Theta hypergeometric integrals
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- by V. P. Spiridonov
- St. Petersburg Math. J. 15 (2004), 929-967
- DOI: https://doi.org/10.1090/S1061-0022-04-00839-8
- Published electronically: November 16, 2004
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Abstract:
A general class of (multiple) hypergeometric type integrals associated with the Jacobi theta functions is defined. These integrals are related to theta hypergeometric series via the residue calculus. In the one variable case, theta function extensions of the Meijer function are obtained. A number of multiple generalizations of the elliptic beta integral 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.References
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Bibliographic Information
- V. P. Spiridonov
- Affiliation: Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Region 141980, Russia
- Email: spiridon@thsun1.jinr.ru
- Received by editor(s): March 15, 2003
- Published electronically: November 16, 2004
- Additional Notes: Supported in part by the RFBR (grant no. 03-01-00781).
- © Copyright 2004 American Mathematical Society
- Journal: St. Petersburg Math. J. 15 (2004), 929-967
- MSC (2000): Primary 33C67, 33D70
- DOI: https://doi.org/10.1090/S1061-0022-04-00839-8
- MathSciNet review: 2044635
Dedicated: Dedicated to Mizan Rahman