dspenc.f
DOUBLE PRECISION FUNCTION DSPENC (X)
C***BEGIN PROLOGUE DSPENC
C***PURPOSE Compute a form of Spence's integral due to K. Mitchell.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY C5
C***TYPE DOUBLE PRECISION (SPENC-S, DSPENC-D)
C***KEYWORDS FNLIB, SPECIAL FUNCTIONS, SPENCE'S INTEGRAL
C***AUTHOR Fullerton, W., (LANL)
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 -LOG(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 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 - 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
C***REFERENCES (NONE)
C***ROUTINES CALLED D1MACH, DCSEVL, INITDS
C***REVISION HISTORY (YYMMDD)
C 780201 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 891115 Corrected third argument in reference to INITDS. (WRB)
C 891115 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C***END PROLOGUE DSPENC