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### IMSL_ELRJ

IMSL_ELRJ

The IMSL_ELRJ function evaluates Carlson’s elliptic integral of the third kind RJ (x, y, z, ρ).

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

The arguments must be nonnegative. In addition, x + y, x + z, y + z and ρ must be greater than or equal to (5s)1/3 and less than or equal to 0.3(b/5)1/3, where s is the smallest representable floating-point number. Should any of these conditions fail IMSL_ELRJ is set to b, the largest floating-point number.

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

## Example

The integral RJ (2, 3, 4, 5) is computed.

`PRINT, IMSL_ELRJ(2.0, 3.0, 4.0, 5.0)`
`  0.142976`

## Syntax

Result = IMSL_ELRJ(X, Y, Z, Rho [, /DOUBLE]

## Return Value

The complete elliptic integral RJ (x, y, z, ρ).

## Arguments

### Rho

Fourth argument for which the function value is desired. It must be positive.

### 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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