*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