Dynamics of a continued fraction of Ramanujan with random coefficients | Zendy

Jonathan M. Borwein | Zendy; D. Lüke | Zendy

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Dynamics of a continued fraction of Ramanujan with random coefficients

Author(s) -

Jonathan M. Borwein,

D. Lüke

Publication year - 2005

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/aaa.2005.449

Subject(s) - mathematics , fraction (chemistry) , ramanujan's sum , generalization , divergence (linguistics) , convergence (economics) , stability (learning theory) , continued fraction , mathematical analysis , pure mathematics , arithmetic , linguistics , chemistry , philosophy , organic chemistry , machine learning , computer science , economics , remainder , economic growth

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

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