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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
Published electronically: July 22, 2001
MathSciNet review: 1863002
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Abstract: 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

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