DOUBLE PRECISION FUNCTION DBESY1(X)
C***BEGIN PROLOGUE  DBESY1
C***DATE WRITTEN   770701   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  C10A1
C***KEYWORDS  BESSEL FUNCTION,DOUBLE PRECISION,ORDER ONE,SECOND KIND,
C             SPECIAL FUNCTION
C***AUTHOR  FULLERTON, W., (LANL)
C***PURPOSE  Computes the d.p. Bessel function of the second kind of
C            order one.
C***DESCRIPTION
C
C DBESY1(X) calculates the double precision Bessel function of the
C second kind of order for double precision argument X.
C
C Series for BY1        on the interval  0.          to  1.60000E+01
C                                        with weighted error   8.65E-33
C                                         log weighted error  32.06
C                               significant figures required  32.17
C                                    decimal places required  32.71
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH,D9B1MP,DBESJ1,DCSEVL,INITDS,XERROR
C***END PROLOGUE  DBESY1
      DOUBLE PRECISION X, BY1CS(20), AMPL, THETA, TWODPI, XMIN, XSML,
     1  Y, Z, D1MACH, DCSEVL, DBESJ1
      DATA BY1 CS(  1) / +.3208047100 6119086293 2352018628 015 D-1    /
      DATA BY1 CS(  2) / +.1262707897 4335004495 3431725999 727 D+1    /
      DATA BY1 CS(  3) / +.6499961899 9231750009 7490637314 144 D-2    /
      DATA BY1 CS(  4) / -.8936164528 8605041165 3144160009 712 D-1    /
      DATA BY1 CS(  5) / +.1325088122 1757095451 2375510370 043 D-1    /
      DATA BY1 CS(  6) / -.8979059119 6483523775 3039508298 105 D-3    /
      DATA BY1 CS(  7) / +.3647361487 9583067824 2287368165 349 D-4    /
      DATA BY1 CS(  8) / -.1001374381 6660005554 9075523845 295 D-5    /
      DATA BY1 CS(  9) / +.1994539657 3901739703 1159372421 243 D-7    /
      DATA BY1 CS( 10) / -.3023065601 8033816728 4799332520 743 D-9    /
      DATA BY1 CS( 11) / +.3609878156 9478119611 6252914242 474 D-11   /
      DATA BY1 CS( 12) / -.3487488297 2875824241 4552947409 066 D-13   /
      DATA BY1 CS( 13) / +.2783878971 5591766581 3507698517 333 D-15   /
      DATA BY1 CS( 14) / -.1867870968 6194876876 6825352533 333 D-17   /
      DATA BY1 CS( 15) / +.1068531533 9116825975 7070336000 000 D-19   /
      DATA BY1 CS( 16) / -.5274721956 6844822894 3872000000 000 D-22   /
      DATA BY1 CS( 17) / +.2270199403 1556641437 0133333333 333 D-24   /
      DATA BY1 CS( 18) / -.8595390353 9452310869 3333333333 333 D-27   /
      DATA BY1 CS( 19) / +.2885404379 8337945600 0000000000 000 D-29   /
      DATA BY1 CS( 20) / -.8647541138 9371733333 3333333333 333 D-32   /
      DATA TWODPI / 0.6366197723 6758134307 5535053490 057 D0 /
      DATA NTY1, XMIN, XSML / 0, 2*0.D0 /
C***FIRST EXECUTABLE STATEMENT  DBESY1
      IF (NTY1.NE.0) GO TO 10
      NTY1 = INITDS (BY1CS, 20, 0.1*SNGL(D1MACH(3)))
C
      XMIN = 1.571D0 * DEXP (DMAX1(DLOG(D1MACH(1)), -DLOG(D1MACH(2))) +
     1  0.01D0)
      XSML = DSQRT (4.0D0*D1MACH(3))
C
 10   IF (X.LE.0.D0) CALL XERROR ( 'DBESY1  X IS ZERO OR NEGATIVE', 29,
     1  1, 2)
      IF (X.GT.4.0D0) GO TO 20
C
      IF (X.LT.XMIN) CALL XERROR ( 'DBESY1  X SO SMALL Y1 OVERFLOWS',
     1  31, 3, 2)
      Y = 0.D0
      IF (X.GT.XSML) Y = X*X
      DBESY1 = TWODPI * DLOG(0.5D0*X)*DBESJ1(X) + (0.5D0 +
     1  DCSEVL (.125D0*Y-1.D0, BY1CS, NTY1))/X
      RETURN
C
 20   CALL D9B1MP (X, AMPL, THETA)
      DBESY1 = AMPL * DSIN(THETA)
      RETURN
C
      END