The IMSL_ELRD function evaluates Carlson’s elliptic integral of the second kind RD(x, y, z).
This routine requires an IDL Advanced Math and Stats license. For more information, contact your sales or technical support representative.
Carlson’s elliptic integral of the second kind is defined to be:
Arguments must be nonnegative and less than or equal to 0.69(-lne)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 IMSL_ELRD returns b.
The IMSL_ELRD function is based on the code by Carlson and Notis (1981) and the work of Carlson (1979).
Example
The integral RD(0, 2, 1) is computed.
PRINT, IMSL_ELRD(0.0, 2.0, 1.0)
1.79721
Syntax
Result = IMSL_ELRD(X, Y, Z [, /DOUBLE]
Return Value
The complete elliptic integral RD(x, y, z).
Arguments
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 (optional)
If present and nonzero, double precision is used.
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