMA management mechanisms for
multiprocessors on FPGA / 275--280 / doi:
10.1109/ASAP.2008.4580191 \\
P. de Langen and B. Juurlink / Memory copies in
multi-level memory systems / 281--286 / doi:
10.1109/ASAP.2008.4580192 \\
R. Adrsha, Mythri, S. K. Nandy and R. Narayan /
Architecture of a polymorphic ASIC for interoperability
across multi-mode H.264 decoders / 287--292 / doi:
10.1109/ASAP.2008.4580193 \\
R. R. Osorio and J. D. Bruguera / An FPGA architecture
for CABAC decoding in manycore systems / 293--298 /
doi: 10.1109/ASAP.2008.4580194 \\
A. Guntoro and M. Glesner / Novel approach on
lifting-based DWT and IDWT processor with multi-context
configuration to support different wavelet filters /
299--304 / doi: 10.1109/ASAP.2008.4580195 \\
B. K. Mohanty and P. K. Meher / Throughput-scalable
hybrid-pipeline architecture for multilevel lifting 2-D
DWT of JPEG 2000 coder / 305--309 / doi:
10.1109/ASAP.2008.4580196 \\
Author index / 310--321 / doi:
10.1109/ASAP.2008.4580201",
}
@Proceedings{Bruguera:2009:PIS,
editor = "Javier D. Bruguera and Marius Cornea and Debjit
DasSarma and John Harrison",
booktitle = "{Proceedings of the 19th IEEE Symposium on Computer
Arithmetic, June 8--10, 2009, Portland, Oregon, USA}",
title = "{Proceedings of the 19th IEEE Symposium on Computer
Arithmetic, June 8--10, 2009, Portland, Oregon, USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 235",
year = "2009",
ISBN = "0-7695-3670-0, 1-4244-4329-6",
ISBN-13 = "978-0-7695-3670-5, 978-1-4244-4329-1",
ISSN = "1063-6889",
LCCN = "QA76.6 .S887 2009",
bibdate = "Fri Jun 12 12:24:37 2009",
bibsource = "http://www.ac.usc.es/arith19/;
https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://www.ac.usc.es/arith19/",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
tableofcontents = "Keynote Talk \\
Anton: A Specialized Machine for Millisecond-Scale
Molecular Dynamics Simulations of Proteins / David E.
Shaw / 3 \\
Session 1: Algorithms and Number Systems \\
Efficient Data Structure and Algorithms for Sparse
Integers, Sets and Predicates / Jean E. Vuillemin / 7
\\
A Dual-Purpose Real/Complex Logarithmic Number System
ALU / Mark G. Arnold and Sylvain Collange / 15 \\
Selected RNS Bases for Modular Multiplication / J. C.
Bajard, M. Kaihara, and T. Plantard / 25 \\
Invited Talk \\
A Historical Perspective on Computer Arithmetic /
Stanley Mazor / 35 \\
Session 2: Arithmetic Hardware \\
Higher Radix Squaring Operations Employing
Left-to-Right Dual Recoding / David W. Matula / 39 \\
Advanced Clockgating Schemes for
Fused-Multiply-Add-Type Floating-Point Units / Jochen
Preiss, Maarten Boersma, and Silvia Melitta Mueller /
48 \\
Unified Approach to the Design of Modulo-$(2^n \pm 1)$
Adders Based on Signed-LSB Representation of Residues /
Ghassem Jaberipur and Behrooz Parhami / 57 \\
Session 3: Finite Fields and Cryptography \\
Subquadratic Space Complexity Multiplier for a Class of
Binary Fields Using Toeplitz Matrix Approach / M. A.
Hasan and C. Negre / 67 \\
Hybrid Binary-Ternary Joint Form and Its Application in
Elliptic Curve / Cryptography / Jithra Adikari, Vassil
Dimitrov, and Laurent Imbert / 76 \\
Polynomial Multiplication over Finite Fields Using
Field Extensions and Interpolation / Murat Cenk, Cetin
Kaya Koc, and Ferruh Ozbudak / 84 \\
Session 4: Mathematical Software \\
A New Binary Floating-Point Division Algorithm and Its
Software Implementation on the ST231 Processor /
Claude-Pierre Jeannerod, Herve Knochel, Christophe
Monat, Guillaume Revy, and Gilles Villard / 95 \\
Fast and Accurate Bessel Function Computation / John
Harrison / 104 \\
Implementation Specific Verification of Divide and
Square Root Instructions / Elena Guralnik, Ariel J.
Birnbaum, Anatoly Koyfinan, and Avi Kaplan / 114 \\
Session 5: Decimal Hardware \\
A Decimal Floating-Point Adder with Decoded Operands
and a Decimal Leading-Zero Anticipator / Liang-Kai Wang
and Michael J. Schulte / 125 \\
A High-Performance Significand BCD Adder with IEEE
754-2008 Decimal Rounding / Alvaro Vazquez and Elisardo
Antelo / 135 \\
Fully Redundant Decimal Arithmetic / Saeid Gorgin and
Ghassem Jaberipur / 145 \\
Session 6: Floating-Point Techniques \\
On the Computation of Correctly-Rounded Sums / P.
Kornerup, V. Lefevre, N. Louvet, and J. M. Muller / 155
\\
Multi-operand Floating-Point Addition / Alexandre F.
Tenca / 161 \\
Certified and Fast Computation of Supremum Norms of
Approximation Errors / Sylvain Chevillard, Mioara
Jolde{\c{s}}, and Christoph Lauter / 169 \\
Session 7: Decimal Transcendentals \\
Computation of Decimal Transcendental Functions Using
the CORDIC Algorithm / {\'A}lvaro V{\'a}zquez, Julio
Villalba, and Elisardo Antelo / 179 \\
Decimal Transcendentals via Binary / John Harrison /
187 \\
A 32-bit Decimal Floating-Point Logarithmic Converter /
Dongdong Chen, Yu Zhang, Younhee Choi, Moon Ho Lee, and
Seok-Bum Ko / 195 \\
Special Session on Automated Synthesis of Arithmetic
Operations \\
Datapath Synthesis for Standard-Cell Design / Reto
Zimmermann / 207 \\
Design Space Exploration for Power-Efficient
Mixed-Radix Ling Adders / Chung-Kuan Cheng / 212 \\
Challenges in Automatic Optimization of Arithmetic
Circuits / Ajay K. Verma, Philip Brisk, and Paolo Ienne
/ 213 \\
Panel on Decimal Arithmetic in Industry \\
Energy and Delay Improvement via Decimal Floating Point
Units / Hossam A. H. Fahmy, Ramy Raafat, Amira M.
Abdel-Majeed, Rodina Samy, Torek ElDeeb, and Yasmin
Farouk / 221 \\
IEEE 754-2008 Decimal Floating-Point for Intel
Architecture Processors / Marius Cornea / 225 \\
Special Session on Interval Arithmetic \\
IEEE Interval Standard Working Group --- P1788: Current
Status / William Edmonson and Guillaume Melquiond / 231
\\
Author Index",
}
@Proceedings{Fukuda:2010:MSI,
editor = "Komei Fukuda and Joris van der Hoeven and Michael
Joswig and Nobuki Takayama",
booktitle = "{Mathematical software --- ICMS 2010: third
International Congress on Mathematical Software,
K{\=o}be, Japan, September 13--17, 2010: proceedings}",
title = "{Mathematical software --- ICMS 2010: third
International Congress on Mathematical Software,
K{\=o}be, Japan, September 13--17, 2010: proceedings}",
volume = "6327",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 368",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6",
ISBN = "3-642-15581-2 (paperback), 3-642-15582-0 (e-book)",
ISBN-13 = "978-3-642-15581-9 (paperback), 978-3-642-15582-6
(e-book)",
LCCN = "QA76.95 .I5654 2010",
bibdate = "Sat Aug 9 14:06:27 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNCS,
URL = "http://link.springer.com/book/10.1007/978-3-642-15582-6",
acknowledgement = ack-nhfb,
subject = "Mathematics; Data processing; Congresses; Computer
software",
tableofcontents = "Plenary \\
Computational Discrete Geometry / Thomas C. Hales /
1--3 \\
Exploiting Structured Sparsity in Large Scale
Semidefinite Programming Problems / Masakazu Kojima /
4--9 \\
Reliable and Efficient Geometric Computing / Kurt
Mehlhorn / 10--11 \\
The Sage Project: Unifying Free Mathematical Software
to Create a Viable Alternative to Magma, Maple,
Mathematica and MATLAB / Bur{\c{c}}in Er{\"o}cal,
William Stein / 12--27 \\
Computation of Special Functions (Invited) \\
Sollya: An Environment for the Development of Numerical
Codes / Sylvain Chevillard, Mioara Jolde , Christoph
Lauter / 28--31 \\
Validated Special Functions Software / Annie Cuyt,
Franky Backeljauw, Stefan Becuwe, Joris Van Deun /
32--34 \\
The Dynamic Dictionary of Mathematical Functions (DDMF)
/ Alexandre Benoit, Fr{\'e}d{\'e}ric Chyzak, Alexis
Darrasse, Stefan Gerhold, Marc Mezzarobba, Bruno Salvy
/ 35--41 \\
Reliable Computing with GNU MPFR / Paul Zimmermann /
42--45 \\
Computational Group Theory (Invited) \\
Simplicial Cohomology of Smooth Orbifolds in GAP /
Mohamed Barakat, Simon G{\"o}rtzen / 46--49 \\
Computing Polycyclic Quotients of Finitely
(L-)Presented Groups via Groebner Bases / Bettina Eick,
Max Horn / 50--53 \\
Constructive Membership Testing in Black-Box Classical
Groups / Sophie Ambrose, Scott H. Murray, Cheryl E.
Praeger, Csaba Schneider / 54--57 \\
Computational Group Theory (Contributed) \\
Towards High-Performance Computational Algebra with GAP
/ Reimer Behrends, Alexander Konovalov, Steve Linton,
Frank L{\"u}beck, Max Neunh{\"o}effer / 58--61 \\
An Improvement of a Function Computing Normalizers for
Permutation Groups / Izumi Miyamoto / 62--68 \\
A GAP Package for Computation with Coherent
Configurations / Dmitrii V. Pasechnik, Keshav Kini /
69--72 \\
Computer Algebra (Invited) \\
CoCoALib: A C++ Library for Computations in Commutative
Algebra \ldots{} and Beyond / John Abbott, Anna M.
Bigatti / 73--76 \\
LinBox Founding Scope Allocation, Parallel Building
Blocks, and Separate Compilation / Jean-Guillaume
Dumas, Thierry Gautier, Cl{\'e}ment Pernet, B. David
Saunders / 77--83 \\
FGb: A Library for Computing Gr{\"o}bner Bases /
Jean-Charles Faug{\`e}re / 84--87 \\
Fast Library for Number Theory: An Introduction /
William B. Hart / 88--91 \\
Exact Numeric Computation for Algebraic and Geometric
Computation (Invited) \\
Controlled Perturbation for Certified Geometric
Computing with Fixed-Precision Arithmetic / Dan
Halperin / 92--95 \\
Exact Numeric Computation for Algebraic and Geometric
Computation (Invited) \\
Exact Geometric and Algebraic Computations in CGAL /
Menelaos I. Karavelas / 96--99 \\
On Solving Systems of Bivariate Polynomials / Fabrice
Rouillier / 100--104 \\
Accurate and Reliable Computing in Floating-Point
Arithmetic / Siegfried M. Rump / 105--108 \\
Exact Numeric Computation for Algebraic and Geometric
Computation (Contributed) \\
Deferring Dag Construction by Storing Sums of Floats
Speeds-Up Exact Decision Computations Based on
Expression Dags / Marc M{\"o}rig / 109--120 \\
The Design of Core 2: A Library for Exact Numeric
Computation in Geometry and Algebra / Jihun Yu, Chee
Yap, Zilin Du, Sylvain Pion, Herv{\'e} Br{\"o}nnimann /
121--141 \\
Formal Proof (Invited) \\
Introducing HOL Zero / Mark Adams / 142--143 \\
Euler s Polyhedron Formula in mizar / Jesse Alama /
144--147 \\
Building a Library of Mechanized Mathematical Proofs:
Why Do It? and What Is It Like to Do? / R. D. Arthan /
148--148 \\
Linear Programs for the Kepler Conjecture / Thomas C.
Hales / 149--151 \\
A Formal Proof of Pick s Theorem / John Harrison /
152--154 \\
Formal Proof (Contributed) \\
Evaluation of Automated Theorem Proving on the Mizar
Mathematical Library / Josef Urban, Krystof Hoder,
Andrei Voronkov / 155--166 \\
Geometry and Visualization (Invited) \\
On Local Deformations of Planar Quad-Meshes / Tim
Hoffmann / 167--169 \\
Construction of Harmonic Surfaces with Prescribed
Geometry / Matthias Weber / 170--173 \\
Geometry and Visualization (Contributed) \\
A Library of OpenGL-Based Mathematical Image Filters /
Martin von Gagern, Christian Mercat / 174--185 \\
MD-jeep: An Implementation of a Branch and Prune
Algorithm for Distance Geometry Problems / Antonio
Mucherino, Leo Liberti, Carlile Lavor / 186--197 \\
TADD: A Computational Framework for Data Analysis Using
Discrete Morse Theory / Jan Reininghaus, David
G{\"u}nther, Ingrid Hotz, Steffen Prohaska,
Hans-Christian Hege / 198--208 \\
Groebner Bases and Applications (Invited) \\
Introduction to Normaliz 2.5 / Winfried Bruns, Bogdan
Ichim, Christof S{\"o}ger / 209--212 \\
Computer Algebra Methods in Tropical Geometry / Thomas
Markwig / 213--216 \\
Groebner Bases and Applications (Contributed) \\
A New Desingularization Algorithm for Binomial
Varieties in Arbitrary Characteristic / Roc{\'\i}o
Blanco / 217--220 \\
An Algorithm of Computing Inhomogeneous Differential
Equations for Definite Integrals / Hiromasa Nakayama,
Kenta Nishiyama / 221--232 \\
Groebner Bases and Applications (Contributed) \\
New Algorithms for Computing Primary Decomposition of
Polynomial Ideals / Masayuki Noro / 233--244 \\
An Automated Confluence Proof for an Infinite Rewrite
System Parametrized over an Integro-Differential
Algebra / Loredana Tec, Georg Regensburger, Markus
Rosenkranz, Bruno Buchberger / 245--248 \\
Operadic Gr{\"o}bner Bases: An Implementation /
Vladimir Dotsenko, Mikael Vejdemo-Johansson / 249--252
\\
Number Theoretical Software (Invited) \\
Magma - A Tool for Number Theory / John Cannon, Steve
Donnelly, Claus Fieker, Mark Watkins / 253--255 \\
Number Theoretical Software (Contributed) \\
Enumerating Galois Representations in Sage / Craig
Citro, Alexandru Ghitza / 256--259 \\
NZMATH 1.0 / Satoru Tanaka, Naoki Ogura, Ken Nakamula,
Tetsushi Matsui, Shigenori Uchiyama / 260--269 \\
Software for Optimization and Polyhedral Computation
(Invited) \\
Removing Redundant Quadratic Constraints / David
Adjiashvili, Michel Baes, Philipp Rostalski / 270--281
\\
Traversing Symmetric Polyhedral Fans / Anders
Nedergaard Jensen / 282--294 \\
C++ Tools for Exploiting Polyhedral Symmetries / Thomas
Rehn, Achill Sch{\"u}rmann / 295--298 \\
isl: An Integer Set Library for the Polyhedral Model /
Sven Verdoolaege / 299--302 \\
Software for Optimization and Polyhedral Computation
(Contributed) \\
The Reformulation-Optimization Software Engine / Leo
Liberti, Sonia Cafieri, David Savourey / 303--314 \\
Generating Smooth Lattice Polytopes / Christian Haase,
Benjamin Lorenz, Andreas Paffenholz / 315--328 \\
Reliable Computation (Invited) \\
Mathemagix: Towards Large Scale Programming for
Symbolic and Certified Numeric Computations /
Gr{\'e}goire Lecerf / 329--332 \\
Complex Inclusion Functions in the CoStLy C++ Class
Library / Markus Neher / 333--336 \\
Standardized Interval Arithmetic and Interval
Arithmetic Used in Libraries / Nathalie Revol /
337--341 \\
Reliable Computation (Contributed) \\
Efficient Evaluation of Large Polynomials / Charles E.
Leiserson, Liyun Li, Marc Moreno Maza, Yuzhen Xie /
342--353 \\
Communicating Functional Expressions from Mathematica
to C-XSC / Evgenija D. Popova, Walter Kr{\"a}mer /
354--365 \\
Author Index / 367--368",
}
@Book{Olver:2010:NHM,
editor = "Frank W. J. Olver and Daniel W. Lozier and Ronald F.
Boisvert and Charles W. Clark",
key = "NIST",
booktitle = "{NIST} Handbook of Mathematical Functions",
title = "{NIST} Handbook of Mathematical Functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xv + 951",
year = "2010",
ISBN = "0-521-19225-0",
ISBN-13 = "978-0-521-19225-5",
LCCN = "QA331 .N57 2010",
bibdate = "Sat May 15 09:08:09 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
price = "US\$99.00",
URL = "http://dlmf.nist.gov/;
http://www.cambridge.org/9780521140638",
acknowledgement = ack-nhfb,
remark = "Includes a DVD with a searchable PDF of each
chapter.",
tableofcontents = "1. Algebraic and analytic methods [Ranjan Roy,
Frank W. J. Olver, Richard A. Askey and Roderick S. C.
Wong] \\
2. Asymptotic approximations [Frank W. J. Olver and
Roderick S. C. Wong] \\
3. Numerical methods [Nico M. Temme] \\
4. Elementary functions [Ranjan Roy and Frank W. J.
Olver] \\
5. Gamma function [Richard A. Askey and Ranjan Roy] \\
6. Exponential, logarithmic, sine and cosine integrals
[Nico M. Temme] \\
7. Error functions, Dawson's and Fresnel integrals
[Nico M. Temme] \\
8. Incomplete gamma and related functions [Richard B.
Paris] \\
9. Airy and related functions [Frank W. J. Olver] \\
10. Bessel functions [Frank W. J. Olver and Leonard C.
Maximon] \\
11. Struve and related functions [Richard B. Paris] \\
12. Parabolic cylinder functions [Nico M. Temme] \\
13. Confluent hypergeometric functions [Adri B. Olde
Daalhuis] \\
14. Legendre and related functions [T. Mark Dunster]
\\
15. Hypergeometric function [Adri B. Olde Daalhuis] \\
16. Generalized hypergeometric functions and Meijer
G-function [Richard A. Askey and Adri B. Olde Daalhuis]
\\
17. q-Hypergeometric and related functions [George E.
Andrews] \\
18. Orthogonal polynomials [Tom H. Koornwinder,
Roderick S. C. Wong, Roelof Koekoek and Rene F.
Swarttouw] \\
19. Elliptic integrals [Bille C. Carlson] \\
20. Theta functions [William P. Reinhardt and Peter L.
Walker] \\
21. Multidimensional theta functions [Bernard
Deconinck] \\
22. Jacobian elliptic functions [William P. Reinhardt
and Peter L. Walker] \\
23. Weierstrass elliptic and modular functions [William
P. Reinhardt and Peter L. Walker] \\
24. Bernoulli and Euler polynomials [Karl Dilcher] \\
25. Zeta and related functions [Tom M. Apostol] \\
26. Combinatorial analysis [David M. Bressoud] \\
27. Functions of number theory [Tom M. Apostol] \\
28. Mathieu functions and Hill's equation [Gerhard
Wolf] \\
29. Lam{\'e} functions [Hans Volkmer] \\
30. Spheroidal wave functions [Hans Volkmer] \\
31. Heun functions [Brian D. Sleeman and Vadim
Kuznetsov] \\
32. Painlev{\'e} transcendents [Peter A. Clarkson] \\
33. Coulomb functions [Ian J. Thompson] \\
34. 3j, 6j, 9j symbols [Leonard C. Maximon] \\
35. Functions of matrix argument [Donald St. P.
Richards] \\
36. Integrals with coalescing saddles [Michael V. Berry
and Chris Howls]",
}
@Book{Polyanin:2011:CHM,
editor = "A. D. (Andrei Dmitrievich) Polyanin and A. I.
Chernoutisan",
booktitle = "A Concise Handbook of Mathematics, Physics, and
Engineering Sciences",
title = "A Concise Handbook of Mathematics, Physics, and
Engineering Sciences",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
pages = "xxviii + 1097",
year = "2011",
DOI = "https://doi.org/10.1201/b10276",
ISBN = "0-429-13137-2, 1-282-90264-4, 1-4398-0639-X
(hardcover), 1-4398-0640-3 (PDF)",
ISBN-13 = "978-0-429-13137-0, 978-1-282-90264-0,
978-1-4398-0639-5 (hardcover), 978-1-4398-0640-1
(PDF)",
LCCN = "QA40 .C65 2010",
bibdate = "Wed Jun 12 15:24:00 MDT 2024",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "\booktitle{A Concise Handbook of Mathematics, Physics,
and Engineering Sciences} takes a practical approach to
the basic notions, formulas, equations, problems,
theorems, methods, and laws that most frequently occur
in scientific and engineering applications and
university education. The authors pay special attention
to issues that many engineers and students find
difficult to understand. The first part of the book
contains chapters on arithmetic, elementary and
analytic geometry, algebra, differential and integral
calculus, functions of complex variables, integral
transforms, ordinary and partial differential
equations. \ldots{} .",
acknowledgement = ack-nhfb,
remark = "Chapter authors: A. I. Chernoutisan, A. V. Egorov, A.
V. Manzhirov, A. D. Polyanin, V. D. Polyanin, V. A.
Popov, B. V. Putyatin, Yu. V. Repina, V. M. Safrai, A.
I. Zhurov.",
subject = "Mathematics; Handbooks, manuals, etc; Physics;
Engineering; Math{\'e}matiques; Guides, manuels, etc;
Physique; Ing{\'e}nierie; Engineering; Mathematics;
Physics",
tableofcontents = "Preface \\
Editors \\
\\
Part I: Mathematics \\
M1: Arithmetic and Elementary Algebra \\
M2: Elementary Functions \\
M3: Elementary Geometry \\
M4: Analytic Geometry \\
M5: Algebra \\
M6: Limits and Derivatives \\
M7: Integrals \\
M8: Series \\
M9: Functions of Complex Variable \\
M10: Integral Transforms \\
M11: Ordinary Differential Equations \\
M12: Partial Differential Equations \\
M13: Special Functions and Their Properties \\
M14: Probability Theory \\
\\
Part II: Physics \\
P1: Physical Foundations of Mechanics \\
P2: Molecular Physics and Thermodynamics \\
P3: Electrodynamics \\
P4: Oscillations and Waves \\
P5: Optics \\
P6: Quantum Mechanics. Atomic Physics \\
P7: Quantum Theory of Crystals \\
P8: Elements of Nuclear Physics \\
\\
Part III: Elements of Applied and Engineering Sciences
\\
E1: Dimensions and Similarity \\
E2: Mechanics of Point Particles and Rigid Bodies \\
E3: Elements of Strength of Materials \\
E4: Hydrodynamics \\
E5: Mass and Heat Transfer \\
E6: Electrical Engineering \\
E7: Empirical and Engineering Formulas and Criteria for
Their Applicability \\
\\
Part IV: Supplements \\
S1: Integrals \\
S2: Integral Transforms \\
S3: Orthogonal Curvilinear Systems of Coordinates \\
S4: Ordinary Differential Equations \\
S5: Some Useful Electronic Mathematical Resources \\
S6: Physical Tables \\
S7: Periodic Table \\
Index",
}
@Proceedings{Schost:2011:IPI,
editor = "{\'E}ric Schost and Ioannis Z. Emiris",
booktitle = "{ISSAC 2011: Proceedings of the 2011 International
Symposium on Symbolic and Algebraic Computation, June
7--11, 2011, San Jose, CA, USA}",
title = "{ISSAC 2011: Proceedings of the 2011 International
Symposium on Symbolic and Algebraic Computation, June
7--11, 2011, San Jose, CA, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "362 (est.)",
year = "2011",
ISBN = "1-4503-0675-6",
ISBN-13 = "978-1-4503-0675-1",
LCCN = "QA76.95 .I59 2011",
bibdate = "Fri Mar 14 12:24:11 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/issac.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Schwarz:2011:PIS,
editor = "Eric Schwarz and Vojin G. Oklobdzija",
booktitle = "{Proceedings of the 20th IEEE Symposium on Computer
Arithmetic, July 25--27, 2011, T{\"u}bingen, Germany}",
title = "{Proceedings of the 20th IEEE Symposium on Computer
Arithmetic, July 25--27, 2011, T{\"u}bingen, Germany}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xix + 253",
year = "2011",
ISBN = "0-7695-4318-9, 1-4244-9457-5",
ISBN-13 = "978-0-7695-4318-5, 978-1-4244-9457-6",
LCCN = "QA76.6",
bibdate = "Sat Aug 20 09:19:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
tableofcontents = "Foreword / ix \\
Dedication / x \\
Steering Committee / xv \\
Symposium Committee / xvi \\
Program Committee / xvii \\
Additional Reviewers / xviii \\
Corporate Sponsors / xix \\
Session 1: Keynote Talk: Chair: Eric Schwarz and Vojin
G. Oklobdzija \\
High Intelligence Computing: The New Era of High
Performance Computing / Ralf Fischer / 3 \\
Session 2: Multiple-Precision Algorithms: Chair: Marius
Cornea \\
Short Division of Long Integers / David Harvey and Paul
Zimmermann / 7 \\
High Degree Toom'n'Half for Balanced and Unbalanced
Multiplication / Marco Bodrato / 15 \\
Augmented Precision Square Roots and 2-D Norms, and
Discussion on Correctly Rounding sqrt($x^2 + y^2$) /
Nicolas Brisebarre, Mioara Jolde{\c{s}}, Peter
Kornerup, Erik Martin-Dorel, and Jean-Michel Muller /
23 \\
Session 3: Transcendental Methods: Chair: Naofumi
Takagi \\
Towards a Quaternion Complex Logarithmic Number System
/ Mark G. Arnold, John Cowles, Vassilis Paliouras, and
Ioannis Kouretas / 33 \\
ROM-less LNS / R. Che Ismail and J. N. Coleman / 43 \\
Composite Iterative Algorithm and Architecture for q-th
Root Calculation / Alvaro Vazquez and Javier D.
Bruguera / 52 \\
On the Fixed-Point Accuracy Analysis and Optimization
of FFT Units with CORDIC Multipliers / Omid Sarbishei
and Katarzyna Radecka / 62 \\
Session 4: Special Session on Industrial Practices:
Chair: Mike Schulte \\
Self Checking in Current Floating-Point Units / Daniel
Lipetz and Eric Schwarz / 73 \\
How to Square Floats Accurately and Efficiently on the
ST231 Integer Processor/ Claude-Pierre Jeannerod,
Jingyan Jourdan-Lu, Christophe Monat, and Guillaume
Revy / 77 \\
A 1.5 Ghz VLIW DSP CPU with Integrated Floating Point
and Fixed Point Instructions in 40 nm CMOS / Timothy
Anderson, Due Bui, Shriram Moharil, Soujanya Narnur,
Mujibur Rahman, Anthony Lell, Eric Biscondi, Ashish
Shrivastava, Peter Dent, Mingjian Yan, and Hasan
Mahmood / 82 \\
The POWER7 Binary Floating-Point Unit / Maarten
Boersma, Michael Kroner, Christophe Layer, Petra Leber,
Silvia M. Muller, and Kerstin Schelm / 87 \\
Session 5: Addition: Chair: Alberto Nannarelli \\
Accelerating Computations on FPGA Carry Chains by
Operand Compaction / Thomas B. Preus{\ss}er, Martin
Zabel, and Rainer G. Spallek / 95 \\
Fast Ripple-Carry Adders in Standard-Cell CMOS VLSI /
Neil Burgess / 103 \\
A Family of High Radix Signed Digit Adders / Saeid
Gorgin and Ghassem Jaberipur / 112 \\
Session 6: Floating-Point Units: Chair: Javier Bruguera
\\
Fused Multiply-Add Microarchitecture Comprising
Separate Early-Normalizing Multiply and Add Pipelines /
David R. Lutz / 123 \\
Latency Sensitive FMA Design / Sameh Galal and Mark
Horowitz / 129 \\
The IBM zEnterprise-196 Decimal Floating-Point
Accelerator / Steven Carlough, Adam Collura, Silvia
Mueller, and Michael Kroener / 139 \\
Session 7: Division, Square-Root and Reciprocal
Square-Root: Chair: Peter Kornerup \\
Radix-8 Digit-by-Rounding: Achieving High-Performance
Reciprocals, Square Roots, and Reciprocal Square Roots
/ J. Adam Butts, Ping Tak Peter Tang, Ron O. Dror, and
David E. Shaw / 149 \\
Tight Certification Techniques for Digit-by-Rounding
Algorithms with Application to a New 1/sqrt(x) Design /
Ping Tak Peter Tang, J. Adam Butts, Ron O. Dror, and
David E. Shaw / 159 \\
Radix-16 Combined Division and Square Root Unit /
Alberto Nannarelli / 169 \\
A Prescale-Lookup-Postscale Additive Procedure for
Obtaining a Single Precision Ulp Accurate Reciprocal /
David W. Matula and Mihai T. Panu / 177 \\
Session 8: Special Session on High Performance
Arithmetic for FPGA's: Chair: Martin Langhammer \\
Teraflop FPGA Design / Martin Langhammer / 187 \\
The Arithmetic Operators You Will Never See in a
Microprocessor / Florent de Dinechin / 189 \\
Accelerating Large-Scale HPC Applications Using FPGAs /
Rob Dimond, Sebastien Racaniere, and Oliver Pell / 191
\\
Session 9: Arithmetic Algorithms for Cryptography:
Chair: David Matula \\
A General Approach for Improving RNS Montgomery
Exponentiation Using Pre-processing / Filippo Gandino,
Fabrizio Lamberti, Paolo Montuschi, and Jean-Claude
Bajard / 195 \\
Bit-Sliced Binary Normal Basis Multiplication / Billy
Bob Brumley and Dan Page / 205 \\
Efficient SIMD Arithmetic Modulo a Mersenne Number /
Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra, and
Peter L. Montgomery / 213 \\
Session 10: Tools for Formal Certified Code: Chair:
Martin Schmookler \\
Automatic Generation of Code for the Evaluation of
Constant Expressions at Any Precision with a Guaranteed
Error Bound / Sylvain Chevillard / 225 \\
Automatic Generation of Fast and Certified Code for
Polynomial Evaluation / Christophe Mouilleron and
Guillaume Revy / 233 \\
Flocq: A Unified Library for Proving Floating-Point
Algorithms in Coq / Sylvie Boldo and Guillaume
Melquiond / 243 \\
Author Index / 253",
}
@Book{Hwu:2012:GCG,
editor = "Wen-mei Hwu",
booktitle = "{GPU} computing gems",
title = "{GPU} computing gems",
publisher = "Morgan Kaufmann",
address = "Boston, MA",
edition = "Jade",
pages = "xvi + 541 + 16",
year = "2012",
ISBN = "0-12-385963-8 (hardback)",
ISBN-13 = "978-0-12-385963-1 (hardback)",
LCCN = "T385 .G6875 2012",
bibdate = "Sat Feb 8 18:16:05 MST 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
series = "Applications of GPU computing series",
abstract = "Since the introduction of CUDA in 2007, more than 100
million computers with CUDA capable GPUs have been
shipped to end users. GPU computing application
developers can now expect their application to have a
mass market. With the introduction of OpenCL in 2010,
researchers can now expect to develop GPU applications
that can run on hardware from multiple vendors.",
acknowledgement = ack-nhfb,
subject = "Graphics processing units; Programming; Imaging
systems; Computer graphics; Image processing; Digital
techniques",
tableofcontents = "Part 1: Parallel Algorithms and Data Structures ---
Paulius Micikevicius, NVIDIA \\
1 Large-Scale GPU Search \\
2 Edge v. Node Parallelism for Graph Centrality Metrics
\\
3 Optimizing parallel prefix operations for the Fermi
architecture \\
4 Building an Efficient Hash Table on the GPU \\
5 An Efficient CUDA Algorithm for the Maximum Network
Flow Problem \\
6 On Improved Memory Access Patterns for Cellular
Automata Using CUDA \\
7 Fast Minimum Spanning Tree Computation on Large
Graphs \\
8 Fast in-place sorting with CUDA based on bitonic sort
\\
Part 2: Numerical Algorithms --- Frank Jargstorff,
NVIDIA \\
9 Interval Arithmetic in CUDA \\
10 Approximating the erfinv Function \\
11 A Hybrid Method for Solving Tridiagonal Systems on
the GPU \\
12 LU Decomposition in CULA \\
13 GPU Accelerated Derivative-free Optimization \\
Part 3: Engineering Simulation --- Peng Wang, NVIDIA
\\
14 Large-scale gas turbine simulations on GPU clusters
\\
15 GPU acceleration of rarefied gas dynamic simulations
\\
16 Assembly of Finite Element Methods on Graphics
Processors \\
17 CUDA implementation of Vertex-Centered, Finite
Volume CFD methods on Unstructured Grids with Flow
Control Applications \\
18 Solving Wave Equations on Unstructured Geometries
\\
19 Fast electromagnetic integral equation solvers on
graphics processing units (GPUs) \\
Part 4: Interactive Physics for Games and Engineering
Simulation --- Richard Tonge, NVIDIA \\
20 Solving Large Multi-Body Dynamics Problems on the
GPU \\
21 Implicit FEM Solver in CUDA \\
22 Real-time Adaptive GPU multi-agent path planning \\
Part 5: Computational Finance --- Thomas Bradley,
NVIDIA \\
23 High performance finite difference PDE solvers on
GPUs for financial option pricing \\
24 Identifying and Mitigating Credit Risk using
Large-scale Economic Capital Simulations \\
25 Financial Market Value-at-Risk Estimation using the
Monte Carlo Method \\
Part 6: Programming Tools and Techniques --- Cliff
Wooley, NVIDIA \\
26 Thrust: A Productivity-Oriented Library for CUDA \\
27 GPU Scripting and Code Generation with PyCUDA \\
28 Jacket: GPU Powered MATLAB Acceleration \\
29 Accelerating Development and Execution Speed with
Just In Time GPU Code Generation \\
30 GPU Application Development, Debugging, and
Performance Tuning with GPU Ocelot \\
31 Abstraction for AoS and SoA Layout in C++ \\
32 Processing Device Arrays with C++ Metaprogramming
\\
33 GPU Metaprogramming: A Case Study in
Biologically-Inspired Machine Vision \\
34 A Hybridization Methodology for High-Performance
Linear Algebra Software for GPUs \\
35 Dynamic Load Balancing using Work-Stealing \\
36 Applying software-managed caching and CPU/GPU task
scheduling for accelerating dynamic workloads",
}
@Book{Arfken:2013:MMP,
author = "George B. (George Brown) Arfken and Hans-J{\"u}rgen
Weber and Frank E. Harris",
booktitle = "Mathematical Methods for Physicists: a Comprehensive
Guide",
title = "Mathematical Methods for Physicists: a Comprehensive
Guide",
publisher = pub-ELSEVIER-ACADEMIC,
address = pub-ELSEVIER-ACADEMIC:adr,
edition = "Seventh",
pages = "xiii + 1205",
year = "2013",
ISBN = "0-12-384654-4 (hardcover)",
ISBN-13 = "978-0-12-384654-9 (hardcover)",
LCCN = "QA37.3 .A74 2013",
bibdate = "Thu May 3 08:02:53 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
jenson.stanford.edu:2210/unicorn",
acknowledgement = ack-nhfb,
subject = "Mathematical analysis; Mathematical physics",
tableofcontents = "Preface / xi--xiii \\
1: Mathematical Preliminaries / 1--82 \\
2: Determinants and Matrices / 83--121 \\
3: Vector Analysis / 123--203 \\
4: Tensors and Differential Forms / 205--249 \\
5: Vector Spaces / 251--297 \\
6: Eigenvalue Problems / 299--328 \\
7: Ordinary Differential Equations / 329--380 \\
8: Sturm--Liouville Theory / 381--399 \\
9: Partial Differential Equations / 401--445 \\
10: Green's Functions / 447--467 \\
11: Complex Variable Theory / 469--550 \\
12: Further Topics in Analysis / 551--598 \\
13: Gamma Function / 599--641 \\
14: Bessel Functions / 643--713 \\
15: Legendre Functions / 715--772 \\
16: Angular Momentum / 773--814 \\
17: Group Theory / 815--870 \\
18: More Special Functions / 871--933 \\
19: Fourier Series / 935--962 \\
20: Integral Transforms / 963--1046 \\
21: Integral Equations / 1047--1079 \\
22: Calculus of Variations / 1081--1124 \\
23: Probability and Statistics / 1125--1179 \\
Index / 1181--1205",
}
@Proceedings{IEEE:2013:PIS,
editor = "{IEEE}",
booktitle = "{Proceedings of the 21st IEEE Symposium on Computer
Arithmetic, Austin, Texas, USA, 8--10 April 2013}",
title = "{Proceedings of the 21st IEEE Symposium on Computer
Arithmetic, Austin, Texas, USA, 8--10 April 2013}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvi + 229",
year = "2013",
ISBN = "0-7695-4957-8",
ISBN-13 = "978-0-7695-4957-6",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2013",
bibdate = "Sat Aug 01 08:03:11 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic units; correctness proofs;
cryptography; domain specific designs; error analysis;
exascale computing; floating point arithmetic;
floating-point error analysis; formal verification;
function approximation; modular arithmetic; theorem
proving; verification",
}
@Proceedings{Hong:2014:MSI,
editor = "Hoon Hong and Chee Yap",
booktitle = "Mathematical Software --- {ICMS 2014: 4th
International Conference, Seoul, South Korea, August
5--9, 2014, Proceedings}",
title = "Mathematical Software --- {ICMS 2014: 4th
International Conference, Seoul, South Korea, August
5--9, 2014, Proceedings}",
volume = "8592",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxii + 735",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2",
ISBN = "3-662-44198-5 (paperback), 3-662-44199-3 (e-book)",
ISBN-13 = "978-3-662-44198-5 (paperback), 978-3-662-44199-2
(e-book)",
LCCN = "QA76.9.M35",
bibdate = "Sat Sep 23 09:59:48 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Front Matter \\
Invited Talks \\
Experimental Computation and Visual Theorems / Jonathan
M. Borwein / 1--8 \\
Soft Math Math Soft / Bruno Buchberger / 9--15 \\
Mathematical Theory Exploration \\
Flyspecking Flyspeck / Mark Adams / 16--20 \\
Symbolic Computing Package for Mathematica for
Versatile Manipulation of Mathematical Expressions /
Youngjoo Chung / 21--25 \\
Representing, Archiving, and Searching the Space of
Mathematical Knowledge / Mihnea Iancu, Michael
Kohlhase, Corneliu Prodescu / 26--30 \\
Early Examples of Software in Mathematical Knowledge
Management / Patrick Ion / 31--35 \\
Discourse-Level Parallel Markup and Meaning Adoption in
Flexiformal Theory Graphs / Michael Kohlhase, Mihnea
Iancu / 36--40 \\
Complexity Analysis of the Bivariate Buchberger
Algorithm in Theorema / Alexander Maletzky, Bruno
Buchberger / 41--48 \\
Theorema 2.0: A System for Mathematical Theory
Exploration / Wolfgang Windsteiger / 49--52 \\
Computational Group Theory \\
New Approaches in Black Box Group Theory / Alexandre
Borovik, {\c{S}}{\"u}kr{\"u} Yal{\c{c}}{\i}nkaya /
53--58 \\
A GAP Package for Computing with Real Semisimple Lie
Algebras / Heiko Dietrich, Paolo Faccin, Willem A. de
Graaf / 59--66 \\
Bacterial Genomics and Computational Group Theory: The
BioGAP Package for GAP / Attila Egri-Nagy, Andrew R.
Francis, Volker Gebhardt / 67--74 \\
SgpDec: Cascade (De)Compositions of Finite
Transformation Semigroups and Permutation Groups /
Attila Egri-Nagy, James D. Mitchell, Chrystopher L.
Nehaniv / 75--82 \\
Approximating Generators for Integral Arithmetic Groups
/ Bettina Eick / 83--86 \\
Software for Groups: Theory and Practice / Alexander
Hulpke / 87--91 \\
Computation of Genus 0 Belyi Functions / Mark van
Hoeij, Raimundas Vidunas / 92--98 \\
On Computation of the First Baues--Wirsching Cohomology
of a Freely-Generated Small Category / Yasuhiro Momose,
Yasuhide Numata / 99--105 \\
Coding Theory \\
Codes over a Non Chain Ring with Some Applications /
Aysegul Bayram, Elif Segah Oztas, Irfan Siap / 106--110
\\
On the Weight Enumerators of the Projections of the
2-adic Golay Code of Length 24 to $\mathbb{Z}_{2^e}$ /
Sunghyu Han / 111--114 \\
Coding Theory \\
Computer Based Reconstruction of Binary Extremal
Self-dual Codes of Length 32 / Jon-Lark Kim / 115--118
\\
Magma Implementation of Decoding Algorithms for General
Algebraic Geometry Codes / Kwankyu Lee / 119--123 \\
Reversible Codes and Applications to DNA / Elif Segah
Oztas, Irfan Siap, Bahattin Yildiz / 124--128 \\
Computational Topology \\
javaPlex: A Research Software Package for Persistent
(Co)Homology / Henry Adams, Andrew Tausz, Mikael
Vejdemo-Johansson / 129--136 \\
PHAT --- Persistent Homology Algorithms Toolbox /
Ulrich Bauer, Michael Kerber, Jan Reininghaus, Hubert
Wagner / 137--143 \\
Computing Persistence Modules on Commutative Ladders of
Finite Type / Emerson G. Escolar, Yasuaki Hiraoka /
144--151 \\
Heuristics for Sphere Recognition / Michael Joswig,
Frank H. Lutz, Mimi Tsuruga / 152--159 \\
CAPD::RedHom v2 --- Homology Software Based on
Reduction Algorithms / Mateusz Juda, Marian Mrozek /
160--166 \\
The Gudhi Library: Simplicial Complexes and Persistent
Homology / Cl{\'e}ment Maria, Jean-Daniel Boissonnat,
Marc Glisse, Mariette Yvinec / 167--174 \\
Numerical Algebraic Geometry \\
Bertini_real: Software for One- and Two-Dimensional
Real Algebraic Sets / Daniel A. Brake, Daniel J. Bates,
Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese,
CharlesW. Wampler / 175--182 \\
Hom4PS-3: A Parallel Numerical Solver for Systems of
Polynomial Equations Based on Polyhedral Homotopy
Continuation Methods / Tianran Chen, Tsung-Lin Lee,
Tien-Yien Li / 183--190 \\
Geometry \\
CGAL --- Reliable Geometric Computing for Academia and
Industry / Eric Berberich / 191--197 \\
Implementing the $L_\infty$ Segment Voronoi Diagram in
CGAL and Applying in VLSI Pattern Analysis / Panagiotis
Cheilaris, Sandeep Kumar Dey, Maria Gabrani, Evanthia
Papadopoulou / 198--205 \\
BULL! --- The Molecular Geometry Engine Based on
Voronoi Diagram, Quasi-Triangulation, and Beta-Complex
/ Deok-Soo Kim, Youngsong Cho, Jae-Kwan Kim, Joonghyun
Ryu, Mokwon Lee, Jehyun Cha et al. / 206--213 \\
Integrating Circumradius and Area Formulae for Cyclic
Pentagons / Shuichi Moritsugu / 214--221 \\
Computer Aided Geometry / Douglas Navarro Guevara,
Adrian Navarro Alvarez / 222--229 \\
The Sustainability of Digital Educational Resources /
Yongsheng Rao, Ying Wang, Yu Zou, Jingzhong Zhang /
230--234 \\
A Touch-Operation-Based Dynamic Geometry System: Design
and Implementation / Wei Su, Paul S. Wang, Chuan Cai,
Lian Li / 235--239 \\
OpenGeo: An Open Geometric Knowledge Base / Dongming
Wang, Xiaoyu Chen, Wenya An, Lei Jiang, Dan Song /
240--245 \\
Curves and Surfaces \\
On Computing a Cell Decomposition of a Real Surface
Containing Infinitely Many Singularities / Daniel J.
Bates, Daniel A. Brake, Jonathan D. Hauenstein, Andrew
J. Sommese, Charles W. Wampler / 246--252 \\
Robustly and Efficiently Computing Algebraic Curves and
Surfaces / Eric Berberich / 253--260 \\
Computing the Orthogonal Projection of Rational Curves
onto Rational Parameterized Surface by Symbolic Methods
/ Zhiwang Gan, Meng Zhou / 261--268 \\
Isotopic $\epsilon$-Approximation of Algebraic Curves /
Kai Jin / 269--276 \\
Isotopic Arrangement of Simple Curves: An Exact
Numerical Approach Based on Subdivision / Jyh-Ming
Lien, Vikram Sharma, Gert Vegter, Chee Yap / 277--282
\\
Quantified Reasoning \\
Real Quantifier Elimination in the RegularChains
Library / Changbo Chen, Marc Moreno Maza / 283--290 \\
Software for Quantifier Elimination in Propositional
Logic / Eugene Goldberg, Panagiotis Manolios / 291--294
\\
Quantifier Elimination for Linear Modular Constraints /
Ajith K. John, Supratik Chakraborty / 295--302 \\
Skolemization Modulo Theories / Konstantin Korovin,
Margus Veanes / 303--306 \\
Incremental QBF Solving by DepQBF / Florian Lonsing,
Uwe Egly / 307--314 \\
NLCertify: A Tool for Formal Nonlinear Optimization /
Victor Magron / 315--320 \\
Special Functions and Concrete Mathematics \\
Developing Linear Algebra Packages on Risa/Asir for
Eigenproblems / Katsuyoshi Ohara, Shinichi Tajima,
Akira Terui / 321--324 \\
Mathematical Software for Modified Bessel Functions /
Juri Rappoport / 325--332 \\
BetaSCP2: A Program for the Optimal Prediction of
Side-Chains in Proteins / Joonghyun Ryu, Mokwon Lee,
Jehyun Cha, Chanyoung Song, Deok-Soo Kim / 333--340 \\
Computation of an Improved Lower Bound to Giuga's
Primality Conjecture / Matthew Skerritt / 341--345 \\
An Extension and Efficient Calculation of the Horner's
Rule for Matrices / Shinichi Tajima, Katsuyoshi Ohara,
Akira Terui / 346--351 \\
Groebner Bases \\
What Is New in CoCoA? / John Abbott, Anna Maria Bigatti
/ 352--358 \\
Maximizing Likelihood Function for Parameter Estimation
in Point Clouds via Groebner Basis / Joseph Awange,
B{\'e}la Pal{\'a}ncz, Robert Lewis / 359--366 \\
Groebner Basis in Geodesy and Geoinformatics / Joseph
Awange, B{\'e}la Pal{\'a}ncz, Robert Lewis / 367--373
\\
Groebner Bases in Theorema / Bruno Buchberger,
Alexander Maletzky / 374--381 \\
Effective Computation of Radical of Ideals and Its
Application to Invariant Theory / Amir Hashemi /
382--389 \\
Generic and Parallel Groebner Bases in JAS / Heinz
Kredel / 390--397 \\
Application of Groebner Basis Methodology to Nonlinear
Mechanics Problems / Y. Jane Liu, John Peddieson /
398--405 \\
Software for Discussing Parametric Polynomial Systems:
The Gr{\"o}bner Cover / Antonio Montes, Michael Wibmer
/ 406--413 \\
An Algorithm for Computing Standard Bases by Change of
Ordering via Algebraic Local Cohomology / Katsusuke
Nabeshima, Shinichi Tajima / 414--418 \\
Verification of Gr{\"o}bner Basis Candidates / Masayuki
Noro, Kazuhiro Yokoyama / 419--424 \\
Triangular Decompositions of Polynomial Systems \\
Cylindrical Algebraic Decomposition in the
RegularChains Library / Changbo Chen, Marc Moreno Maza
/ 425--433 \\
Hierarchical Comprehensive Triangular Decomposition /
Zhenghong Chen, Xiaoxian Tang, Bican Xia / 434--441 \\
A Package for Parametric Matrix Computations / Robert
M. Corless, Steven E. Thornton / 442--449 \\
Choosing a Variable Ordering for Truth-Table Invariant
Cylindrical Algebraic Decomposition by Incremental
Triangular Decomposition / Matthew England, Russell
Bradford, James H. Davenport, David Wilson / 450--457
\\
Using the Regular Chains Library to Build Cylindrical
Algebraic Decompositions by Projecting and Lifting /
Matthew England, David Wilson, Russell Bradford, James
H. Davenport / 458--465 \\
An Improvement of Rosenfeld--Gr{\"o}bner Algorithm /
Amir Hashemi, Zahra Touraji / 466--471 \\
Doing Algebraic Geometry with the RegularChains Library
/ Parisa Alvandi, Changbo Chen, Steffen Marcus, Marc
Moreno Maza, {\'E}ric Schost, Paul Vrbik / 472--479 \\
On Multivariate Birkhoff Rational Interpolation / Peng
Xia, Bao-Xin Shang, Na Lei / 480--483 \\
Computing Moore--Penrose Inverses of Ore Polynomial
Matrices / Yang Zhang / 484--491 \\
Parametric Polynomial Systems \\
Software Using the Gr{\"o}bner Cover for Geometrical
Loci Computation and Classification / Miguel A.
Ab{\'a}nades, Francisco Botana, Antonio Montes,
Tom{\'a}s Recio / 492--499 \\
Using Maple's RegularChains Library to Automatically
Classify Plane Geometric Loci / Francisco Botana,
Tom{\'a}s Recio / 500--503 \\
Solving Parametric Polynomial Systems by
RealComprehensiveTriangularize / Changbo Chen, Marc
Moreno Maza / 504--511 \\
QE Software Based on Comprehensive Gr{\"o}bner Systems
/ Ryoya Fukasaku / 512--517 \\
SyNRAC: A Toolbox for Solving Real Algebraic
Constraints / Hidenao Iwane, Hitoshi Yanami, Hirokazu
Anai / 518--522 \\
An Algorithm for Computing Tjurina Stratifications of
$\mu$-Constant Deformations by Using Local Cohomology
Classes with Parameters / Katsusuke Nabeshima, Shinichi
Tajima / 523--530 \\
An Implementation Method of Boolean Gr{\"o}bner Bases
and Comprehensive Boolean Gr{\"o}bner Bases on General
Computer Algebra Systems / Akira Nagai, Shutaro Inoue /
531--536 \\
A Method to Determine if Two Parametric Polynomial
Systems Are Equal / Jie Zhou, Dingkang Wang / 537--544
\\
Mathematical Web/Mobile Interfaces and Visualization
\\
An Implementation Method of a CAS with a Handwriting
Interface on Tablet Devices / Mitsushi Fujimoto /
545--548 \\
New Way of Explanation of the Stochastic Interpretation
of Wave Functions and Its Teaching Materials Using
KETpic / Kenji Fukazawa / 549--553 \\
{IFSGen4\LaTeX}: Interactive Graphical User Interface
for Generation and Visualization of Iterated Function
Systems in {\LaTeX} / Akemi G{\'a}lvez, Kiyoshi
Kitahara, Masataka Kaneko / 554--561 \\
GNU {\TeX}MACS: towards a Scientific Office Suite /
Massimiliano Gubinelli, Joris van der Hoeven,
Fran{\c{c}}ois Poulain, Denis Raux / 562--569 \\
Computer Software Program for Representation and
Visualization of Free-Form Curves through Bio-inspired
Optimization Techniques / Andr{\'e}s Iglesias, Akemi
G{\'a}lvez / 570--577 \\
On Some Attempts to Verify the Effect of Using
High-Quality Graphics in Mathematics Education /
Kiyoshi Kitahara, Tadashi Takahashi, Masataka Kaneko /
578--585 \\
Math Web Search Interfaces and the Generation Gap of
Mathematicians / Andrea Kohlhase / 586--593 \\
Practice with Computer Algebra Systems in Mathematics
Education and Teacher Training Courses / Hideyo
Makishita / 594--600 \\
Development of Visual Aid Materials in Teaching the
Bivariate Normal Distributions / Toshifumi Nomachi,
Toshihiko Koshiba, Shunji Ouchi / 601--606 \\
Creating Interactive Graphics for Mathematics Education
Utilizing KETpic / Shunji Ouchi, Yoshifumi Maeda,
Kiyoshi Kitahara, Naoki Hamaguchi / 607--613 \\
A Tablet-Compatible Web-Interface for Mathematical
Collaboration / Marco Pollanen, Jeff Hooper, Bruce
Cater, Sohee Kang / 614--620 \\
Development and Evaluation of a Web-Based Drill System
to Master Basic Math Formulae Using a New Interactive
Math Input Method / Shizuka Shirai, Tetsuo Fukui /
621--628 \\
Generating Data of Mathematical Figures for 3D Printers
with KETpic and Educational Impact of the Printed
Models / Setsuo Takato, Naoki Hamaguchi, Haiduke
Sarafian / 629--634 \\
A Touch-Based Mathematical Expression Editor / Wei Su,
Paul S. Wang, Lian Li / 635--640 \\
Establishment of KETpic Programming Styles for Drawing
/ Satoshi Yamashita, Yoshifumi Maeda, Hisashi Usui,
Kiyoshi Kitahara, Hideyo Makishita, Kazushi Ahara /
641--646 \\
General Session \\
Integration of Libnormaliz in CoCoALib and CoCoA 5 /
John Abbott, Anna Maria Bigatti, Christof S{\"o}ger /
647--653 \\
Elements of Design for Containers and Solutions in the
LinBox Library / Brice Boyer, Jean-Guillaume Dumas,
Pascal Giorgi, Cl{\'e}ment Pernet, B. David Saunders /
654--662 \\
Recent Developments in Normaliz / Winfried Bruns,
Christof S{\"o}ger / 663--668 \\
The Basic Polynomial Algebra Subprograms / Changbo
Chen, Svyatoslav Covanov, Farnam Mansouri, Marc Moreno
Maza, Ning Xie, Yuzhen Xie / 669--676 \\
Function Interval Arithmetic / Jan Duracz, Amin
Farjudian, Michal Kone{\v{c}}n{\'y}, Walid Taha /
677--684 \\
Generating Optimized Sparse Matrix Vector Product over
Finite Fields / Pascal Giorgi, Bastien Vialla /
685--690 \\
swMATH --- An Information Service for Mathematical
Software / Gert-Martin Greuel, Wolfram Sperber /
691--701 \\
MathLibre: Modifiable Desktop Environment for
Mathematics / Tatsuyoshi Hamada / 702--705 \\
Software Packages for Holonomic Gradient Method / Tamio
Koyama, Hiromasa Nakayama, Katsuyoshi Ohara, Tomonari
Sei, Nobuki Takayama / 706--712 \\
Metalibm: A Mathematical Functions Code Generator /
Olga Kupriianova, Christoph Lauter / 713--717 \\
From Calculus to Algorithms without Errors / Norbert
M{\"u}ller, Martin Ziegler / 718--724 \\
Dense Arithmetic over Finite Fields with the CUMODP
Library / Sardar Anisul Haque, Xin Li, Farnam Mansouri,
Marc Moreno Maza, Wei Pan, Ning Xie / 725--732 \\
Back Matter / / 733--735",
}
@Book{Higham:2015:PCA,
editor = "Nicholas J. Higham and Mark R. Dennis and Paul
Glendinning and Paul A. Martin and Fadil Santosa and
Jared Tanner",
booktitle = "The {Princeton} Companion to Applied Mathematics",
title = "The {Princeton} Companion to Applied Mathematics",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "994 (est.)",
year = "2015",
ISBN = "0-691-15039-7 (hardcover)",
ISBN-13 = "978-0-691-15039-0 (hardcover)",
LCCN = "QA155 .P75 2015",
bibdate = "Wed Sep 9 05:32:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Algebra; Mathematics; Mathematical models",
tableofcontents = "Preface / ix \\
Contributors / xiii \\
Part I: Introduction to Applied Mathematics \\
I.1 What Is Applied Mathematics? / 1 \\
I.2 The Language of Applied Mathematics / 8 \\
I.3 Methods of Solution / 27 \\
I.4 Algorithms / 40 \\
I.5 Goals of Applied Mathematical Research / 48 \\
I.6 The History of Applied Mathematics / 55 \\
Part II: Concepts \\
II.1 Asymptotics / 81 \\
II.2 Boundary Layer / 82 \\
II.3 Chaos and Ergodicity / 82 \\
II.4 Complex Systems / 83 \\
II.5 Conformal Mapping / 84 \\
II.6 Conservation Laws / 86 \\
II.7 Control / 88 \\
II.8 Convexity / 89 \\
II.9 Dimensional Analysis and Scaling / 90 \\
II.10 The Fast Fourier Transform / 94 \\
II.11 Finite Differences / 95 \\
II.12 The Finite-Element Method / 96 \\
II.13 Floating-Point Arithmetic / 96 \\
II.14 Functions of Matrices / 97 \\
II.15 Function Spaces / 99 \\
II.16 Graph Theory / 101 \\
II.17 Homogenization / 103 \\
II.18 Hybrid Systems / 103 \\
II.19 Integral Transforms and Convolution / 104 \\
II.20 Interval Analysis / 105 \\
II.21 Invariants and Conservation Laws / 106 \\
II.22 The Jordan Canonical Form / 112 \\
II.23 Krylov Subspaces / 113 \\
II.24 The Level Set Method / 114 \\
II.25 Markov Chains / 116 \\
II.26 Model Reduction / 117 \\
II.27 Multiscale Modeling / 119 \\
II.28 Nonlinear Equations and Newton's Method / 120 \\
II.29 Orthogonal Polynomials / 122 \\
II.30 Shocks / 122 \\
II.31 Singularities / 124 \\
II.32 The Singular Value Decomposition / 126 \\
II.33 Tensors and Manifolds / 127 \\
II.34 Uncertainty Quantification / 131 \\
II.35 Variational Principle / 134 \\
II.36 Wave Phenomena / 134 \\
Part III: Equations, Laws, and Functions of Applied
Mathematics \\
III.1 Benford's Law / 135 \\
III.2 Bessel Functions / 137 \\
III.3 The Black--Scholes Equation / 137 \\
III.4 The Burgers Equation / 138 \\
III.5 The Cahn--Hilliard Equation / 138 \\
III.6 The Cauchy--Riemann Equations / 139 \\
III.7 The Delta Function and Generalized Functions /
139 \\
III.8 The Diffusion Equation / 142 \\
III.9 The Dirac Equation / 142 \\
III.10 Einstein's Field Equations / 144 \\
III.11 The Euler Equations / 146 \\
III.12 The Euler--Lagrange Equations / 147 \\
III.13 The Gamma Function / 148 \\
III.14 The Ginzburg--Landau Equation / 148 \\
III.15 Hooke's Law / 149 \\
III.16 The Korteweg--de Vries Equation / 150 \\
III.17 The Lambert $W$ Function / 151 \\
III.18 Laplace's Equation / 155 \\
III.19 The Logistic Equation / 156 \\
III.20 The Lorenz Equations / 158 \\
III.21 Mathieu Functions / 159 \\
III.22 Maxwell's Equations / 160 \\
III.23 The Navier--Stokes Equations / 162 \\
III.24 The Painlev{\'e} Equations / 163 \\
III.25 The Riccati Equation / 165 \\
III.26 Schr{\"o}dinger's Equation / 167 \\
III.27 The Shallow-Water Equations / 167 \\
III.28 The Sylvester and Lyapunov Equations / 168 \\
III.29 The Thin-Film Equation / 169 \\
III.30 The Tricomi Equation / 170 \\
III.31 The Wave Equation / 171 \\
Part IV: Areas of Applied Mathematics \\
IV.1 Complex Analysis / 173 \\
IV.2 Ordinary Differential Equations / 181 \\
IV.3 Partial Differential Equations / 190 \\
IV.4 Integral Equations / 200 \\
IV.5 Perturbation Theory and Asymptotics / 208 \\
IV.6 Calculus of Variations / 218 \\
IV.7 Special Functions / 227 \\
IV.8 Spectral Theory / 236 \\
IV.9 Approximation Theory / 248 \\
IV.10 Numerical Linear Algebra and Matrix Analysis /
263 \\
IV.11 Continuous Optimization (Nonlinear and Linear
Programming) / 281 \\
IV.12 Numerical Solution of Ordinary Differential
Equations / 293 \\
IV.13 Numerical Solution of Partial Differential
Equations / 306 \\
IV.14 Applications of Stochastic Analysis / 319 \\
IV.15 Inverse Problems / 327 \\
IV.16 Computational Science / 335 \\
IV.17 Data Mining and Analysis / 350 \\
IV.18 Network Analysis / 360 \\
IV.19 Classical Mechanics / 374 \\
IV.20 Dynamical Systems / 383 \\
IV.21 Bifurcation Theory / 393 \\
IV.22 Symmetry in Applied Mathematics / 402 \\
IV.23 Quantum Mechanics / 411 \\
IV.24 Random-Matrix Theory / 419 \\
IV.25 Kinetic Theory / 428 \\
IV.26 Continuum Mechanics / 446 \\
IV.27 Pattern Formation / 458 \\
IV.28 Fluid Dynamics / 467 \\
IV.29 Magnetohydrodynamics / 476 \\
IV.30 Earth System Dynamics / 485 \\
IV.31 Effective Medium Theories / 500 \\
IV.32 Mechanics of Solids / 505 \\
IV.33 Soft Matter / 516 \\
IV.34 Control Theory / 523 \\
IV.35 Signal Processing / 533 \\
IV.36 Information Theory / 545 \\
IV.37 Applied Combinatorics and Graph Theory / 552 \\
IV.38 Combinatorial Optimization / 564 \\
IV.39 Algebraic Geometry / 570 \\
IV.40 General Relativity and Cosmology / 579 \\
Part V: Modeling \\
V.1 The Mathematics of Adaptation (Or the Ten Avatars
of Vishnu) / 591 \\
V.2 Sport / 598 \\
V.3 Inerters / 604 \\
V.4 Mathematical Biomechanics / 609 \\
V.5 Mathematical Physiology / 616 \\
V.6 Cardiac Modeling / 623 \\
V.7 Chemical Reactions / 627 \\
V.8 Divergent Series: Taming the Tails / 634 \\
V.9 Financial Mathematics / 640 \\
V.10 Portfolio Theory / 648 \\
V.11 Bayesian Inference in Applied Mathematics / 658
\\
V.12 A Symmetric Framework with Many Applications / 661
\\
V.13 Granular Flows / 665 \\
V.14 Modern Optics / 673 \\
V.15 Numerical Relativity / 680 \\
V.16 The Spread of Infectious Diseases / 687 \\
V.17 The Mathematics of Sea Ice / 694 \\
V.18 Numerical Weather Prediction / 705 \\
V.19 Tsunami Modeling / 712 \\
V.20 Shock Waves / 720 \\
V.21 Turbulence / 724 \\
Part VI: Example Problems \\
VI.1 Cloaking / 733 \\
VI.2 Bubbles / 735 \\
VI.3 Foams / 737 \\
VI.4 Inverted Pendulums / 741 \\
VI.5 Insect Flight / 743 \\
VI.6 The Flight of a Golf Ball / 746 \\
VI.7 Automatic Differentiation / 749 \\
VI.8 Knotting and Linking of Macromolecules / 752 \\
VI.9 Ranking Web Pages / 755 \\
VI.10 Searching a Graph / 757 \\
VI.11 Evaluating Elementary Functions / 759 \\
VI.12 Random Number Generation / 761 \\
VI.13 Optimal Sensor Location in the Control of
Energy-Efficient Buildings / 763 \\
VI.14 Robotics / 767 \\
VI.15 Slipping, Sliding, Rattling, and Impact:
Nonsmooth Dynamics and Its Applications / 769 \\
VI.16 From the $N$-Body Problem to Astronomy and Dark
Matter / 771 \\
VI.17 The $N$-Body Problem and the Fast Multipole
Method / 775 \\
VI.18 The Traveling Salesman Problem / 778 \\
Part VII: Application Areas \\
VII.1 Aircraft Noise / 783 \\
VII.2 A Hybrid Symbolic--Numeric Approach to Geometry
Processing and Modeling / 787 \\
VII.3 Computer-Aided Proofs via Interval Analysis / 790
\\
VII.4 Applications of Max-Plus Algebra / 795 \\
VII.5 Evolving Social Networks, Attitudes, and Beliefs
--- and Counterterrorism / 800 \\
VII.6 Chip Design / 804 \\
VII.7 Color Spaces and Digital Imaging / 808 \\
VII.8 Mathematical Image Processing / 813 \\
VII.9 Medical Imaging / 816 \\
VII.10 Compressed Sensing / 823 \\
VII.11 Programming Languages: An Applied Mathematics
View / 828 \\
VII.12 High-Performance Computing / 839 \\
VII.13 Visualization / 843 \\
VII.14 Electronic Structure Calculations (Solid State
Physics) / 847 \\
VII.15 Flame Propagation / 852 \\
VII.16 Imaging the Earth Using Green's Theorem / 857
\\
VII.17 Radar Imaging / 860 \\
VII.18 Modeling a Pregnancy Testing Kit / 864 \\
VII.19 Airport Baggage Screening with X-Ray Tomography
/ 866 \\
VII.20 Mathematical Economics / 868 \\
VII.21 Mathematical Neuroscience / 873 \\
VII.22 Systems Biology / 879 \\
VII.23 Communication Networks / 883 \\
VII.24 Text Mining / 887 \\
VII.25 Voting Systems / 891 \\
Part VIII: Final Perspectives \\
VIII.1 Mathematical Writing / 897 \\
VIII.2 How to Read and Understand a Paper / 903 \\
VIII.3 How to Write a General Interest Mathematics Book
/ 906 \\
VIII.4 Workflow / 912 \\
VIII.5 Reproducible Research in the Mathematical
Sciences / 916 \\
VIII.6 Experimental Applied Mathematics / 925 \\
VIII.7 Teaching Applied Mathematics / 933 \\
VIII.8 Mediated Mathematics: Representations of
Mathematics in Popular Culture and Why These Matter /
943 \\
VIII.9 Mathematics and Policy / 953 \\
Index / 963",
}
@Proceedings{Muller:2015:ISC,
editor = "Jean-Michel Muller and Arnaud Tisserand and Julio
Villalba",
booktitle = "{2015 IEEE 22nd Symposium on Computer Arithmetic
(ARITH 2015) Lyon, France, 22--24 June 2015}",
title = "{2015 IEEE 22nd Symposium on Computer Arithmetic
(ARITH 2015) Lyon, France, 22--24 June 2015}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 176",
year = "2015",
ISBN = "1-4799-8665-8, 1-4799-8663-1",
ISBN-13 = "978-1-4799-8665-1, 978-1-4799-8663-7",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2015",
bibdate = "Sat Aug 01 08:03:11 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7193754",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic units; correctness proofs;
cryptography; domain specific designs; error analysis;
exascale computing; floating point arithmetic;
floating-point error analysis; formal verification;
function approximation; modular arithmetic; theorem
proving; verification",
}
@Proceedings{Greuel:2016:MSI,
editor = "Gert-Martin Greuel",
booktitle = "{Mathematical Software --- ICMS 2016: 5th
International Conference, Berlin, Germany, July 11--14,
2016: proceedings}",
title = "{Mathematical Software --- ICMS 2016: 5th
International Conference, Berlin, Germany, July 11--14,
2016: proceedings}",
volume = "9725",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiv + 532",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-42432-3",
ISBN = "3-319-42431-9 (print), 3-319-42432-7 (electronic)",
ISBN-13 = "978-3-319-42431-6 (print), 978-3-319-42432-3
(electronic)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.9.M35",
bibdate = "Mon Feb 5 08:28:37 MST 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = ser-LNCS # "\slash " # ser-LNAI,
URL = "http://zbmath.org/?q=an:1342.68017",
abstract = "This book constitutes the proceedings of the 5th
International Conference on Mathematical Software, ICMS
2015, held in Berlin, Germany, in July 2016. The 68
papers included in this volume were carefully reviewed
and selected from numerous submissions. The papers are
organized in topical sections named: univalent
foundations and proof assistants; software for
mathematical reasoning and applications; algebraic and
toric geometry; algebraic geometry in applications;
software of polynomial systems; software for
numerically solving polynomial systems; high-precision
arithmetic, effective analysis, and special functions;
mathematical optimization; interactive operation to
scientific artwork and mathematical reasoning;
information services for mathematics: software,
services, models, and data; semDML: towards a semantic
layer of a world digital mathematical library;
miscellanea.",
acknowledgement = ack-nhfb,
}
@Proceedings{Montuschi:2016:ISC,
editor = "Paolo Montuschi and Michael Schulte and Javier Hormigo
and Stuart Oberman and Nathalie Revol",
booktitle = "{2016 IEEE 23nd Symposium on Computer Arithmetic
(ARITH 2016), Santa Clara, California, USA, 10--13 July
2016}",
title = "{2016 IEEE 23nd Symposium on Computer Arithmetic
(ARITH 2016), Santa Clara, California, USA, 10--13 July
2016}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxi + 182",
year = "2016",
ISBN = "1-5090-1615-5",
ISBN-13 = "978-1-5090-1615-0",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2016",
bibdate = "Fri Dec 16 15:16:45 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7562813",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic units; correctness proofs;
cryptography; domain specific designs; error analysis;
exascale computing; floating point arithmetic;
floating-point error analysis; formal verification;
function approximation; modular arithmetic; theorem
proving; verification",
}
@Proceedings{Burgess:2017:ISC,
editor = "Neil Burgess and Javier Bruguera and Florent de
Dinechin",
booktitle = "{24th IEEE Symposium on Computer Arithmetic (ARITH
24), London, UK, 24--26 July 2017}",
title = "{2017 IEEE 24th Symposium on Computer Arithmetic
(ARITH 24), London, UK, 24--26 July 2017}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 198",
year = "2017",
ISBN = "1-5386-1966-0 (print), 1-5386-1965-2, 1-5386-1964-4",
ISBN-13 = "978-1-5386-1966-7 (print), 978-1-5386-1965-0,
978-1-5386-1964-3",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2017",
bibdate = "Fri Nov 17 10:14:11 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8019911",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic units; correctness proofs;
cryptography; domain specific designs; error analysis;
exascale computing; floating point arithmetic;
floating-point error analysis; formal verification;
function approximation; modular arithmetic; theorem
proving; verification",
}
@Proceedings{Tenca:2018:PIS,
editor = "Alexandre Tenca and Naofumi Takagi",
booktitle = "Proceedings of the {25th International Symposium on
Computer Arithmetic, 25--27 June 2018 Amherst, MA,
USA}",
title = "Proceedings of the {25th International Symposium on
Computer Arithmetic, 25--27 June 2018 Amherst, MA,
USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "17 + 152",
month = jun,
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464697",
ISBN = "1-5386-2612-8 (USB), 1-5386-2665-9",
ISBN-13 = "978-1-5386-2612-2 (USB), 978-1-5386-2613-9,
978-1-5386-2665-8",
ISSN = "2576-2265",
LCCN = "QA76.9.C62",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number CFP18121-USB.",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
subject = "ARITH-25; Computer arithmetic; Congresses; Computer
programming; Floating-point arithmetic; Computer
arithmetic and logic units",
}
@Proceedings{Takagi:2019:ISC,
editor = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
booktitle = "{2019 IEEE 26th Symposium on Computer Arithmetic
ARITH-26 (2019), Kyoto, Japan, 10--12 June 2019}",
title = "{2019 IEEE 26th Symposium on Computer Arithmetic
ARITH-26 (2019), Kyoto, Japan, 10--12 June 2019}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "15 + 220",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00001",
ISBN = "1-72813-366-1",
ISBN-13 = "978-1-72813-366-9",
ISSN = "1063-6889",
ISSN-L = "1063-6889",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@Proceedings{Bigatti:2020:MSI,
editor = "Anna Maria Bigatti and Jacques Carette and James H.
Davenport and Michael Joswig and Timo de Wolff",
booktitle = "Mathematical Software --- {ICMS 2020: 7th
International Conference, Braunschweig, Germany, July
13--16, 2020, Proceedings}",
title = "Mathematical Software --- {ICMS 2020: 7th
International Conference, Braunschweig, Germany, July
13--16, 2020, Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiii + 494",
year = "2020",
DOI = "https://doi.org/10.1007/978-3-030-52200-1",
bibdate = "Sat Sep 23 06:50:01 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/julia.bib;
https://www.math.utah.edu/pub/tex/bib/macaulay2.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib;
https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Front Matter / / i--xxiii \\
Gr{\"o}bner Bases in Theory and Practice \\
Front Matter / / 1--1 A Design and an Implementation of
an Inverse Kinematics Computation in Robotics Using
Gr{\"o}bner Bases / Noriyuki Horigome, Akira Terui,
Masahiko Mikawa / 3--13 \\
Real Algebraic Geometry \\
Front Matter / / 15--15 \\
Curtains in CAD: Why Are They a Problem and How Do We
Fix Them? / Akshar Nair, James Davenport, Gregory
Sankaran / 17--26 \\
Chordality Preserving Incremental Triangular
Decomposition and Its Implementation / Changbo Chen /
27--36 \\
Algebraic Geometry via Numerical Computation \\
Front Matter / / 37--37 \\
$\mathbb{Q}(\sqrt{-3})$-Integral Points on a Mordell
Curve / Francesca Bianchi / 39--50 \\
A Numerical Approach for Computing Euler
Characteristics of Affine Varieties / Xiaxin Li, Jose
Israel Rodriguez, Botong Wang / 51--60 \\
Evaluating and Differentiating a Polynomial Using a
Pseudo-witness Set / Jonathan D. Hauenstein, Margaret
H. Regan / 61--69 \\
Computational Algebraic Analysis \\
Front Matter / / 71--71 \\
Algorithms for Pfaffian Systems and Cohomology
Intersection Numbers of Hypergeometric Integrals /
Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama / 73--84
\\
Software for Number Theory and Arithmetic Geometry \\
Front Matter / / 85--85 \\
Computations with Algebraic Surfaces / Andreas-Stephan
Elsenhans, J{\"o}rg Jahnel / 87--93 \\
Evaluating Fractional Derivatives of the Riemann Zeta
Function / Ricky E. Farr, Sebastian Pauli, Filip Saidak
/ 94--101 \\
Groups and Group Actions \\
Front Matter / / 103--103 \\
Towards Efficient Normalizers of Primitive Groups /
Sergio Siccha / 105--114 \\
Homomorphic Encryption and Some Black Box Attacks /
Alexandre Borovik, {\c{S}}{\"u}kr{\"u}
Yal{\c{c}}{\i}nkaya / 115--124 \\
Nilpotent Quotients of Associative
$\mathbb{Z}$-Algebras and Augmentation Quotients of
Baumslag--Solitar Groups / Tobias Moede / 125--130 \\
The GAP Package LiePRing / Bettina Eick, Michael
Vaughan-Lee / 131--140 \\
The Classification Problem in Geometry \\
Front Matter / / 141--141 \\
Classifying Simplicial Dissections of Convex Polyhedra
with Symmetry / Anton Betten, Tarun Mukthineni /
143--152 \\
Classification Results for Hyperovals of Generalized
Quadrangles / Bart De Bruyn / 153--161 \\
Isomorphism and Invariants of Parallelisms of
Projective Spaces / Svetlana Topalova, Stela Zhelezova
/ 162--172 \\
Classification of Linear Codes by Extending Their
Residuals / Stefka Bouyuklieva, Iliya Bouyukliev /
173--180 \\
The Program Generation in the Software Package
QextNewEdition / Iliya Bouyukliev / 181--189 \\
Polyhedral Methods in Geometry and Optimization \\
Front Matter / / 191--191 \\
Algebraic Polytopes in Normaliz / Winfried Bruns /
193--201 \\
Real Tropical Hyperfaces by Patchworking in polymake /
Michael Joswig, Paul Vater / 202--211 \\
Practical Volume Estimation of Zonotopes by a New
Annealing Schedule for Cooling Convex Bodies /
Apostolos Chalkis, Ioannis Z. Emiris, Vissarion
Fisikopoulos / 212--221 \\
Slack Ideals in Macaulay2 / Antonio Macchia, Amy Wiebe
/ 222--231 \\
Hyperplane Arrangements in polymake / Lars Kastner,
Marta Panizzut / 232--240 \\
A Convex Programming Approach to Solve Posynomial
Systems / Marianne Akian, Xavier Allamigeon, Marin
Boyet, St{\'e}phane Gaubert / 241--250 \\
Univalent Mathematics: Theory and Implementation \\
Front Matter / / 251--251 \\
Equality Checking for General Type Theories in
Andromeda 2 / Andrej Bauer, Philipp G. Haselwarter,
Anja Petkovi / 253--259 \\
Artificial Intelligence and Mathematical Software \\
Front Matter / / 261--261 \\
GeoLogic --- Graphical Interactive Theorem Prover for
Euclidean Geometry / Miroslav Ol{\v{s}}{\'a}k /
263--271 \\
A Formalization of Properties of Continuous Functions
on Closed Intervals / Yaoshun Fu, Wensheng Yu /
272--280 \\
Variable Ordering Selection for Cylindrical Algebraic
Decomposition with Artificial Neural Networks / Changbo
Chen, Zhangpeng Zhu, Haoyu Chi / 281--291 \\
Applying Machine Learning to Heuristics for Real
Polynomial Constraint Solving / Christopher W. Brown,
Glenn Christopher Daves / 292--301 \\
A Machine Learning Based Software Pipeline to Pick the
Variable Ordering for Algorithms with Polynomial Inputs
/ Dorian Florescu, Matthew England / 302--311 \\
Databases in Mathematics \\
Front Matter / / 313--313 \\
FunGrim: A Symbolic Library for Special Functions /
Fredrik Johansson / 315--323 \\
Accelerating Innovation Speed in Mathematics by Trading
Mathematical Research Data \\
Front Matter / / 325--325 \\
Operational Research Literature as a Use Case for the
Open Research Knowledge Graph / Mila Runnwerth, Markus
Stocker, S{\"o}ren Auer / 327--334 \\
Making Presentation Math Computable: Proposing a
Context Sensitive Approach for Translating {\LaTeX} to
Computer Algebra Systems / Andr{\'e} Greiner-Petter,
Moritz Schubotz, Akiko Aizawa, Bela Gipp / 335--341 \\
Employing C++ Templates in the Design of a Computer
Algebra Library / Alexander Brandt, Robert H. C. Moir,
Marc Moreno Maza / 342--352 \\
Mathematical World Knowledge Contained in the
Multilingual Wikipedia Project / Dennis Tobias Halbach
/ 353--361 \\
Archiving and Referencing Source Code with Software
Heritage / Roberto Di Cosmo / 362--373 \\
The Jupyter Environment for Computational Mathematics
\\
Front Matter / / 375--375 \\
Polymake.jl: A New Interface to polymake / Marek
Kaluba, Benjamin Lorenz, Sascha Timme / 377--385 \\
Web Based Notebooks for Teaching, an Experience at
Universidad de Zaragoza / Miguel Angel Marco Buzunariz
/ 386--392 \\
Phase Portraits of Bi-dimensional Zeta Values / Olivier
Bouillot / 393--405 \\
Prototyping Controlled Mathematical Languages in
Jupyter Notebooks / Jan Frederik Schaefer, Kai Amann,
Michael Kohlhase / 406--415 \\
General Session \\
Front Matter / / 417--417 \\
Method to Create Multiple Choice Exercises for Computer
Algebra System / Tatsuyoshi Hamada, Yoshiyuki Nakagawa,
Makoto Tamura / 419--425 \\
A Flow-Based Programming Environment for Geometrical
Construction / Kento Nakamura, Kazushi Ahara / 426--431
\\
MORLAB --- A Model Order Reduction Framework in MATLAB
and Octave / Peter Benner, Steffen W. R. Werner /
432--441 \\
FlexRiLoG --- A SageMath Package for Motions of Graphs
/ Georg Grasegger, Jan Legersk{\'y} / 442--450 \\
Markov Transition Matrix Analysis of Mathematical
Expression Input Models / Francis Quinby, Seyeon Kim,
Sohee Kang, Marco Pollanen, Michael G. Reynolds, Wesley
S. Burr / 451--461 \\
Certifying Irreducibility in $\mathbb{Z}[ ]$ / John
Abbott / 462--472 \\
A Content Dictionary for In-Object Comments / Lars
Hellstr{\"o}m / 473--481 \\
Implementing the Tangent Graeffe Root Finding Method /
Joris van der Hoeven, Michael Monagan / 482--492 \\
Back Matter / / 493--494",
}
@Proceedings{Cornea:2020:ISC,
editor = "Marius Cornea and Weiqiang Liu and Arnaud Tisserand",
booktitle = "{2020 27th IEEE Symposium on Computer Arithmetic:
ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
June 2020}",
title = "{2020 27th IEEE Symposium on Computer Arithmetic:
ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
June 2020}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020",
ISBN = "1-72817-120-2, 1-72817-121-0",
ISBN-13 = "978-1-72817-120-3, 978-1-72817-121-0",
LCCN = "????",
bibdate = "Wed Jul 7 06:23:45 MDT 2021",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/servlet/opac?punumber=9146973",
acknowledgement = ack-nhfb,
}
@Book{Ismail:2020:ESF,
editor = "Mourad H. Ismail and Walter Van Assche",
booktitle = "Encyclopedia of Special Functions: the {Askey--Bateman
Project}. Volume 1, Univariate Orthogonal Polynomials",
title = "Encyclopedia of Special Functions: the {Askey--Bateman
Project}. Volume 1, Univariate Orthogonal Polynomials",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiv + 388",
year = "2020",
DOI = "https://doi.org/10.1017/9780511979156",
ISBN = "0-511-97915-0 (e-book), 0-521-19742-2 (hardcover),
1-108-76433-9 (e-book)",
ISBN-13 = "978-0-511-97915-6 (e-book), 978-0-521-19742-7
(hardcover), 978-1-108-76433-9 (e-book)",
LCCN = "QA351 .E63 2020",
bibdate = "Fri Nov 10 17:02:40 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This is the first of three volumes that form the
Encyclopedia of Special Functions, an extensive update
of the Bateman Manuscript Project. Volume 1 contains
most of the material on orthogonal polynomials, from
the classical orthogonal polynomials of Hermite,
Laguerre and Jacobi to the Askey--Wilson polynomials,
which are the most general basic hypergeometric
orthogonal polynomials. Separate chapters cover
orthogonal polynomials on the unit circle, zeros of
orthogonal polynomials and matrix orthogonal
polynomials, with detailed results about matrix-valued
Jacobi polynomials. A chapter on moment problems
provides many examples of indeterminate moment
problems. A thorough bibliography rounds off what will
be an essential reference.",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Encyclopedias; Fonctions
sp{\'e}ciales; Encyclop{\'e}dies; Functions, Special",
tableofcontents = "Frontmatter / i--iv \\
Contents / v--viii \\
Contributors / ix--x \\
Preface / xi--xiv \\
1: Preliminaries / Mourad E. H. Ismail / 1--15 \\
2: General Orthogonal Polynomials / Mourad E. H. Ismail
/ 16--50 \\
3: Jacobi and Related Polynomials / Mourad E. H. Ismail
/ 51--99 \\
4: Recursively Defined Polynomials / Mourad E. H.
Ismail / 100--118 \\
5: Wilson and Related Polynomials / Mourad E. H. Ismail
/ 119--128 \\
6: Discrete Orthogonal Polynomials / Mourad E. H.
Ismail / 129--156 \\
7: Some $q$-Orthogonal Polynomials / Mourad E. H.
Ismail / 157--177 \\
8: The Askey--Wilson Family of Polynomials / Mourad E.
H. Ismail / 178--198 \\
9: Orthogonal Polynomials on the Unit Circle / Leonid
Golinskii / 199--241 \\
10: Zeros of Orthogonal Polynomials / Andrea Laforgia
and Martin E. Muldoon / 242--268 \\
11: The Moment Problem / Christian Berg and Jacob S.
Christiansen / 269--306 \\
12: Matrix--Valued Orthogonal Polynomials and
Differential Equations / Antonio J. Dur{\'a}n and F.
Alberto Gr{\"u}nbaum / 307--333 \\
13: Some Families of Matrix--Valued Jacobi Orthogonal
Polynomials / F. Alberto Gr{\"u}nbaum, I. Pacharoni and
J. A. Tirao / 334--356 \\
References / 357--384 \\
Index / 385--388",
}
@Book{Koornwinder:2020:ESF,
editor = "T. H. Koornwinder and Jasper V. Stokman",
booktitle = "Encyclopedia of Special Functions: the {Askey--Bateman
Project}. Volume 2. Multivariable Special Functions",
title = "Encyclopedia of Special Functions: the {Askey--Bateman
Project}. Volume 2. Multivariable Special Functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xii + 427",
year = "2020",
DOI = "https://doi.org/10.1017/9780511777165",
ISBN = "0-511-77716-7 (e-book), 1-107-00373-3 (hardcover)",
ISBN-13 = "978-0-511-77716-5 (e-book), 978-1-107-00373-6
(hardcover)",
LCCN = "QA351 .E63 2021",
bibdate = "Fri Nov 10 17:39:45 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Frontmatter / i--iv \\
Contents / v--viii \\
List of Contributors / ix--x \\
Preface / xi--xii \\
1: General Overview of Multivariable Special Functions
/ T. H. Koornwinder, J. V. Stokman / 1--18 \\
2: Orthogonal Polynomials of Several Variables / Yuan
Xu / 19--78 \\
3: Appell and Lauricella Hypergeometric Functions / K.
Matsumoto / 79--100 \\
4: A-Hypergeometric Functions / N. Takayama / 101--121
\\
5: Hypergeometric and Basic Hypergeometric Series and
Integrals Associated with Root Systems / M. J.
Schlosser / 122--158 \\
6: Elliptic Hypergeometric Functions Associated with
Root Systems / H. Rosengren, S. O. Warnaar / 159--186
\\
7: Dunkl Operators and Related Special Functions / C.
F. Dunkl / 187--216 \\
8: Jacobi Polynomials and Hypergeometric Functions
Associated with Root Systems / G. J. Heckman, E. M.
Opdam / 217--257 \\
9: Macdonald--Koornwinder Polynomials / J. V. Stokman /
258--313 \\
10: Combinatorial Aspects of Macdonald and Related
Polynomials / J. Haglund / 314--367 \\
11: Knizhnik--Zamolodchikov-Type Equations, Selberg
Integrals and Related Special Functions / V. Tarasov,
A. Varchenko / 368--401 \\
12: $9 j$--Coefficients and Higher / J. Van der Jeugt /
402--419 \\
Index / 420--428",
}
@Proceedings{IEEE:2021:ISC,
editor = "{IEEE}",
booktitle = "{2021 IEEE 28th Symposium on Computer Arithmetic:
ARITH 2021: virtual conference, 14--16 June 2021:
proceedings}",
title = "{2021 IEEE 28th Symposium on Computer Arithmetic:
ARITH 2021: virtual conference, 14--16 June 2021:
proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021",
ISBN = "1-66542-293-9 (print), 1-66544-648-X (e-book)",
ISBN-13 = "978-1-66542-293-2 (print), 978-1-66544-648-8
(e-book)",
LCCN = "????",
bibdate = "Thu Sep 21 10:36:52 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
meetingname = "IEEE International Symposium on Computer Arithmetic
28. 2021",
remark = "The 28th IEEE Symposium on Computer Arithmetic ---
ARITH 2021 --- originally scheduled in Turin, Italy, is
held in June 2021 as a virtual conference due to the
uncertainty of the world health and travel situation.",
}
@Proceedings{IEEE:2022:ISC,
editor = "{IEEE}",
booktitle = "{2022 IEEE 29th Symposium on Computer Arithmetic:
ARITH 2022: virtual conference, 12--14 September 2022:
proceedings}",
title = "{2022 IEEE 29th Symposium on Computer Arithmetic:
ARITH 2022: virtual conference, 12--14 September 2022:
proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022",
ISBN = "1-66547-827-6, 1-66547-828-4",
ISBN-13 = "978-1-66547-827-4, 978-1-66547-828-1",
LCCN = "????",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
meetingname = "IEEE Symposium on Computer Arithmetic 29. 2022",
}
@Proceedings{IEEE:2023:PIS,
editor = "{IEEE}",
booktitle = "Proceedings: {2023 IEEE 30th Symposium on Computer
Arithmetic: ARITH 2023, 4--6 September 2023 Portland,
United States}",
title = "Proceedings: {2023 IEEE 30th Symposium on Computer
Arithmetic: ARITH 2023, 4--6 September 2023 Portland,
United States}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "167",
year = "2023",
ISBN-13 = "979-83-503-1923-1 (print), 979-83-503-1922-4
(electronic)",
LCCN = "????",
bibdate = "Wed May 08 09:18:10 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30",
}
