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Special Values of the Hypergeometric Series


About this Title

Akihito Ebisu

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 248, Number 1177
ISBNs: 978-1-4704-2533-3 (print); 978-1-4704-4056-5 (online)
DOI: https://doi.org/10.1090/memo/1177
Published electronically: March 15, 2017
Keywords:Hypergeometric series, three term relation, special value, solving polynomial systems

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Preliminaries
  • Chapter 3. Derivation of special values
  • Chapter 4. Tables of special values
  • Appendix A. Some hypergeometric identities for generalized hypergeometric series and Appell-Lauricella hypergeometric series
  • Acknowledgments

Abstract


In this paper, we present a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, we get identities for the hypergeometric series ; we show that values of at some points can be expressed in terms of gamma functions, together with certain elementary functions. We tabulate the values of that can be obtained with this method. We find that this set includes almost all previously known values and many previously unknown values.

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