ELRC

This function evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.

Function Return Value

ELRC — Function value. (Output)

Required Arguments

X — First variable of the incomplete elliptic integral. (Input)
It must be nonnegative and satisfy the conditions given in Comments.

Y — Second variable of the incomplete elliptic integral. (Input)
It must be positive and satisfy the conditions given in Comments.

FORTRAN 90 Interface

Generic: ELRC (X, Y)

Specific: The specific interface names are S_ELRC and D_ELRC.

FORTRAN 77 Interface

Single: ELRC (X, Y)

Double: The double precision name is DELRC.

Description

The special case of Carlson’s complete elliptic integral of the first kind is defined to be

 

The argument x must be nonnegative, y must be positive, and x + y must be less than or equal to b/5 and greater than or equal to 5s. If any of these conditions are false, then ELRC is set to b. Here, b = AMACH(2) is the largest and s = AMACH(1) is the smallest representable floating‑point number.

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

Comments

The sum X + Y must be greater than or equal to ARGMIN and both X and Y must be less than or equal to ARGMAX. ARGMIN = s * 5 and ARGMAX = b/5, where s is the machine minimum (AMACH(1)) and b is the machine maximum (AMACH(2)).

Example

In this example, RC(0.0, 1.0) is computed and printed.

 

USE ELRC_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X, Y

! Compute

X = 0.0

Y = 1.0

VALUE = ELRC(X, Y)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, Y, VALUE

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

END

Output

 

ELRC( 0.000, 1.000) = 1.571