Abstract and Applied Analysis
Volume 2005 (2005), Issue 5, Pages 449-467

Dynamics of a continued fraction of Ramanujan with random coefficients

Jonathan M. Borwein1 and D. Russell Luke2

1Faculty of Computer Science, Dalhousie University, Halifax B3H 1W5, NS, Canada
2Department of Mathematical Sciences, College of Arts and Sciences, University of Delaware, Newark 19716-2553, DE, USA

Received 16 November 2004

Copyright © 2005 Jonathan M. Borwein and D. Russell Luke. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study a generalization of a continued fraction of Ramanujan with random, complex-valued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding continued fractions.