Mathematica evidence that Ramanujan kills Baker-Gammel-Wills.
type: Item
instance of: scholarly article
title: Mathematica evidence that Ramanujan kills Baker-Gammel-Wills.
zbMATH Open document ID: 1042.41011
DOI: 10.1016/S0096-3003(01)00077-7
author: Arnold Knopfmacher
author: Doron S. Lubinsky
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The famous Padé conjecture revised on 1961 by Baker, Gammel and Wills asserts that if a function \(f\) is meromorphic in the unit ball, and analytic at zero, then a subsequence of its diagonal Padé approximants converges uniformly in compact subsets omitting poles. Lubinsky and then Buslaev showed recently that this conjecture is false. In this paper the authors present numerical evidence derived using the Mathematica package, that \(f\) given by the Ramanujan continued fraction \(1+\frac{qz}{1+}\frac{q^2z}{1+}\frac{q^3z}{1+}\ldots\) provides a counterexample, provided \(q\) is appropriately chosen on the unit circle.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 1861074
zbMATH Keywords: Padé approximation
describes a project that uses: Mathematica
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00077-7
OpenAlex ID: W2098905067
description: scientific article; zbMATH DE number 1861074