elliptic_integral_RC
Evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.
Synopsis
#include <imsl.h>
float imsl_f_elliptic_integral_RC (float x, float y)
The type double function is imsl_d_elliptic_integral_RC.
Required Arguments
float x (Input)
First variable of the incomplete elliptic integral. It must be nonnegative and must satisfy the conditions given below.
float y (Input)
Second variable of the incomplete elliptic integral. It must be positive and must satisfy the conditions given below.
Return Value
The elliptic integral RC (x, y).
Description
Carlson’s elliptic integral of the third kind is defined to be
The argument
x must be nonnegative,
y must be positive, and
x +
y must be less than or equal to
b/5 and greater than or equal to 5
s. If any of these conditions are false, the
imsl_f_elliptic_integral_RC is set to
b. Here,
b =
imsl_f_machine(2) is the largest and
s =
imsl_f_machine(1) is the smallest representable floating-point number. For more information, see the description for
imsl_f_machine.
The function imsl_f_elliptic_integral_RC is based on the code by Carlson and Notis (1981) and the work of Carlson (1979).
Example
The integral RC (2.25, 2) is computed.
#include <imsl.h>
#include <stdio.h>
int main()
{
float x = 2.25;
float y = 2.0;
float ans;
x = imsl_f_elliptic_integral_RC (x, y);
printf ("RC(2.25, 2.0) = %f\n", x);
}
Output
RC(2.25, 2.0) = 0.693147