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
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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