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Algebra i Analiz, 2003, Volume 15, Issue 6, Pages 161–215 (Mi aa829)  

This article is cited in 82 scientific papers (total in 82 papers)

Research Papers

Theta hypergeometric integrals

V. P. Spiridonov

Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Moscow Region, Dubna, Russia

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 [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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St. Petersburg Mathematical Journal, 2004, 15:6, 929–967

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Received: 15.03.2003
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Citation: V. P. Spiridonov, “Theta hypergeometric integrals”, Algebra i Analiz, 15:6 (2003), 161–215; St. Petersburg Math. J., 15:6 (2004), 929–967

Citation in format AMSBIB
\Bibitem{Spi03}
\by V.~P.~Spiridonov
\paper Theta hypergeometric integrals
\jour Algebra i Analiz
\yr 2003
\vol 15
\issue 6
\pages 161--215
\mathnet{http://mi.mathnet.ru/aa829}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2044635}
\zmath{https://zbmath.org/?q=an:1071.33011}
\transl
\jour St. Petersburg Math. J.
\yr 2004
\vol 15
\issue 6
\pages 929--967
\crossref{https://doi.org/10.1090/S1061-0022-04-00839-8}


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    This publication is cited in the following articles:
    1. V. P. Spiridonov, “A Bailey Tree for Integrals”, Theoret. and Math. Phys., 139:1 (2004), 536–541  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    6. Rosengren H., “New transformations for elliptic hypergeometric series on the root system $A_n$”, Ramanujan J., 12:2 (2006), 155–166  crossref  mathscinet  zmath  isi  scopus
    7. Spiridonov V. P., Warnaar S. O., “Inversions of integral operators and elliptic beta integrals on root systems”, Adv. Math., 207:1 (2006), 91–132  crossref  mathscinet  zmath  isi  elib  scopus
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    11. V. P. Spiridonov, “Elliptic hypergeometric functions and Calogero–Sutherland-type models”, Theoret. and Math. Phys., 150:2 (2007), 266–277  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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    13. Spiridonov V. P., “Short proofs of the elliptic beta integrals”, Ramanujan J., 13:1-3 (2007), 265–283  crossref  mathscinet  zmath  isi  scopus
    14. Spiridonov V. P., Zhedanov A. S., “Elliptic grids, rational functions, and the Padé interpolation”, Ramanujan J., 13:1-3 (2007), 285–310  crossref  mathscinet  zmath  isi  scopus
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    17. V. P. Spiridonov, “Essays on the theory of elliptic hypergeometric functions”, Russian Math. Surveys, 63:3 (2008), 405–472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. V. P. Spiridonov, “Continuous biorthogonality of the elliptic hypergeometric function”, St. Petersburg Math. J., 20:5 (2009), 791–812  mathnet  crossref  mathscinet  zmath  isi  elib
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