 
      DOUBLE PRECISION FUNCTION DSPENC(X)
C***BEGIN PROLOGUE  DSPENC
C***DATE WRITTEN   780201   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  C5
C***KEYWORDS  DOUBLE PRECISION,SPECIAL FUNCTION,SPENCES INTEGRAL
C***AUTHOR  FULLERTON, W., (LANL)
C***PURPOSE  Computes a d.p. form of Spence's integral due to
C            K. Mitchell.
C***DESCRIPTION
C
C DSPENC(X) calculates the double precision Spence's integral
C for double precision argument X.  Spence's function defined by
C        integral from 0 to X of  -ALOG(1-Y)/Y  DY.
C For ABS(X) .LE. 1, the uniformly convergent expansion
C        DSPENC = sum K=1,infinity  X**K / K**2     is valid.
C This is a form of Spence's integral due to K. Mitchell which differs
C from the definition in the NBS Handbook of Mathematical Functions.
C
C Spence's function can be used to evaluate much more general integral
C forms.  For example,
C        integral from 0 to Z of  ALOG(A*X+B)/(C*X+D)  DX  =
C             ALOG(ABS(B-A*D/C))*ALOG(ABS(A*(C*X+D)/(A*D-B*C)))/C
C             - DSPENC (A*(C*Z+D)/(A*D-B*C)) / C.
C
C Ref -- K. Mitchell, Philosophical Magazine, 40, p.351 (1949).
C        Stegun and Abromowitz, AMS 55, p.1004.
C
C
C Series for SPEN       on the interval  0.          to  5.00000E-01
C                                        with weighted error   4.74E-32
C                                         log weighted error  31.32
C                               significant figures required  30.37
C                                    decimal places required  32.11
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH,DCSEVL,INITDS
C***END PROLOGUE  DSPENC
 
 
