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- *DECK BESJ1
- FUNCTION BESJ1 (X)
- C***BEGIN PROLOGUE BESJ1
- C***PURPOSE Compute the Bessel function of the first kind of order one.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C10A1
- C***TYPE SINGLE 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 BESJ1(X) calculates the Bessel function of the first kind of
- C order one for real argument X.
- C
- C Series for BJ1 on the interval 0. to 1.60000D+01
- C with weighted error 4.48E-17
- C log weighted error 16.35
- C significant figures required 15.77
- C decimal places required 16.89
- C
- C Series for BM1 on the interval 0. to 6.25000D-02
- C with weighted error 5.61E-17
- C log weighted error 16.25
- C significant figures required 14.97
- C decimal places required 16.91
- C
- C Series for BTH1 on the interval 0. to 6.25000D-02
- C with weighted error 4.10E-17
- C log weighted error 16.39
- C significant figures required 15.96
- C decimal places required 17.08
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED CSEVL, INITS, R1MACH, XERMSG
- C***REVISION HISTORY (YYMMDD)
- C 780601 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***END PROLOGUE BESJ1
- DIMENSION BJ1CS(12), BM1CS(21), BTH1CS(24)
- LOGICAL FIRST
- SAVE BJ1CS, BM1CS, BTH1CS, PI4, NTJ1, NTM1, NTTH1,
- 1 XSML, XMIN, XMAX, FIRST
- DATA BJ1CS( 1) / -.1172614151 3332787E0 /
- DATA BJ1CS( 2) / -.2536152183 0790640E0 /
- DATA BJ1CS( 3) / .0501270809 84469569E0 /
- DATA BJ1CS( 4) / -.0046315148 09625081E0 /
- DATA BJ1CS( 5) / .0002479962 29415914E0 /
- DATA BJ1CS( 6) / -.0000086789 48686278E0 /
- DATA BJ1CS( 7) / .0000002142 93917143E0 /
- DATA BJ1CS( 8) / -.0000000039 36093079E0 /
- DATA BJ1CS( 9) / .0000000000 55911823E0 /
- DATA BJ1CS(10) / -.0000000000 00632761E0 /
- DATA BJ1CS(11) / .0000000000 00005840E0 /
- DATA BJ1CS(12) / -.0000000000 00000044E0 /
- DATA BM1CS( 1) / .1047362510 931285E0 /
- DATA BM1CS( 2) / .0044244389 3702345E0 /
- DATA BM1CS( 3) / -.0000566163 9504035E0 /
- DATA BM1CS( 4) / .0000023134 9417339E0 /
- DATA BM1CS( 5) / -.0000001737 7182007E0 /
- DATA BM1CS( 6) / .0000000189 3209930E0 /
- DATA BM1CS( 7) / -.0000000026 5416023E0 /
- DATA BM1CS( 8) / .0000000004 4740209E0 /
- DATA BM1CS( 9) / -.0000000000 8691795E0 /
- DATA BM1CS(10) / .0000000000 1891492E0 /
- DATA BM1CS(11) / -.0000000000 0451884E0 /
- DATA BM1CS(12) / .0000000000 0116765E0 /
- DATA BM1CS(13) / -.0000000000 0032265E0 /
- DATA BM1CS(14) / .0000000000 0009450E0 /
- DATA BM1CS(15) / -.0000000000 0002913E0 /
- DATA BM1CS(16) / .0000000000 0000939E0 /
- DATA BM1CS(17) / -.0000000000 0000315E0 /
- DATA BM1CS(18) / .0000000000 0000109E0 /
- DATA BM1CS(19) / -.0000000000 0000039E0 /
- DATA BM1CS(20) / .0000000000 0000014E0 /
- DATA BM1CS(21) / -.0000000000 0000005E0 /
- DATA BTH1CS( 1) / .7406014102 6313850E0 /
- DATA BTH1CS( 2) / -.0045717556 59637690E0 /
- DATA BTH1CS( 3) / .0001198185 10964326E0 /
- DATA BTH1CS( 4) / -.0000069645 61891648E0 /
- DATA BTH1CS( 5) / .0000006554 95621447E0 /
- DATA BTH1CS( 6) / -.0000000840 66228945E0 /
- DATA BTH1CS( 7) / .0000000133 76886564E0 /
- DATA BTH1CS( 8) / -.0000000024 99565654E0 /
- DATA BTH1CS( 9) / .0000000005 29495100E0 /
- DATA BTH1CS(10) / -.0000000001 24135944E0 /
- DATA BTH1CS(11) / .0000000000 31656485E0 /
- DATA BTH1CS(12) / -.0000000000 08668640E0 /
- DATA BTH1CS(13) / .0000000000 02523758E0 /
- DATA BTH1CS(14) / -.0000000000 00775085E0 /
- DATA BTH1CS(15) / .0000000000 00249527E0 /
- DATA BTH1CS(16) / -.0000000000 00083773E0 /
- DATA BTH1CS(17) / .0000000000 00029205E0 /
- DATA BTH1CS(18) / -.0000000000 00010534E0 /
- DATA BTH1CS(19) / .0000000000 00003919E0 /
- DATA BTH1CS(20) / -.0000000000 00001500E0 /
- DATA BTH1CS(21) / .0000000000 00000589E0 /
- DATA BTH1CS(22) / -.0000000000 00000237E0 /
- DATA BTH1CS(23) / .0000000000 00000097E0 /
- DATA BTH1CS(24) / -.0000000000 00000040E0 /
- DATA PI4 / 0.7853981633 9744831E0 /
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT BESJ1
- IF (FIRST) THEN
- NTJ1 = INITS (BJ1CS, 12, 0.1*R1MACH(3))
- NTM1 = INITS (BM1CS, 21, 0.1*R1MACH(3))
- NTTH1 = INITS (BTH1CS, 24, 0.1*R1MACH(3))
- C
- XSML = SQRT (8.0*R1MACH(3))
- XMIN = 2.0*R1MACH(1)
- XMAX = 1.0/R1MACH(4)
- ENDIF
- FIRST = .FALSE.
- C
- Y = ABS(X)
- IF (Y.GT.4.0) GO TO 20
- C
- BESJ1 = 0.
- IF (Y.EQ.0.0) RETURN
- IF (Y .LE. XMIN) CALL XERMSG ('SLATEC', 'BESJ1',
- + 'ABS(X) SO SMALL J1 UNDERFLOWS', 1, 1)
- IF (Y.GT.XMIN) BESJ1 = 0.5*X
- IF (Y.GT.XSML) BESJ1 = X * (.25 + CSEVL(.125*Y*Y-1., BJ1CS, NTJ1))
- RETURN
- C
- 20 IF (Y .GT. XMAX) CALL XERMSG ('SLATEC', 'BESJ1',
- + 'NO PRECISION BECAUSE ABS(X) IS TOO BIG', 2, 2)
- Z = 32.0/Y**2 - 1.0
- AMPL = (0.75 + CSEVL (Z, BM1CS, NTM1)) / SQRT(Y)
- THETA = Y - 3.0*PI4 + CSEVL (Z, BTH1CS, NTTH1) / Y
- BESJ1 = SIGN (AMPL, X) * COS (THETA)
- C
- RETURN
- END
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