elliptic_integral_RJ

Evaluates Carlson’s elliptic integral of the third kind RJ (x, y, z, ρ).

Synopsis

#include <imsl.h>

float imsl_f_elliptic_integral_RJ (float x, float y, float z, float rho)

The type double function is imsl_d_elliptic_integral_RJ.

Required Arguments

float x (Input)
First variable of the incomplete elliptic integral. It must be nonnegative.

float y (Input)
Second variable of the incomplete elliptic integral. It must be nonnegative.

float z (Input)
Third variable of the incomplete elliptic integral. It must be positive.

float rho (Input)
Fourth variable of the incomplete elliptic integral. It must be positive.

Return Value

The complete elliptic integral RJ (x, y, z, ρ).

Description

Carlson’s elliptic integral of the third kind is defined to be

 

The arguments must be nonnegative. In addition, x + y, x + z, y + z and ρ must be greater than or equal to (5s)1/3 and less than or equal to 0.3(b/5)1/3, where s = imsl_f_machine(1) is the smallest representable floating-point number. Should any of these conditions fail, imsl_f_elliptic_integral_RJ is set to b = imsl_f_machine(2), the largest floating-point number. For more information, see the description for imsl_f_machine.

The function imsl_f_elliptic_integral_RJ is based on the code by Carlson and Notis (1981) and the work of Carlson (1979).

Example

The integral RJ (2,  3, 4, 5) is computed.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

float x = 2.0;

float y = 3.0;

float z = 4.0;

float rho = 5.0;

float ans;

 

x = imsl_f_elliptic_integral_RJ (x, y, z, rho);

printf ("RJ(2, 3, 4, 5) = %f\n", x);

}

Output

 

RJ(2, 3, 4, 5) = 0.142976