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 9- 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

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