Theta hypergeometric integrals
Abstract
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- March 2003
- DOI:
- 10.48550/arXiv.math/0303205
- arXiv:
- arXiv:math/0303205
- Bibcode:
- 2003math......3205S
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 33Dxx;
- 33E20;
- 39A13
- E-Print:
- 41 pages, some typos are removed, an appendix is added