DSPENC(3)

SYNOPSIS
DOUBLE PRECISION FUNCTION DSPENC (X)

NAME
dspenc - Compute a form of Spence's integral due to K. Mitchell.

LIBRARY
SLATEC (FNLIB)

CATEGORY
C5

TYPE
DOUBLE PRECISION (SPENC-S, DSPENC-D)

KEYWORDS
FNLIB, SPECIAL FUNCTIONS, SPENCE'S INTEGRAL

AUTHOR
Fullerton, W., (LANL)

DESCRIPTION
DSPENC(X) calculates the double precision Spence's integral for double precision argument X. Spence's function defined by integral from 0 to X of -LOG(1-Y)/Y DY. For ABS(X) .LE. 1, the uniformly convergent expansion DSPENC = sum K=1,infinity X**K / K**2 is valid. This is a form of Spence's integral due to K. Mitchell which differs from the definition in the NBS Handbook of Mathematical Functions. Spence's function can be used to evaluate much more general integral forms. For example, integral from 0 to Z of LOG(A*X+B)/(C*X+D) DX = LOG(ABS(B-A*D/C))*LOG(ABS(A*(C*X+D)/(A*D-B*C)))/C - DSPENC (A*(C*Z+D)/(A*D-B*C)) / C. Ref -- K. Mitchell, Philosophical Magazine, 40, p.351 (1949). Stegun and Abromowitz, AMS 55, p.1004. Series for SPEN on the interval 0. to 5.00000E-01 with weighted error 4.74E-32 log weighted error 31.32 significant figures required 30.37 decimal places required 32.11

REFERENCES
(NONE)

ROUTINES CALLED
D1MACH, DCSEVL, INITDS

REVISION HISTORY (YYMMDD)
780201 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
891115 Corrected third argument in reference to INITDS. (WRB)
891115 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)