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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Automatic reduction of elliptic integrals using Carlson’s relations
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by Norman Gray PDF
Math. Comp. 71 (2002), 311-318 Request permission


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:
  • 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:
  • MathSciNet review: 1863002