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

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