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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 2024 MCQ for Mathematics of Computation is 1.78.

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Rational Landen transformations on $\mathbb {R}$
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by Dante Manna and Victor H. Moll;
Math. Comp. 76 (2007), 2023-2043
DOI: https://doi.org/10.1090/S0025-5718-07-01954-0
Published electronically: May 3, 2007

Abstract:

The Landen transformation $(a,b) \mapsto ( (a+b)/2,\sqrt {ab} )$ preserves the value of an elliptic integral, and its iteration produces the classical arithmetic-geometric mean $\text {AGM}(a,b)$. We present analogous transformations for rational functions integrated over the whole real line.
References
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Bibliographic Information
  • Dante Manna
  • Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisianna 70118
  • Address at time of publication: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
  • Email: dmanna@mathstat.dal.ca
  • Victor H. Moll
  • Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisianna 70118
  • Email: vhm@math.tulane.edu
  • Received by editor(s): November 2, 2005
  • Published electronically: May 3, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 2023-2043
  • MSC (2000): Primary 33F05; Secondary 26C15
  • DOI: https://doi.org/10.1090/S0025-5718-07-01954-0
  • MathSciNet review: 2336279