ENGLISH

Dynamics of generalizations of the AGM continued fraction of Ramanujan: divergence

By Borwein J.M. , Luke D.R.

Book information

Year
2004
Language
english
Format
DJVU
Filesize
260 kB (266471 bytes)
Volume
Part 1
Pages
32\32
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

Description

We study several generalizaions of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were determined for certain complex parameters [2, 3, 4]. A study of the AGM continued fraction is equivalent to an analysis of the convergence of certain difference equations and the stability of dynamical systems. Using the matrix analytical tools developed in [4]. we determine the convergence properties of deterministic, and stochastic difference equations and so divergence of their corresponding continued fractions.

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