This function evaluates the complete elliptic integral of the second kind E(x).
Function Return Value
ELE — Function value. (Output)
Required Arguments
X — Argument for
which the function value is desired. (Input)
X must be greater than
or equal to 0 and less than or equal to 1.
FORTRAN 90 Interface
Generic: ELE (X)
Specific: The specific interface names are S_ELE and D_ELE.
FORTRAN 77 Interface
Single: ELE (X)
Double: The double precision name is DELE.
Description
The complete elliptic integral of the second kind is defined to be
The argument x must satisfy 0 ≤ x < 1; otherwise, ELE is set to b = AMACH(2), the largest representable floating-point number.
The function E(x) is computed using the routines ELRF and ELRD. The computation is done using the relation
For a plot of E(x), see Figure 9- 1.
Example
In this example, E(0.33) is computed and printed.
USE ELE_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
REAL VALUE, X
! Compute
X = 0.33
VALUE = ELE(X)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) X, VALUE
99999 FORMAT (' ELE(', F6.3, ') = ', F6.3)
END
Output
ELE( 0.330) = 1.432
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