Determinants of elliptic hypergeometric integrals

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Abstract

We start from an interpretation of the BC 2-symmetric “Type I” (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation and then generalize this construction to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding formulas for the elliptic beta integral and symmetry transformation in a new way, by proving that both sides satisfy the same difference equations and that these difference equations satisfy a needed Galois-theoretic condition ensuring the uniqueness of the simultaneous solution.

Key words

elliptic hypergeometric function difference equation determinant difference Galois theory 
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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Department of MathematicsCaltech, PasadenaRussia
  2. 2.Bogoliubov Laboratory of Theoretical PhysicsJINRDubna, MoscowRussia

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