index from slatec 2. intrinsic functions and fundamental functions sngl. dble. name notation prec. prec. complex unpack floating point call number r9upak(x,y,n) d9upak -- pack floating point r9pak(y,n) d9pak -- number initialize orthogonal inits(os,nos,eta) initds -- polynomial series evaluate chebyshev summation for csevl(x,cs,n) dcsevl -- series i = 1 to n of cs(i)*(2*x)**(i-1) 3. elementary functions sngl. dble. name notation prec. prec. complex argument = theta in z = \ z \ * -- -- carg(z) radians e**(i * theta) cube root cbrt(x) dcbrt ccbrt relative error exponen- ((e**x) -1) / x exprel(x) dexprl cexprl tial from first order common logarithm log to the base 10 -- -- clog10( of z relative error logarithm ln(1 + x) alnrel(x) dlnrel clnrel relative error logarithm (ln(1 + x) - x r9ln2r(x) d9ln2r c9ln2r from second order of + x**2/2) / x**3 expansion 4. trigonometric and hyperbolic functions sngl. dble. name notation prec. prec. complex tangent tan z -- -- ctan(z) cotangent cot x cot(x) dcot ccot sine x in degrees sin ((2 * pi * x) sindg(x) dsindg -- / 360) cosine x in degrees cos ((2 * pi * x) cosdg(x) dcosdg -- / 360) arc sine arcsin (z) -- -- casin(z arc cosine arccos (z) -- -- cacos(z arc tangent arctan (z) -- -- catan(z quadrant correct arctan (sin(z) / -- -- catan2( arc tangent cos(z)) hyperbolic sine sinh x sinh(x) dsinh csinh hyperbolic cosine cosh x cosh(x) dcosh ccosh hyperbolic tangent tanh x tanh(x) dtanh ctanh arc hyperbolic sine arcsinh (x) asinh(x) dasinh casinh arc hyperbolic cosine arccosh (x) acosh(x) dacosh cacosh arc hyperbolic tangent arctanh (x) atanh(x) datanh catanh relative error arc (arctan (x) - x) r9atn1(x) d9atn1 -- tangent from first order / x**3 5. exponential integrals and related functions sngl. dble. name notation prec. prec. complex exponential integral ei(x) = ei(x) dei -- the integral from -x to infinity of (e**-t / t)dt exponential integral e sub 1 (x) = e1(x) de1 -- the integral from x to infinity of (e**-t / t) dt logarithmic integral li(x) = the ali(x) dli -- integral from 0 to x of (1 / ln t) dt 6. gamma functions and related functions sngl. dble. name notation prec. prec. complex factorial n! fac(n) dfac -- binomial n! / (m! * (n-m)!) binom(n,m) dbinom -- gamma gamma(x) gamma(x) dgamma cgamma gamma(x) under and call overflow limits gamlim(xmin,xmax) dgamlm -- reciprocal gamma 1 / gamma(x) gamr(x) dgamr cgamr log abs gamma ln \gamma(x)\ alngam(x) dlngam -- log gamma ln gamma(z) -- -- clngam log abs gamma g = ln \gamma(x)\ call with sign of gamma s = sign gamma(x) algams(x,g,s) dlgams -- incomplete gamma gamma(a,x) = gami(a,x) dgami -- the integral from 0 to x of (t**(a-1) * e**-t)dt complementary gamma(a,x) = gamic(a,x) dgamic -- incomplete gamma the integral from x to infinity of (t**(a-1) * e**-t)dt tricomi's gamma super star(a,x) gamit(a,x) dgamit -- incomplete gamma = x**-a * incomplete gamma(a,x) / gamma(a) psi (digamma) psi(x) = gamma'(x) psi(x) dpsi cpsi / gamma(x) pochhammer's (a) sub x = gamma(a+x) poch(a,x) dpoch -- generalized symbol / gamma(a) pochhammer's symbol ((a) sub x -1) / x poch1(a,x) dpoch1 -- from first order beta b(a,b) = (gamma(a) beta(a,b) dbeta cbeta * gamma(b)) / gamma(a+b) = the integral from 0 to 1 of (t**(a-1) * (1-t)**(b-1))dt log beta ln b(a,b) albeta(a,b) dlbeta clbeta incomplete beta i sub x (a,b) = betai(x,a,b) dbetai __ b sub x (a,b) / b(a,b) = 1 / b(a,b) * the integral from 0 to x of (t**(a-1) * (1-t)**(b-1))dt log gamma correction ln gamma(x) - r9lgmc(x) d9lgmc c9lgmc term when stirling's (ln(2 * pi))/2 - approximation is valid (x - 1/2) * ln(x) + x 7. error functions and fresnel integrals sngl. dble. name notation prec. prec. complex error function erf x = (2 / erf(x) derf -- square root of pi) * the integral from 0 to x of e**(-t**2)dt complementary erfc x = (2 / erfc(x) derfc -- error function square root of pi) * the integral from x to infinity of e**(-t**2)dt dawson's function f(x) = e**(-x**2) daws(x) ddaws -- * the integral from from 0 to x of e**(t**2)dt 9. bessel functions sngl. dble. name notation prec. prec. complex bessel functions of special integer order first kind, order zero j sub 0 (x) besj0(x) dbesj0 -- first kind, order one j sub 1 (x) besj1(x) dbesj1 -- second kind, order zero y sub 0 (x) besy0(x) dbesy0 -- second kind, order one y sub 1 (x) besy1(x) dbesy1 -- modified (hyperbolic) bessel functions of special integer order first kind, order zero i sub 0 (x) besi0(x) dbesi0 -- first kind, order one i sub 1 (x) besi1(x) dbesi1 -- third kind, order zero k sub 0 (x) besk0(x) dbesk0 -- third kind, order one k sub 1 (x) besk1(x) dbesk1 -- modified (hyperbolic) bessel functions of special integer order scaled by an exponential first kind, order zero e**-\x\ * i sub 0(x) besi0e(x) dbsi0e -- first kind, order one e**-\x\ * i sub 1(x) besi1e(x) dbsi1e -- third kind, order zero e**x * k sub 0 (x) besk0e(x) dbsk0e -- third kind, order one e**x * k sub 1 (x) besk1e(x) dbsk1e -- sequences of bessel functions. \n\ values are computed where i = 0, 1, 2, ..., n-1 for n > 0 or i = 0, -1, -2, ..., n+1 for n < 0. modified third kind k sub v+i (x) call besks( dbesks -- xnu,x,n,bk) sequences of bessel functions scaled by an exponential. \n\ values are computed where i = 0, 1, 2, ..., n-1 for n > 0 or i = 0, -1, -2, ..., n+1 for n < 0. modified third kind e**x * call k sub v+i (x) beskes( dbskes -- xnu,x,n,bk) 10. bessel functions of fractional order sngl. dble. name notation prec. prec. complex airy functions airy ai(x) ai(x) dai -- bairy bi(x) bi(x) dbi -- exponentially scaled airy functions airy ai(x), x <= 0 aie(x) daie -- exp(2/3 * x**(3/2)) * ai(x), x >= 0 bairy bi(x), x <= 0 bie(x) dbie -- exp(-2/3 * x**(3/2)) * bi(x), x >= 0 13. confluent hypergeometric functions sngl. dble. name notation prec. prec. complex confluent u(a,b,x) chu(a,b,x) dchu -- hypergeometric 27. miscellaneous functions sngl. dble. name notation prec. prec. complex spence s(x) = - the spenc(x) dspenc -- dilogarithm integral from 0 to x of ((ln \1-y\) / y)dy ***end prologue fnlibd ***first executable statement fnlibd return end