Automatic reduction of elliptic integrals using Carlson's relations

Author:
Norman Gray

Journal:
Math. Comp. **71** (2002), 311-318

MSC (2000):
Primary 33E05; Secondary 33-04

DOI:
https://doi.org/10.1090/S0025-5718-01-01333-3

Published electronically:
July 22, 2001

MathSciNet review:
1863002

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Abstract | References | Similar Articles | Additional Information

In a series of papers, B. C. Carlson produced tables of elliptic integrals, evaluating them in terms of easily computed symmetrical functions, using a group of multivariate recurrence relations. These relations are, however, cumbersome to use by hand and, in the absence of a specific reductive algorithm, difficult to use with computer algebra. This paper presents such an algorithm, guaranteed to reduce a general elliptic integral to a set of fundamental ones.

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Additional Information

**Norman Gray**

Affiliation:
Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, United Kingdom

Email:
norman@astro.gla.ac.uk

DOI:
https://doi.org/10.1090/S0025-5718-01-01333-3

Keywords:
Carlson elliptic integrals

Received by editor(s):
August 16, 1999

Received by editor(s) in revised form:
May 5, 2000

Published electronically:
July 22, 2001

Article copyright:
© Copyright 2001
American Mathematical Society