DOUBLE PRECISION FUNCTION DBESJ1(X)
C***BEGIN PROLOGUE  DBESJ1
C***DATE WRITTEN   780601   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  C10A1
C***KEYWORDS  BESSEL FUNCTION,DOUBLE PRECISION,FIRST KIND,ORDER ONE,
C             SPECIAL FUNCTION
C***AUTHOR  FULLERTON, W., (LANL)
C***PURPOSE  Computes the d.p. Bessel function of the first kind of
C            order one.
C***DESCRIPTION
C
C DBESJ1(X) calculates the double precision Bessel function of the
C first kind of order one for double precision argument X.
C
C Series for BJ1        on the interval  0.          to  1.60000E+01
C                                        with weighted error   1.16E-33
C                                         log weighted error  32.93
C                               significant figures required  32.36
C                                    decimal places required  33.57
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH,D9B1MP,DCSEVL,INITDS,XERROR
C***END PROLOGUE  DBESJ1
      DOUBLE PRECISION X, BJ1CS(19), AMPL, THETA, XSML, XMIN, Y,
     1  D1MACH, DCSEVL
      DATA BJ1 CS(  1) / -.1172614151 3332786560 6240574524 003 D+0    /
      DATA BJ1 CS(  2) / -.2536152183 0790639562 3030884554 698 D+0    /
      DATA BJ1 CS(  3) / +.5012708098 4469568505 3656363203 743 D-1    /
      DATA BJ1 CS(  4) / -.4631514809 6250819184 2619728789 772 D-2    /
      DATA BJ1 CS(  5) / +.2479962294 1591402453 9124064592 364 D-3    /
      DATA BJ1 CS(  6) / -.8678948686 2788258452 1246435176 416 D-5    /
      DATA BJ1 CS(  7) / +.2142939171 4379369150 2766250991 292 D-6    /
      DATA BJ1 CS(  8) / -.3936093079 1831797922 9322764073 061 D-8    /
      DATA BJ1 CS(  9) / +.5591182317 9468800401 8248059864 032 D-10   /
      DATA BJ1 CS( 10) / -.6327616404 6613930247 7695274014 880 D-12   /
      DATA BJ1 CS( 11) / +.5840991610 8572470032 6945563268 266 D-14   /
      DATA BJ1 CS( 12) / -.4482533818 7012581903 9135059199 999 D-16   /
      DATA BJ1 CS( 13) / +.2905384492 6250246630 6018688000 000 D-18   /
      DATA BJ1 CS( 14) / -.1611732197 8414416541 2118186666 666 D-20   /
      DATA BJ1 CS( 15) / +.7739478819 3927463729 8346666666 666 D-23   /
      DATA BJ1 CS( 16) / -.3248693782 1119984114 3466666666 666 D-25   /
      DATA BJ1 CS( 17) / +.1202237677 2274102272 0000000000 000 D-27   /
      DATA BJ1 CS( 18) / -.3952012212 6513493333 3333333333 333 D-30   /
      DATA BJ1 CS( 19) / +.1161678082 2664533333 3333333333 333 D-32   /
      DATA NTJ1, XSML, XMIN / 0, 2*0.D0 /
C***FIRST EXECUTABLE STATEMENT  DBESJ1
      IF (NTJ1.NE.0) GO TO 10
      NTJ1 = INITDS (BJ1CS, 19, 0.1*SNGL(D1MACH(3)))
C
      XSML = DSQRT (4.0D0*D1MACH(3))
      XMIN = 2.0D0*D1MACH(1)
C
 10   Y = DABS(X)
      IF (Y.GT.4.0D0) GO TO 20
C
      DBESJ1 = 0.0D0
      IF (Y.EQ.0.0D0) RETURN
      IF (Y.LT.XMIN) CALL XERROR ( 'DBESJ1  DABS(X) DO SMALL J1 UNDERFLO
     1WS', 38, 1, 1)
      IF (Y.GT.XSML) DBESJ1 = X*(.25D0 + DCSEVL (.125D0*Y*Y-1.D0,
     1  BJ1CS, NTJ1) )
      RETURN
C
 20   CALL D9B1MP (Y, AMPL, THETA)
      DBESJ1 = AMPL * DCOS(THETA)
C
      RETURN
      END