Ames Laboratory, Department of Energy, ISU, Ames, Iowa

Abstract.
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than the others, asymptotic approximations with error bounds are presented. In most cases they are derived from a uniform approximation to the integrand. As an application the symmetric elliptic integrals of the first, second, and third kinds are proved to be linearly independent with respect to coefficients that are rational functions.

Key words. Elliptic integral, asymptotic approximation, inequalities, hypergeometric (R )-function

AMS(MOS) subject classifications. primary 33A25, 41A60 26D15; secondary 33A30, 26D20

Abbreviated title ASYMPTOTIC APPROXIMATIONS FOR ELLIPTIC INTEGRALS

• Introduction
• Results
• Proofs
• Application to linear independence
• Elementary inequalities
• References
• About this document ...

This work was supported by the Director of Energy Research, Office of Basic Energy Sciences. The Ames Laboratory is operated for the U. S. Department of Energy by Iowa State University under Contract W-7405-ENG-82.

Contact: John Gustafson john.gustafson@sun.com
The URL for this document is http://www.scl.ameslab.gov

Oct 9, 1995 edition