IDL Analyst Reference Guide: Special Functions

IMSL_ELRJ

The IMSL_ELRJ function evaluates Carlson's elliptic integral of the third kind R_J (x, y, z, r).

Syntax

Result = IMSL_ELRJ(x, y, z, rho [, /DOUBLE])

Return Value

The complete elliptic integral R_J (x, y, z, r).

Arguments

rho

Fourth argument for which the function value is desired. It must be positive.

x

First argument for which the function value is desired. It must be nonnegative.

y

Second argument for which the function value is desired. It must be nonnegative.

z

Third argument for which the function value is desired. It must be positive.

Keywords

DOUBLE

If present and nonzero, double precision is used.

Discussion

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 r must be greater than or equal to (5s)^1/3 and less than or equal to 0.3(b/5)^1/3, where s is the smallest representable floating-point number. Should any of these conditions fail IMSL_ELRJ is set to b, the largest floating-point number.

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

Example

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

PRINT, IMSL_ELRJ(2.0, 3.0, 4.0, 5.0)  
     0.142976