Dynamics of a Ramanujan-type continued fraction with cyclic coefficients

Title: Dynamics of a Ramanujan-type continued fraction with cyclic coefficients
Creator: Borwein, Jonathan M.; Luke, D. Russell
Relation: The Ramanujan Journal Vol. 16, p. 285-304
Publisher Link: http://dx.doi.org/10.1007/s11139-007-9096-7
Publisher: Springer
Resource Type: journal article
Date: 2008
Description: 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 (Borwein et al., Exp. Math. 13, 275–286, 2004, Ramanujan J., in press, 2004; Borwein and Crandall, Exp. Math. 12, 287–296, 2004). 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 2004, we determine the convergence properties of deterministic difference equations and so divergence of their corresponding continued fractions.
Subject: continued fractions; Ramanujan AGM relation; difference equations; atrix analysis
Identifier: http://hdl.handle.net/1959.13/940072
Identifier: uon:12941
Identifier: ISSN:1382-4090
Language: eng
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