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Multiple Hypergeometric Series: Appell Series and Beyond

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Computer Algebra in Quantum Field Theory

Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

Abstract

This survey article provides a small collection of basic material on multiple hypergeometric series of Appell-type and of more general series of related type.

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Notes

  1. 1.

    Researchers working with Feynman integrals who are in demand of effective manipulation of Appell-type series including differential reductions and ε-expansions may find HYPERDIRE (located at https://sites.google.com/site/loopcalculations/) useful, which is a set of Wolfram Mathematica based programs for differential reduction of Horn-type hypergeometric functions, see V. Bytev et al. [9].

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Acknowledgements

I would like to thank Tom Koornwinder for pointing out references on group theoretic interpretations of Lauricella series. This work was partially supported by FWF Austrian Science Fund grants S9607 & F50-08.

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  1. Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090, Vienna, Austria

    Michael J. Schlosser

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  1. Michael J. Schlosser
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Correspondence to Michael J. Schlosser .

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  1. RISC, Johannes Kepler University, Linz, Austria

    Carsten Schneider

  2. DESY, Zeuthen, Germany

    Johannes Blümlein

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Schlosser, M.J. (2013). Multiple Hypergeometric Series: Appell Series and Beyond. In: Schneider, C., Blümlein, J. (eds) Computer Algebra in Quantum Field Theory. Texts & Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1616-6_13

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  • DOI: https://doi.org/10.1007/978-3-7091-1616-6_13

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