IMSL_ELRF

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

The IMSL_ELRF function evaluates Carlson's elliptic integral of the first kind R_F(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_ELRF(x, y, z [, /DOUBLE])

Return Value

The complete elliptic integral R_F(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 nonnegative.

Keywords

DOUBLE

If present and nonzero, double precision is used.

Discussion

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

The arguments must be nonnegative and less than or equal to b/5. In addition, x + y, x + z, and y + z must be greater than or equal to 5s. Should any of these conditions fail, IMSL_ELRF is set to b. Here, b is the largest and is the smallest representable number.

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

Example

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

PRINT, IMSL_ELRF(0.0, 1.0, 2.0) 
      1.31103 

Version History