IMSL_ELRD

Syntax | Return Value | Arguments | Keywords | Discussion | Example | Version History

The IMSL_ELRD function evaluates Carlson's elliptic integral of the second kind R_D(x, y, z).

Note
This routine requires an IDL Advanced Math and Stats license. For more information, contact your ITT Visual Information Solutions sales or technical support representative.

Syntax

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

Return Value

The complete elliptic integral R_D(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

If present and nonzero, double precision is used.

Discussion

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{3s^2/3, 3/b^2/3}, 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 R_D(0, 2, 1) is computed.

PRINT, IMSL_ELRD(0.0, 2.0, 1.0) 
      1.79721 

Version History