posted on 2025-05-11, 07:49authored byJonathan M. Borwein, D. Russell Luke
We study a generalization of a continued fraction of Ramanujan with random, complexvalued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of randomdynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding continued fractions.