Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Rational Landen transformations on $\mathbb{R}$

Author(s): Dante Manna; Victor H. Moll.
Journal: Math. Comp. 76 (2007), 2023-2043.
MSC (2000): Primary 33F05; Secondary 26C15
Posted: May 3, 2007
MathSciNet review: 2336279
Retrieve article in: PDF

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. We present analogous transformations for rational functions integrated over the whole real line.

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