elliptic_integral_K

Evaluates the complete elliptic integral of the kind K(x).

Synopsis

#include <imsl.h>

float imsl_f_elliptic_integral_K (float x)

The type double function is imsl_d_elliptic_integral_K.

Required Arguments

float x (Input)
Argument for which the function value is desired.

Return Value

The complete elliptic integral K(x).

Description

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

 

The argument x must satisfy 0 ≤ x < 1; otherwise, imsl_f_elliptic_integral_K returns imsl_f_machine(2), the largest representable floating-point number. For more information, see the description for machine (float).

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

Example

The integral K(0) is evaluated.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

float x = 0.0;

float ans;

 

x = imsl_f_elliptic_integral_K (x);

printf ("K(0.0) = %f\n", x);

}

Output

 

K(0.0) = 1.570796