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

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

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