SPENC(3)

SYNOPSIS
FUNCTION SPENC (X)

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

LIBRARY
SLATEC (FNLIB)

CATEGORY
C5

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

KEYWORDS
FNLIB, SPECIAL FUNCTIONS, SPENCE'S INTEGRAL

AUTHOR
Fullerton, W., (LANL)

DESCRIPTION
Evaluate a form of 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 SPENC = sum K=1,infinity X**K / K**2 is valid. 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 - SPENC (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 5.00000D-01 with weighted error 6.82E-17 log weighted error 16.17 significant figures required 15.22 decimal places required 16.81

REFERENCES
(NONE)

ROUTINES CALLED
CSEVL, INITS, R1MACH

REVISION HISTORY (YYMMDD)
780201 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890531 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)