ELK

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

Function Return Value

ELK — 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 1.

FORTRAN 90 Interface

Generic: ELK (X)

Specific: The specific interface names are S_ELK and D_ELK.

FORTRAN 77 Interface

Single: ELK (X)

Double: The double precision name is DELK.

Description

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

 

 

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

The function K(x) is computed using the routine ELRF and the relation K(x) = RF(0, 1 ‑ x, 1).

 

Figure 1,  Plot of K(x) and E(x)

Example

In this example, K(0) is computed and printed.

 

USE ELK_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = 0.0

VALUE = ELK(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

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

END

Output

 

ELK( 0.000) = 1.571