Evaluates Carlson’s elliptic integral of the second kind RD(x, y, z).

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.

result—The complete elliptic integral RD(x, y, z)

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

Carlson’s elliptic integral of the second kind is defined to be:

Arguments must be nonnegative and less than or equal to 0.69(−lnε)1/9s-2/3 where e is the machine precision, s is the smallest representable positive number. Furthermore, x + y and z must be greater than max{3s2/3, 3/b2/3}, where b is the largest floating point number. If any of these conditions is false, then ELRD returns b.

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

The integral RD(0, 2, 1) is computed.

PRINT, ELRD(0.0, 2.0, 1.0)

; PV-WAVE prints: 1.79721