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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Theta hypergeometric integrals

Author: V. P. Spiridonov
Original publication: Algebra i Analiz, tom 15 (2003), nomer 6.
Journal: St. Petersburg Math. J. 15 (2004), 929-967
MSC (2000): Primary 33C67, 33D70
Published electronically: November 16, 2004
MathSciNet review: 2044635
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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.

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Additional Information

V. P. Spiridonov
Affiliation: Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Region 141980, Russia

Keywords: Multiple hypergeometric integrals, Jacobi theta functions, elliptic beta integral, root system
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).
Dedicated: Dedicated to Mizan Rahman
Article copyright: © Copyright 2004 American Mathematical Society

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