Derive_v5_05 / Derive / Users / SpecialFunctions / CarlsonEllipticIntegrals

		CARLSON.DOC Carlson elliptic integrals.
		    Jim FitzSimons cherry@neta.com

The utility CARLSON.MTH contains the best way to numerically evaluate
elliptic integrals. It contains the definition of the Carlson elliptic
integrals RF(x,y,z), RJ(x,y,z,p), RC(x,y), RD(x,y,z), and RG(x,y,z).
It contains the definitions of the Legendre elliptic integrals
ELLIPTIC_F(phi,m), ELLIPTIC_E(phi,m), and ELLIPTIC_PI(phi,m,n).

The numerical algorithms are based on Numerical Algorithms 10(1995)13-26.
B.C. Carlson Numerical computation of real or complex elliptic integrals
The numerical Carlson elliptic integral are R_F(x,y,z), R_C(x,y),
R_J(x,y,z,p), R_D(x,y,z), and R_G(x,y,z).
The numerical Legendre elliptic integral are LEGENDRE_F(phi,m),
LEGENDRE_E(phi,m), and LEGENDRE_PI(phi,m,n).

These algorithms are good for calculating the elliptic integrals to very
large precision, and with both real and complex arguments.
There is a demonstration file CARLSON.DMO which tests the elliptic integrals
for both real and complex arguments.