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Theta Hypergeometric Series

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Asymptotic Combinatorics with Application to Mathematical Physics

Part of the book series: NATO Science Series ((NAII,volume 77))

Abstract

We formulate general principles of building hypergeometric type series from the Jacobi theta functions that generalize the plain and basic hypergeometric series. Single and multivariable elliptic hypergeometric series are considered in detail. A characterization theorem for a single variable totally elliptic hypergeometric series is proved.

Work supported in part by the Russian Foundation for Basic Research (RFBR) grant no. 00-01-00299.

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Author information

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Moscow Region, Russia

    V. P. Spiridonov

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  1. V. P. Spiridonov
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Editor information

Editors and Affiliations

  1. I.N.R.I.A., Le Chesnay, France

    Vadim Malyshev

  2. Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

    Anatoly Vershik

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Spiridonov, V.P. (2002). Theta Hypergeometric Series. In: Malyshev, V., Vershik, A. (eds) Asymptotic Combinatorics with Application to Mathematical Physics. NATO Science Series, vol 77. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0575-3_15

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  • DOI: https://doi.org/10.1007/978-94-010-0575-3_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0793-4

  • Online ISBN: 978-94-010-0575-3

  • eBook Packages: Springer Book Archive

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