ELE

This function evaluates the complete elliptic integral of the second kind E(x).

Function Return Value

ELE — Function value. (Output)

Required Arguments

X — Argument for which the function value is desired. (Input)
X must be greater than or equal to 0 and less than or equal to 1.

FORTRAN 90 Interface

Generic: ELE (X)

Specific: The specific interface names are S_ELE and D_ELE.

FORTRAN 77 Interface

Single: ELE (X)

Double: The double precision name is DELE.

Description

The complete elliptic integral of the second kind is defined to be

 

The argument x must satisfy 0  ≤ x < 1; otherwise, ELE is set to b = AMACH(2), the largest representable floating‑point number.

The function E(x) is computed using the routines ELRF and ELRD. The computation is done using the relation

 

For a plot of E(x), see Figure 1,  , Plot of K(x) and E(x)

Example

In this example, E(0.33) is computed and printed.

 

USE ELE_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 0.33

VALUE = ELE(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' ELE(', F6.3, ') = ', F6.3)

END

Output

 

ELE( 0.330) = 1.432