ELRD
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 ɛ)1∕9 s−2∕3 where ɛ = 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
