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### IMSL_ELRD

IMSL_ELRD

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

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.

## Version History

 6.4 Introduced

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