Determinants of elliptic hypergeometric integrals

Details Determinants of elliptic hypergeometric integrals Determinants of elliptic hypergeometric integrals

2007-12-27

arxiv.org/abs/0712.4253v2

Funct. Analysis and its Appl. 43 (2009), no. 4, 297-311

Mathematics

Classical Analysis and ODEs

17 pages; minor modifications

Scientific paper

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 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.

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