# spenc.f

          FUNCTION SPENC (X)
    C***BEGIN PROLOGUE  SPENC
    C***PURPOSE  Compute a form of Spence's integral due to K. Mitchell.
    C***LIBRARY   SLATEC (FNLIB)
    C***CATEGORY  C5
    C***TYPE      SINGLE PRECISION (SPENC-S, DSPENC-D)
    C***KEYWORDS  FNLIB, SPECIAL FUNCTIONS, SPENCE'S INTEGRAL
    C***AUTHOR  Fullerton, W., (LANL)
    C***DESCRIPTION
    C
    C Evaluate a form of Spence's function defined by
    C        integral from 0 to X of  -LOG(1-Y)/Y  DY.
    C For ABS(X) .LE. 1, the uniformly convergent expansion
    C        SPENC = sum K=1,infinity  X**K / K**2     is valid.
    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  LOG(A*X+B)/(C*X+D)  DX  =
    C             LOG(ABS(B-A*D/C))*LOG(ABS(A*(C*X+D)/(A*D-B*C)))/C
    C             - SPENC (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  5.00000D-01
    C                                        with weighted error   6.82E-17
    C                                         log weighted error  16.17
    C                               significant figures required  15.22
    C                                    decimal places required  16.81
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  CSEVL, INITS, R1MACH
    C***REVISION HISTORY  (YYMMDD)
    C   780201  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***END PROLOGUE  SPENC