A Simple Example of a New Class of Landen Transformations

Author: Manna Dante   Moll Victor H.  

Publisher: Mathematical Association of America

ISSN: 1930-0972

Source: American Mathematical Monthly, Vol.114, Iss.3, 2007-03, pp. : 232-241

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Abstract

The classical arithmetic-geometric mean discovered by Gauss is based on a transformation of the parameters of an elliptic integral that leaves the integral invariant. The authors present the simplest example of such transformations in the case of the integral of a rational function. We present an explicit algorithm that leaves the integral invariant and establish the convergence of its iterates.