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Ten Problems in Experimental Mathematics
, 2006
"... Challenge ” of Nick Trefethen, beautifully described in [12] (see also [13]). Indeed, these ten numeric challenge problems are also listed in [15, pp. 22–26], where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent in [15] was to present ..."
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Cited by 11 (5 self)
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Challenge ” of Nick Trefethen, beautifully described in [12] (see also [13]). Indeed, these ten numeric challenge problems are also listed in [15, pp. 22–26], where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent in [15] was to present ten problems that are characteristic of the sorts of problems
Dynamics of generalizations of the AGM continued fraction of Ramanujan. Part I: Divergence
, 2004
"... We 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 [2, 3, 4]. A study of the AGM continued ..."
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Cited by 4 (3 self)
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We 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 [2, 3, 4]. 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 [4], we determine the convergence properties of deterministic, and stochastic difference equations and so divergence of their corresponding continued fractions.
Dynamics of Random Continued Fractions
, 2004
"... We 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 ..."
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We 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. 1
Srinivasa Ramanujan: Going Strong at 125, Part I
, 2013
"... on December 22, 2012. To mark this occasion, the Notices offers the following feature article, which appears in two installments. The article contains an introductory piece describing various major developments in the world of Ramanujan since his centennial in 1987, followed by seven pieces describi ..."
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on December 22, 2012. To mark this occasion, the Notices offers the following feature article, which appears in two installments. The article contains an introductory piece describing various major developments in the world of Ramanujan since his centennial in 1987, followed by seven pieces describing important research advances in several areas of mathematics influenced by him. The first installment in the present issue of the Notices contains the introductory piece by Krishnaswami Alladi, plus pieces
Dynamics of a Ramanujantype Continued Fraction with Cyclic Coefficients
, 2005
"... We 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 ..."
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We 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.
On the Ramanujan AGM fraction. Part I: The realparameter case
, 2003
"... Abstract. The Ramanujan AGM continued fraction is a construct Rη(a, b) = a η + b2 η + ..."
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Abstract. The Ramanujan AGM continued fraction is a construct Rη(a, b) = a η + b2 η +