DocServer

Dynamics of generalizations of the AGM continued fraction of Ramanujan. Part I: divergence.

Borwein, Jonathan M. and Luke, D. Russell (2004) Dynamics of generalizations of the AGM continued fraction of Ramanujan. Part I: divergence. [Preprint]

[img]
Preview
PDF
Download (1044Kb) | Preview

    Abstract

    We study several generalizations 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. 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 matrix analytical tools, we determine the convergence properties of deterministic difference equations and so divergence of their corresponding continued fractions.

    Item Type: Preprint
    Additional Information: pubdom FALSE
    Uncontrolled Keywords: Continued fractions, Ramanujan AGM relation, difference equations, matrix analysis
    Subjects: 11-xx Number theory > 11Jxx Diophantine approximation, transcendental number theory
    Faculty: UNSPECIFIED
    Depositing User: Russell Luke
    Date Deposited: 14 Mar 2005
    Last Modified: 21 Apr 2010 11:13
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/276

    Actions (login required)

    View Item