This function evaluates Carlson's incomplete elliptic integral of the second kind RD(X, Y, Z).

Function Return Value

ELRD — 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 positive.

FORTRAN 90 Interface

Generic:                              ELRD (X, Y, Z)

Specific:                             The specific interface names are S_ELRD and D_ELRD.

FORTRAN 77 Interface

Single:                                ELRD (X, Y, Z)

Double:                              The double precision name is DELRD.

Description

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

The arguments must be nonnegative and less than or equal to 0.69(−ln ε)1∕9 s−2∕3 where
ε = AMACH(4) is the machine precision, s = AMACH(1) is the smallest representable positive number. Furthermore, x + y and z must be greater than max{3s2∕3, 3/b2∕3}, where b = AMACH(2) is the largest floating-point number. If any of these conditions are false, then ELRD is set to b.

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

Example

In this example, RD(0, 2, 1) is computed and printed.

 

      USE ELRD_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NOUT

      REAL       VALUE, X, Y, Z

!                                 Compute

      X     = 0.0

      Y     = 2.0

      Z     = 1.0

      VALUE = ELRD(X, Y, Z)

!                                 Print the results

      CALL UMACH (2, NOUT)

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

99999 FORMAT (' ELRD(', F6.3, ',', F6.3, ',', F6.3, ') = ', F6.3)

      END

Output

 

ELRD( 0.000, 2.000, 1.000) = 1.797

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