DE1(3)

SYNOPSIS
DOUBLE PRECISION FUNCTION DE1 (X)

NAME
de1 - Compute the exponential integral E1(X).

LIBRARY
SLATEC (FNLIB)

CATEGORY
C5

TYPE
DOUBLE PRECISION (E1-S, DE1-D)

KEYWORDS
E1 FUNCTION, EXPONENTIAL INTEGRAL, FNLIB, SPECIAL FUNCTIONS

AUTHOR
Fullerton, W., (LANL)

DESCRIPTION
DE1 calculates the double precision exponential integral, E1(X), for positive double precision argument X and the Cauchy principal value for negative X. If principal values are used everywhere, then, for all X, E1(X) = -Ei(-X) or Ei(X) = -E1(-X). Series for AE10 on the interval -3.12500E-02 to 0. with weighted error 4.62E-32 log weighted error 31.34 significant figures required 29.70 decimal places required 32.18 Series for AE11 on the interval -1.25000E-01 to -3.12500E-02 with weighted error 2.22E-32 log weighted error 31.65 significant figures required 30.75 decimal places required 32.54 Series for AE12 on the interval -2.50000E-01 to -1.25000E-01 with weighted error 5.19E-32 log weighted error 31.28 significant figures required 30.82 decimal places required 32.09 Series for E11 on the interval -4.00000E+00 to -1.00000E+00 with weighted error 8.49E-34 log weighted error 33.07 significant figures required 34.13 decimal places required 33.80 Series for E12 on the interval -1.00000E+00 to 1.00000E+00 with weighted error 8.08E-33 log weighted error 32.09 approx significant figures required 30.4 decimal places required 32.79 Series for AE13 on the interval 2.50000E-01 to 1.00000E+00 with weighted error 6.65E-32 log weighted error 31.18 significant figures required 30.69 decimal places required 32.03 Series for AE14 on the interval 0. to 2.50000E-01 with weighted error 5.07E-32 log weighted error 31.30 significant figures required 30.40 decimal places required 32.20

REFERENCES
(NONE)

ROUTINES CALLED
D1MACH, DCSEVL, INITDS, XERMSG

REVISION HISTORY (YYMMDD)
770701 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
891115 Modified prologue description. (WRB)
891115 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
920618 Removed space from variable names. (RWC, WRB)