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Reflections on the Baker–Gammel–Wills (Padé) Conjecture

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Analytic Number Theory, Approximation Theory, and Special Functions

Abstract

In 1961, Baker, Gammel, and Wills formulated their famous conjecture that if a function f is meromorphic in the unit ball and analytic at 0, then a subsequence of its diagonal Padé approximants converges uniformly in compact subsets to f. This conjecture was disproved in 2001, but it generated a number of related unresolved conjectures. We review their status.

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Acknowledgements

Research supported by NSF grant DMS1001182 and US-Israel BSF grant 2008399.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Doron S. Lubinsky

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  1. Doron S. Lubinsky
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Correspondence to Doron S. Lubinsky .

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  1. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Gradimir V. Milovanović

  2. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Michael Th. Rassias

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Dedicated to Professor Hari M. Srivastava

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Lubinsky, D.S. (2014). Reflections on the Baker–Gammel–Wills (Padé) Conjecture. In: Milovanović, G., Rassias, M. (eds) Analytic Number Theory, Approximation Theory, and Special Functions. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0258-3_21

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