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- *DECK BESY1
- FUNCTION BESY1 (X)
- C***BEGIN PROLOGUE BESY1
- C***PURPOSE Compute the Bessel function of the second kind of order
- C one.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C10A1
- C***TYPE SINGLE PRECISION (BESY1-S, DBESY1-D)
- C***KEYWORDS BESSEL FUNCTION, FNLIB, ORDER ONE, SECOND KIND,
- C SPECIAL FUNCTIONS
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C BESY1(X) calculates the Bessel function of the second kind of
- C order one for real argument X.
- C
- C Series for BY1 on the interval 0. to 1.60000D+01
- C with weighted error 1.87E-18
- C log weighted error 17.73
- C significant figures required 17.83
- C decimal places required 18.30
- 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 BESJ1, CSEVL, INITS, R1MACH, XERMSG
- C***REVISION HISTORY (YYMMDD)
- C 770401 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 900326 Removed duplicate information from DESCRIPTION section.
- C (WRB)
- C***END PROLOGUE BESY1
- DIMENSION BY1CS(14), BM1CS(21), BTH1CS(24)
- LOGICAL FIRST
- SAVE BY1CS, BM1CS, BTH1CS, TWODPI, PI4,
- 1 NTY1, NTM1, NTTH1, XMIN, XSML, XMAX, FIRST
- DATA BY1CS( 1) / .0320804710 0611908629E0 /
- DATA BY1CS( 2) / 1.2627078974 33500450E0 /
- DATA BY1CS( 3) / .0064999618 9992317500E0 /
- DATA BY1CS( 4) / -.0893616452 8860504117E0 /
- DATA BY1CS( 5) / .0132508812 2175709545E0 /
- DATA BY1CS( 6) / -.0008979059 1196483523E0 /
- DATA BY1CS( 7) / .0000364736 1487958306E0 /
- DATA BY1CS( 8) / -.0000010013 7438166600E0 /
- DATA BY1CS( 9) / .0000000199 4539657390E0 /
- DATA BY1CS(10) / -.0000000003 0230656018E0 /
- DATA BY1CS(11) / .0000000000 0360987815E0 /
- DATA BY1CS(12) / -.0000000000 0003487488E0 /
- DATA BY1CS(13) / .0000000000 0000027838E0 /
- DATA BY1CS(14) / -.0000000000 0000000186E0 /
- 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 TWODPI / 0.6366197723 6758134E0 /
- DATA PI4 / 0.7853981633 9744831E0 /
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT BESY1
- IF (FIRST) THEN
- NTY1 = INITS (BY1CS, 14, 0.1*R1MACH(3))
- NTM1 = INITS (BM1CS, 21, 0.1*R1MACH(3))
- NTTH1 = INITS (BTH1CS, 24, 0.1*R1MACH(3))
- C
- XMIN = 1.571*EXP ( MAX(LOG(R1MACH(1)), -LOG(R1MACH(2)))+.01)
- XSML = SQRT (4.0*R1MACH(3))
- XMAX = 1.0/R1MACH(4)
- ENDIF
- FIRST = .FALSE.
- C
- IF (X .LE. 0.) CALL XERMSG ('SLATEC', 'BESY1',
- + 'X IS ZERO OR NEGATIVE', 1, 2)
- IF (X.GT.4.0) GO TO 20
- C
- IF (X .LT. XMIN) CALL XERMSG ('SLATEC', 'BESY1',
- + 'X SO SMALL Y1 OVERFLOWS', 3, 2)
- Y = 0.
- IF (X.GT.XSML) Y = X*X
- BESY1 = TWODPI*LOG(0.5*X)*BESJ1(X) +
- 1 (0.5 + CSEVL (.125*Y-1., BY1CS, NTY1))/X
- RETURN
- C
- 20 IF (X .GT. XMAX) CALL XERMSG ('SLATEC', 'BESY1',
- + 'NO PRECISION BECAUSE X IS BIG', 2, 2)
- C
- Z = 32.0/X**2 - 1.0
- AMPL = (0.75 + CSEVL (Z, BM1CS, NTM1)) / SQRT(X)
- THETA = X - 3.0*PI4 + CSEVL (Z, BTH1CS, NTTH1) / X
- BESY1 = AMPL * SIN (THETA)
- C
- RETURN
- END
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