Evaluates the exponential integral of integer order for arguments greater than zero scaled by EXP(X).

Required Arguments

X — Argument for which the integral is to be evaluated.    (Input)
It must be greater than zero.

N — Integer specifying the maximum order for which the exponential integral is to be calculated.    (Input)

F — Vector of length N containing the computed exponential integrals scaled by EXP(X).    (Output)

FORTRAN 90 Interface

Generic:                              CALL ENE (X, N, F)

Specific:                             The specific interface names are S_ENE and D_ENE.

FORTRAN 77 Interface

Single:                                CALL ENE  (X, N, F)

Double:                              The double precision function name is DENE.

Description

The scaled exponential integral of order n, En(x), is defined to be

The argument x must satisfy x > 0. The integer n must also be greater than zero. This code is based on a code due to Gautschi (1974).

Example

In this example, Ez(10) for n = 1, ..., n is computed and printed.

 

      USE ENE_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    N

      PARAMETER  (N=10)

!

      INTEGER    K, NOUT

      REAL       F(N), X

!                                 Compute

      X = 10.0

      CALL ENE (X, N, F)

!                                 Print the results

      CALL UMACH (2, NOUT)

      DO 10  K=1, N

         WRITE (NOUT,99999) K, X, F(K)

   10 CONTINUE

99999 FORMAT (' E sub ', I2, ' (', F6.3, ') = ', F6.3)

      END

Output

 

 E sub  1 (10.000) =  0.092

 E sub  2 (10.000) =  0.084

 E sub  3 (10.000) =  0.078

 E sub  4 (10.000) =  0.073

 E sub  5 (10.000) =  0.068

 E sub  6 (10.000) =  0.064

 E sub  7 (10.000) =  0.060

 E sub  8 (10.000) =  0.057

 E sub  9 (10.000) =  0.054

 E sub 10 (10.000) =  0.051

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