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Hypergeometric Functions, Toric Varieties and Newton Polyhedra

  • I. M. Gelfand
  • M. M. Kapranov
  • A. V. Zelevinsky

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.

Keywords

Convex Hull Hypergeometric Function Toric Variety Cotangent Bundle Laurent Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • I. M. Gelfand
    • 1
  • M. M. Kapranov
    • 2
  • A. V. Zelevinsky
    • 2
  1. 1.Laboratory of Biorganic ChemistryMoscow State UniversityCorpus A, Moscow IUSSR
  2. 2.Scientific Council for CyberneticsMoscowUSSR

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