Theta hypergeometric integrals

Details Theta hypergeometric integrals Theta hypergeometric integrals

2003-03-17

arxiv.org/abs/math/0303205v2

Algebra i Analiz (St. Petersburg Math. J.) 15 (2003) 161-215

Mathematics

Classical Analysis and ODEs

41 pages, some typos are removed, an appendix is added

Scientific paper

We define a general class of (multiple) integrals of hypergeometric type associated with the Jacobi theta functions. These integrals are related to theta hypergeometric series through the residue calculus. In the one variable case, we get theta function extensions of the Meijer function. A number of multiple generalizations of the elliptic beta integral [S2] associated with the root systems $A_n$ and $C_n$ is described. Some of the $C_n$-examples were proposed earlier by van Diejen and the author, but other integrals are new. An example of the biorthogonality relations associated with the elliptic beta integrals is considered in detail.

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