E1

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

Function Return Value

E1 — Function value. (Output)

Required Arguments

X — Argument for which the integral is to be evaluated. (Input)

FORTRAN 90 Interface

Generic: E1 (X)

Specific: The specific interface names are S_E1 and D_E1.

FORTRAN 77 Interface

Single: E1 (X)

Double: The double precision function name is DE1.

Description

The alternate definition of the exponential integral, E1(x), is

 

The path of integration must exclude the origin and not cross the negative real axis.

The argument x must be large enough that e−x does not overflow, and x must be small enough to insure that e−x/x does not underflow.

Comments

Informational Error

 

Type	Code	Description
3	2	The function underflows because X is too large.

Example

In this example, E1 (1.3) is computed and printed.

 

USE E1_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 1.3

VALUE = E1(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' E1(', F6.3, ') = ', F6.3)

END

Output

 

E1( 1.300) = 0.135