E1(3)

SYNOPSIS
FUNCTION E1 (X)

NAME
e1 - Compute the exponential integral E1(X).

LIBRARY
SLATEC (FNLIB)

CATEGORY
C5

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

KEYWORDS
E1 FUNCTION, EXPONENTIAL INTEGRAL, FNLIB, SPECIAL FUNCTIONS

AUTHOR
Fullerton, W., (LANL)

DESCRIPTION
E1 calculates the single precision exponential integral, E1(X), for positive single 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 AE11 on the interval -1.00000D-01 to 0. with weighted error 1.76E-17 log weighted error 16.75 significant figures required 15.70 decimal places required 17.55 Series for AE12 on the interval -2.50000D-01 to -1.00000D-01 with weighted error 5.83E-17 log weighted error 16.23 significant figures required 15.76 decimal places required 16.93 Series for E11 on the interval -4.00000D+00 to -1.00000D+00 with weighted error 1.08E-18 log weighted error 17.97 significant figures required 19.02 decimal places required 18.61 Series for E12 on the interval -1.00000D+00 to 1.00000D+00 with weighted error 3.15E-18 log weighted error 17.50 approx significant figures required 15.8 decimal places required 18.10 Series for AE13 on the interval 2.50000D-01 to 1.00000D+00 with weighted error 2.34E-17 log weighted error 16.63 significant figures required 16.14 decimal places required 17.33 Series for AE14 on the interval 0. to 2.50000D-01 with weighted error 5.41E-17 log weighted error 16.27 significant figures required 15.38 decimal places required 16.97

REFERENCES
(NONE)

ROUTINES CALLED
CSEVL, INITS, R1MACH, 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)