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 5s. 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.

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>

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

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