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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Rational Landen transformations on $ \mathbb{R}$


Authors: Dante Manna and Victor H. Moll
Journal: Math. Comp. 76 (2007), 2023-2043
MSC (2000): Primary 33F05; Secondary 26C15
Published electronically: May 3, 2007
MathSciNet review: 2336279
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Abstract | References | Similar Articles | Additional Information

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 AGM$ (a,b)$. We present analogous transformations for rational functions integrated over the whole real line.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01954-0
PII: S 0025-5718(07)01954-0
Keywords: Integrals, transformations
Received by editor(s): November 2, 2005
Published electronically: May 3, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.