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Hypergeometric Functions, Toric Varieties and Newton Polyhedra

  • Conference paper
ICM-90 Satellite Conference Proceedings

Abstract

In this talk we give a survey of our recent results on multidimensional hypergeometric functions [GZK 1,2,7], Before developing the general theory we briefly discuss main features of the classical Gauss function F(x)= 2F1 (a,b;c;x). By definition, F(x) is the solution of the hypergeometric equation

$$ x\left( {1 - x} \right)\frac{{{d^{2}}F}}{{d{x^{2}}}} + \left[ {c - \left( {a + b + 1} \right)x} \right]\frac{{dF}}{{dx}} - abF = 0 $$
((1))

regular at x=0 and normalized by F(0)=1. Here a,b and c are complex parameters.

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Author information

Authors and Affiliations

  1. Laboratory of Biorganic Chemistry, Moscow State University, Corpus A, Moscow I, 7-34, USSR

    I. M. Gelfand

  2. Scientific Council for Cybernetics, 40, Vavilova St., 117333, Moscow, USSR

    M. M. Kapranov & A. V. Zelevinsky

Authors
  1. I. M. Gelfand
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  2. M. M. Kapranov
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  3. A. V. Zelevinsky
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Editor information

Editors and Affiliations

  1. RIMS, Kyoto University, Sakyoku, Kyoto 606, Japan

    Masaki Kashiwara  & Tetsuji Miwa  & 

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© 1991 Springer-Verlag Tokyo

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Gelfand, I.M., Kapranov, M.M., Zelevinsky, A.V. (1991). Hypergeometric Functions, Toric Varieties and Newton Polyhedra. In: Kashiwara, M., Miwa, T. (eds) ICM-90 Satellite Conference Proceedings. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68170-0_6

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  • DOI: https://doi.org/10.1007/978-4-431-68170-0_6

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-70085-2

  • Online ISBN: 978-4-431-68170-0

  • eBook Packages: Springer Book Archive

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