elliptic_integral_E

Evaluates the complete elliptic integral of the second kind E(x).

Synopsis

#include <imsl.h>

float imsl_f_elliptic_integral_E (float x)

The type double function is imsl_d_elliptic_integral_E.

Required Arguments

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

Return Value

The complete elliptic integral E(x).

Description

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

 

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

The function E(x) is computed using the routine imsl_f_elliptic_integral_RF and imsl_f_elliptic_integral_RD. The computation is done using the relation

 

Example

The integral E(0.33) is evaluated.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

float x = 0.33;

float ans;

 

x = imsl_f_elliptic_integral_E (x);

printf ("E(0.33) = %f\n", x);

}

Output

 

E(0.33) = 1.431832