Automatic reduction of elliptic integrals using Carlson's relations

Gray, N. (2001) Automatic reduction of elliptic integrals using Carlson's relations. Mathematics of Computation, 71(237), pp. 311-319. (doi: 10.1090/S0025-5718-01-01333-3)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Gray, Dr Norman
Authors: Gray, N.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Mathematics of Computation
Publisher:American Mathematical Society
ISSN (Online):1088-6842
Copyright Holders:Copyright © 2001 American Mathematical Society
First Published:First published in Mathematics of Computation 71(237):311-319
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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