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

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.

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

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

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

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 is the smallest representable floating-point number. Should any of these conditions fail ELRJ is set to b, the largest floating-point number.

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

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

PRINT, ELRJ(2.0, 3.0, 4.0, 5.0)

; PV-WAVE prints: 0.142976