Automatic reduction of elliptic integrals using Carlson’s relations
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- Math. Comp. 71 (2002), 311-318 Request permission
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.References
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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
- Received by editor(s): August 16, 1999
- Received by editor(s) in revised form: May 5, 2000
- Published electronically: July 22, 2001
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1863002