Abstract and Applied Analysis
Volume 2005 (2005), Issue 5, Pages 449-467
doi:10.1155/AAA.2005.449
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
Abstract
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.