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