ENE

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

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)

Generic: CALL ENE (X, N, F)

Specific: The specific interface names are S_ENE and D_ENE.

Single: CALL ENE (X, N, F)

Double: The double precision function name is DENE.

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).

In this example, En(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

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