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
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
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.
Related content
A class of simple proper Bol loops
By Nagy Gábor
manuscripta mathematica, Vol. 127, Iss. 1, 2008-09 ,pp. :
A Simple Algorithm for the Evaluation of a Class of Generalized Hypergeometric Series
STUDIES IN APPLIED MATHEMATICS, Vol. 22-2526, Iss. 1, 1992-01 ,pp. :