Browsing by Author "Borwein, J. M."
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Item Dynamics of generalizations of the AGM continued fraction of Ramanujan. Part I: divergence.(Department of Mathematical Sciences, 2004-11-19) Borwein, J. M.; Luke, D. RussellWe 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 [4, 3, 2]. 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 [2], we determine the convergence properties of deterministic difference equations and so divergence of their corresponding continued fractions.Item Dynamics of Random Continued Fractions(Department of Mathematical Sciences, 2004-11-16) Borwein, J. M.; Luke, D. RussellWe study a generalization of a continued fraction of Ramanujan with random 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 divergence of their corresponding continued fractions.