EI
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
