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A class of algorithms for obtaining rational approximants to functions which are defined by power series

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Abstract

The problem of converting power series to different types of continued fractions is treated by demonstrating the generality of application of an often neglected class of algorithms. As an example, a new expansion is obtained for the gamma function.

Zusammenfassung

Die Arbeit behandelt die Umwandlung von Potenzreihen in entsprechende Kettenbrüche. Es wird die allgemeine Anwendbarkeit einer häufig unberücksichtigten Klasse von Algorithmen gezeigt. Als Anwendung wird eine neue Entwicklung der Gammafunktion hergeleitet.

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Authors and Affiliations

  1. Dept of Mathematics, Brunel University, Uxbridge, England

    J. A. Murphy

  2. Dept of Mathematics, University of Manchester, Manchester, England

    M. R. O'Donohoe

Authors
  1. J. A. Murphy
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  2. M. R. O'Donohoe
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Murphy, J.A., O'Donohoe, M.R. A class of algorithms for obtaining rational approximants to functions which are defined by power series. Journal of Applied Mathematics and Physics (ZAMP) 28, 1121–1131 (1977). https://doi.org/10.1007/BF01601678

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  • DOI: https://doi.org/10.1007/BF01601678

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