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84 lines
3.7 KiB
Fortran
84 lines
3.7 KiB
Fortran
*DECK DBESY1
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DOUBLE PRECISION FUNCTION DBESY1 (X)
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C***BEGIN PROLOGUE DBESY1
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C***PURPOSE Compute the Bessel function of the second kind of order
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C one.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C10A1
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C***TYPE DOUBLE PRECISION (BESY1-S, DBESY1-D)
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C***KEYWORDS BESSEL FUNCTION, FNLIB, ORDER ONE, SECOND KIND,
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C SPECIAL FUNCTIONS
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C***AUTHOR Fullerton, W., (LANL)
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C***DESCRIPTION
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C
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C DBESY1(X) calculates the double precision Bessel function of the
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C second kind of order for double precision argument X.
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C
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C Series for BY1 on the interval 0. to 1.60000E+01
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C with weighted error 8.65E-33
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C log weighted error 32.06
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C significant figures required 32.17
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C decimal places required 32.71
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED D1MACH, D9B1MP, DBESJ1, DCSEVL, INITDS, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 770701 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890531 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C***END PROLOGUE DBESY1
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DOUBLE PRECISION X, BY1CS(20), AMPL, THETA, TWODPI, XMIN, XSML,
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1 Y, D1MACH, DCSEVL, DBESJ1
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LOGICAL FIRST
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SAVE BY1CS, TWODPI, NTY1, XMIN, XSML, FIRST
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DATA BY1CS( 1) / +.3208047100 6119086293 2352018628 015 D-1 /
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DATA BY1CS( 2) / +.1262707897 4335004495 3431725999 727 D+1 /
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DATA BY1CS( 3) / +.6499961899 9231750009 7490637314 144 D-2 /
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DATA BY1CS( 4) / -.8936164528 8605041165 3144160009 712 D-1 /
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DATA BY1CS( 5) / +.1325088122 1757095451 2375510370 043 D-1 /
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DATA BY1CS( 6) / -.8979059119 6483523775 3039508298 105 D-3 /
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DATA BY1CS( 7) / +.3647361487 9583067824 2287368165 349 D-4 /
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DATA BY1CS( 8) / -.1001374381 6660005554 9075523845 295 D-5 /
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DATA BY1CS( 9) / +.1994539657 3901739703 1159372421 243 D-7 /
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DATA BY1CS( 10) / -.3023065601 8033816728 4799332520 743 D-9 /
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DATA BY1CS( 11) / +.3609878156 9478119611 6252914242 474 D-11 /
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DATA BY1CS( 12) / -.3487488297 2875824241 4552947409 066 D-13 /
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DATA BY1CS( 13) / +.2783878971 5591766581 3507698517 333 D-15 /
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DATA BY1CS( 14) / -.1867870968 6194876876 6825352533 333 D-17 /
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DATA BY1CS( 15) / +.1068531533 9116825975 7070336000 000 D-19 /
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DATA BY1CS( 16) / -.5274721956 6844822894 3872000000 000 D-22 /
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DATA BY1CS( 17) / +.2270199403 1556641437 0133333333 333 D-24 /
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DATA BY1CS( 18) / -.8595390353 9452310869 3333333333 333 D-27 /
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DATA BY1CS( 19) / +.2885404379 8337945600 0000000000 000 D-29 /
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DATA BY1CS( 20) / -.8647541138 9371733333 3333333333 333 D-32 /
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DATA TWODPI / 0.6366197723 6758134307 5535053490 057 D0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT DBESY1
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IF (FIRST) THEN
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NTY1 = INITDS (BY1CS, 20, 0.1*REAL(D1MACH(3)))
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C
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XMIN = 1.571D0 * EXP (MAX(LOG(D1MACH(1)), -LOG(D1MACH(2))) +
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1 0.01D0)
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XSML = SQRT(4.0D0*D1MACH(3))
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ENDIF
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FIRST = .FALSE.
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C
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IF (X .LE. 0.D0) CALL XERMSG ('SLATEC', 'DBESY1',
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+ 'X IS ZERO OR NEGATIVE', 1, 2)
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IF (X.GT.4.0D0) GO TO 20
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C
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IF (X .LT. XMIN) CALL XERMSG ('SLATEC', 'DBESY1',
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+ 'X SO SMALL Y1 OVERFLOWS', 3, 2)
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Y = 0.D0
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IF (X.GT.XSML) Y = X*X
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DBESY1 = TWODPI * LOG(0.5D0*X)*DBESJ1(X) + (0.5D0 +
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1 DCSEVL (.125D0*Y-1.D0, BY1CS, NTY1))/X
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RETURN
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C
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20 CALL D9B1MP (X, AMPL, THETA)
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DBESY1 = AMPL * SIN(THETA)
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RETURN
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C
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END
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