C337 Exponential Integral

Function subprograms REXPIN and DEXPIN calculate the exponential integral

$E$₁(x) = -Ei(-x) = ∫_x^&inf;{e^-tt}dt

for real arguments x. For x<0, the real part of the principal value of the integral is taken.

On CDC and Cray computers, the double-precision versions DEXPIN and DEXPIE are not available.

Structure:

FUNCTION subprograms
User Entry Names: REXPIN, REXPIE, DEXPIN, DEXPIE
Obsolete User Entry Names: EXPINT $\equiv$ REXPIN
Files Referenced: Unit 6
External References: MTLMTR (N002), ABEND (Z035)

Usage:

In any arithmetic expression, REXPIN(X) or DEXPIN(X) has the value $E$₁(X) ,
REXPIE(X) or DEXPIE(X) has the value $eX\hspace{0.17em}E$₁(X) ,

where REXPIN and REXPIE are of type REAL, DEXPIN and DEXPIE are of type DOUBLE PRECISION, and X has the same type as the function name.

Method:

Polynomial and rational approximations.

Accuracy:

REXPIN and REXPIE (except on CDC and Cray computers) have full single-precision accuracy. For most values of the argument X, DEXPIN, DEXPIE (and REXPIN, REXPIE on CDC and Cray computers) have an accuracy of approximately one significant digit less than the machine precision.

Error handling:

Error C337.1: $X=0$ . The function value is set equal to zero, and a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

References:

1. W.J. Cody and H.C. Thatcher,Jr., Rational Chebyshev approximations for the exponential integral $E$₁(x) , Math. Comp. 22 (1968) 641--649.
2. W.J. Cody and H.C. Thatcher,Jr., Chebyshev approximations for the exponential integral Ei(x), Math. Comp. 23 (1969) 289--303.

C338