ELRJ

This function evaluates Carlson’s incomplete elliptic integral of the third kind RJ(X, Y, Z, RHO)

Function Return Value

ELRJ — Function value. (Output)

Required Arguments

X — First variable of the incomplete elliptic integral. (Input)
It must be nonnegative.

Y — Second variable of the incomplete elliptic integral. (Input)
It must be nonnegative.

Z — Third variable of the incomplete elliptic integral. (Input)
It must be nonnegative.

RHO — Fourth variable of the incomplete elliptic integral. (Input)
It must be positive.

FORTRAN 90 Interface

Generic: ELRJ (X, Y, Z, RHO)

Specific: The specific interface names are S_ELRJ and D_ELRJ.

FORTRAN 77 Interface

Single: ELRJ (X, Y, Z, RHO)

Double: The double precision name is DELRJ.

Description

The Carlson’s complete 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 and less than or equal to , where s = AMACH(1) is the smallest representable floating-point number. Should any of these conditions fail, ELRJ is set to b = AMACH(2), the largest floating-point number.

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

Example

In this example, RJ(2, 3, 4, 5) is computed and printed.

 

USE ELRJ_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL RHO, VALUE, X, Y, Z

! Compute

X = 2.0

Y = 3.0

Z = 4.0

RHO = 5.0

VALUE = ELRJ(X, Y, Z, RHO)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, Y, Z, RHO, VALUE

99999 FORMAT (' ELRJ(', F6.3, ',', F6.3, ',', F6.3, ',', F6.3, &

') = ', F6.3)

END

Output

 

ELRJ( 2.000, 3.000, 4.000, 5.000) = 0.143