ELRC Function

Evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.

Usage

result = ELRC(x, y)

Input Parameters

x—First argument for which the function value is desired. It must be nonnegative and must satisfy the conditions given below.

y—Second argument for which the function value is desired. It must be nonnegative and must satisfy the conditions given below.

Returned Value

result—The elliptic integral R_C (x, y).

Input Keywords

Double—If present and nonzero, double precision is used.

Discussion

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 ELRC is set to b. Here, b is the largest and s is the smallest representable floating-point number.

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

Example

The integral R_C (2.25, 2) is computed.

PRINT, ELRC(2.25, 2.0)

; PV-WAVE prints: 0.693147