EI

This function evaluates the exponential integral for arguments greater than zero and the Cauchy principal value for arguments less than zero.

Function Return Value

EI — Function value. (Output)

Required Arguments

X — Argument for which the function value is desired. (Input)

FORTRAN 90 Interface

Generic: EI (X)

Specific: The specific interface names are S_EI and D_EI.

FORTRAN 77 Interface

Single: EI (X)

Double: The double precision function name is DEI.

Description

The exponential integral, Ei(x), is defined to be

 

The argument x must be large enough to insure that the asymptotic formula ex/x does not underflow, and x must not be so large that ex overflows.

Comments

If principal values are used everywhere, then for all X, EI(X) = ‑E1(‑X) and E1(X) = ‑EI(‑X).

Example

In this example, Ei(1.15) is computed and printed.

 

USE EI_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 1.15

VALUE = EI(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' EI(', F6.3, ') = ', F6.3)

END

Output

 

EI( 1.150) = 2.304