*DECK BESI1E
FUNCTION BESI1E (X)
C***BEGIN PROLOGUE BESI1E
C***PURPOSE Compute the exponentially scaled modified (hyperbolic)
C Bessel function of the first kind of order one.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY C10B1
C***TYPE SINGLE PRECISION (BESI1E-S, DBSI1E-D)
C***KEYWORDS EXPONENTIALLY SCALED, FIRST KIND, FNLIB,
C HYPERBOLIC BESSEL FUNCTION, MODIFIED BESSEL FUNCTION,
C ORDER ONE, SPECIAL FUNCTIONS
C***AUTHOR Fullerton, W., (LANL)
C***DESCRIPTION
C
C BESI1E(X) calculates the exponentially scaled modified (hyperbolic)
C Bessel function of the first kind of order one for real argument X;
C i.e., EXP(-ABS(X))*I1(X).
C
C Series for BI1 on the interval 0. to 9.00000D+00
C with weighted error 2.40E-17
C log weighted error 16.62
C significant figures required 16.23
C decimal places required 17.14
C
C Series for AI1 on the interval 1.25000D-01 to 3.33333D-01
C with weighted error 6.98E-17
C log weighted error 16.16
C significant figures required 14.53
C decimal places required 16.82
C
C Series for AI12 on the interval 0. to 1.25000D-01
C with weighted error 3.55E-17
C log weighted error 16.45
C significant figures required 14.69
C decimal places required 17.12
C
C***REFERENCES (NONE)
C***ROUTINES CALLED CSEVL, INITS, R1MACH, XERMSG
C***REVISION HISTORY (YYMMDD)
C 770401 DATE WRITTEN
C 890210 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920618 Removed space from variable names. (RWC, WRB)
C***END PROLOGUE BESI1E
DIMENSION BI1CS(11), AI1CS(21), AI12CS(22)
LOGICAL FIRST
SAVE BI1CS, AI1CS, AI12CS, NTI1, NTAI1, NTAI12, XMIN, XSML, FIRST
DATA BI1CS( 1) / -.0019717132 61099859E0 /
DATA BI1CS( 2) / .4073488766 7546481E0 /
DATA BI1CS( 3) / .0348389942 99959456E0 /
DATA BI1CS( 4) / .0015453945 56300123E0 /
DATA BI1CS( 5) / .0000418885 21098377E0 /
DATA BI1CS( 6) / .0000007649 02676483E0 /
DATA BI1CS( 7) / .0000000100 42493924E0 /
DATA BI1CS( 8) / .0000000000 99322077E0 /
DATA BI1CS( 9) / .0000000000 00766380E0 /
DATA BI1CS(10) / .0000000000 00004741E0 /
DATA BI1CS(11) / .0000000000 00000024E0 /
DATA AI1CS( 1) / -.0284674418 1881479E0 /
DATA AI1CS( 2) / -.0192295323 1443221E0 /
DATA AI1CS( 3) / -.0006115185 8579437E0 /
DATA AI1CS( 4) / -.0000206997 1253350E0 /
DATA AI1CS( 5) / .0000085856 1914581E0 /
DATA AI1CS( 6) / .0000010494 9824671E0 /
DATA AI1CS( 7) / -.0000002918 3389184E0 /
DATA AI1CS( 8) / -.0000000155 9378146E0 /
DATA AI1CS( 9) / .0000000131 8012367E0 /
DATA AI1CS(10) / -.0000000014 4842341E0 /
DATA AI1CS(11) / -.0000000002 9085122E0 /
DATA AI1CS(12) / .0000000001 2663889E0 /
DATA AI1CS(13) / -.0000000000 1664947E0 /
DATA AI1CS(14) / -.0000000000 0166665E0 /
DATA AI1CS(15) / .0000000000 0124260E0 /
DATA AI1CS(16) / -.0000000000 0027315E0 /
DATA AI1CS(17) / .0000000000 0002023E0 /
DATA AI1CS(18) / .0000000000 0000730E0 /
DATA AI1CS(19) / -.0000000000 0000333E0 /
DATA AI1CS(20) / .0000000000 0000071E0 /
DATA AI1CS(21) / -.0000000000 0000006E0 /
DATA AI12CS( 1) / .0285762350 1828014E0 /
DATA AI12CS( 2) / -.0097610974 9136147E0 /
DATA AI12CS( 3) / -.0001105889 3876263E0 /
DATA AI12CS( 4) / -.0000038825 6480887E0 /
DATA AI12CS( 5) / -.0000002512 2362377E0 /
DATA AI12CS( 6) / -.0000000263 1468847E0 /
DATA AI12CS( 7) / -.0000000038 3538039E0 /
DATA AI12CS( 8) / -.0000000005 5897433E0 /
DATA AI12CS( 9) / -.0000000000 1897495E0 /
DATA AI12CS(10) / .0000000000 3252602E0 /
DATA AI12CS(11) / .0000000000 1412580E0 /
DATA AI12CS(12) / .0000000000 0203564E0 /
DATA AI12CS(13) / -.0000000000 0071985E0 /
DATA AI12CS(14) / -.0000000000 0040836E0 /
DATA AI12CS(15) / -.0000000000 0002101E0 /
DATA AI12CS(16) / .0000000000 0004273E0 /
DATA AI12CS(17) / .0000000000 0001041E0 /
DATA AI12CS(18) / -.0000000000 0000382E0 /
DATA AI12CS(19) / -.0000000000 0000186E0 /
DATA AI12CS(20) / .0000000000 0000033E0 /
DATA AI12CS(21) / .0000000000 0000028E0 /
DATA AI12CS(22) / -.0000000000 0000003E0 /
DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT BESI1E
IF (FIRST) THEN
NTI1 = INITS (BI1CS, 11, 0.1*R1MACH(3))
NTAI1 = INITS (AI1CS, 21, 0.1*R1MACH(3))
NTAI12 = INITS (AI12CS, 22, 0.1*R1MACH(3))
C
XMIN = 2.0*R1MACH(1)
XSML = SQRT (4.5*R1MACH(3))
ENDIF
FIRST = .FALSE.
C
Y = ABS(X)
IF (Y.GT.3.0) GO TO 20
C
BESI1E = 0.0
IF (Y.EQ.0.0) RETURN
C
IF (Y .LE. XMIN) CALL XERMSG ('SLATEC', 'BESI1E',
+ 'ABS(X) SO SMALL I1 UNDERFLOWS', 1, 1)
IF (Y.GT.XMIN) BESI1E = 0.5*X
IF (Y.GT.XSML) BESI1E = X * (.875 + CSEVL(Y*Y/4.5-1., BI1CS,NTI1))
BESI1E = EXP(-Y) * BESI1E
RETURN
C
20 IF (Y.LE.8.) BESI1E = (.375 + CSEVL ((48./Y-11.)/5., AI1CS, NTAI1)
1 ) / SQRT(Y)
IF (Y.GT.8.) BESI1E = (.375 + CSEVL (16./Y-1.0, AI12CS, NTAI12))
1 / SQRT(Y)
BESI1E = SIGN (BESI1E, X)
C
RETURN
END