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*DECK DBESJ1
DOUBLE PRECISION FUNCTION DBESJ1 (X)
C***BEGIN PROLOGUE DBESJ1
C***PURPOSE Compute the Bessel function of the first kind of order one.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY C10A1
C***TYPE DOUBLE PRECISION (BESJ1-S, DBESJ1-D)
C***KEYWORDS BESSEL FUNCTION, FIRST KIND, FNLIB, ORDER ONE,
C SPECIAL FUNCTIONS
C***AUTHOR Fullerton, W., (LANL)
C***DESCRIPTION
C
C DBESJ1(X) calculates the double precision Bessel function of the
C first kind of order one for double precision argument X.
C
C Series for BJ1 on the interval 0. to 1.60000E+01
C with weighted error 1.16E-33
C log weighted error 32.93
C significant figures required 32.36
C decimal places required 33.57
C
C***REFERENCES (NONE)
C***ROUTINES CALLED D1MACH, D9B1MP, DCSEVL, INITDS, XERMSG
C***REVISION HISTORY (YYMMDD)
C 780601 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 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 910401 Corrected error in code which caused values to have the
C wrong sign for arguments less than 4.0. (WRB)
C***END PROLOGUE DBESJ1
DOUBLE PRECISION X, BJ1CS(19), AMPL, THETA, XSML, XMIN, Y,
1 D1MACH, DCSEVL
LOGICAL FIRST
SAVE BJ1CS, NTJ1, XSML, XMIN, FIRST
DATA BJ1CS( 1) / -.1172614151 3332786560 6240574524 003 D+0 /
DATA BJ1CS( 2) / -.2536152183 0790639562 3030884554 698 D+0 /
DATA BJ1CS( 3) / +.5012708098 4469568505 3656363203 743 D-1 /
DATA BJ1CS( 4) / -.4631514809 6250819184 2619728789 772 D-2 /
DATA BJ1CS( 5) / +.2479962294 1591402453 9124064592 364 D-3 /
DATA BJ1CS( 6) / -.8678948686 2788258452 1246435176 416 D-5 /
DATA BJ1CS( 7) / +.2142939171 4379369150 2766250991 292 D-6 /
DATA BJ1CS( 8) / -.3936093079 1831797922 9322764073 061 D-8 /
DATA BJ1CS( 9) / +.5591182317 9468800401 8248059864 032 D-10 /
DATA BJ1CS( 10) / -.6327616404 6613930247 7695274014 880 D-12 /
DATA BJ1CS( 11) / +.5840991610 8572470032 6945563268 266 D-14 /
DATA BJ1CS( 12) / -.4482533818 7012581903 9135059199 999 D-16 /
DATA BJ1CS( 13) / +.2905384492 6250246630 6018688000 000 D-18 /
DATA BJ1CS( 14) / -.1611732197 8414416541 2118186666 666 D-20 /
DATA BJ1CS( 15) / +.7739478819 3927463729 8346666666 666 D-23 /
DATA BJ1CS( 16) / -.3248693782 1119984114 3466666666 666 D-25 /
DATA BJ1CS( 17) / +.1202237677 2274102272 0000000000 000 D-27 /
DATA BJ1CS( 18) / -.3952012212 6513493333 3333333333 333 D-30 /
DATA BJ1CS( 19) / +.1161678082 2664533333 3333333333 333 D-32 /
DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT DBESJ1
IF (FIRST) THEN
NTJ1 = INITDS (BJ1CS, 19, 0.1*REAL(D1MACH(3)))
C
XSML = SQRT(8.0D0*D1MACH(3))
XMIN = 2.0D0*D1MACH(1)
ENDIF
FIRST = .FALSE.
C
Y = ABS(X)
IF (Y.GT.4.0D0) GO TO 20
C
DBESJ1 = 0.0D0
IF (Y.EQ.0.0D0) RETURN
IF (Y .LE. XMIN) CALL XERMSG ('SLATEC', 'DBESJ1',
+ 'ABS(X) SO SMALL J1 UNDERFLOWS', 1, 1)
IF (Y.GT.XMIN) DBESJ1 = 0.5D0*X
IF (Y.GT.XSML) DBESJ1 = X*(.25D0 + DCSEVL (.125D0*Y*Y-1.D0,
1 BJ1CS, NTJ1) )
RETURN
C
20 CALL D9B1MP (Y, AMPL, THETA)
DBESJ1 = SIGN (AMPL, X) * COS(THETA)
C
RETURN
END
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