Determinants of elliptic hypergeometric integrals

Abstract

We start from an interpretation of the $B{C}_2$-symmetric "Type I" (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation, and give an extension to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding elliptic beta integral and transformation formula in a new way, by proving both sides satisfy the same difference equations, and that the difference equations satisfy a Galois-theoretical condition that ensures uniqueness of simultaneous solution.

17 pages; minor modifications

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• Essays on the theory of elliptic hypergeometric functions