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St. Petersburg Mathematical Journal

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Continuous biorthogonality of an elliptic hypergeometric function


Author: V. P. Spiridonov
Translated by: the author
Original publication: Algebra i Analiz, tom 20 (2008), nomer 5.
Journal: St. Petersburg Math. J. 20 (2009), 791-812
MSC (2000): Primary 33C75, 81R12
DOI: https://doi.org/10.1090/S1061-0022-09-01073-5
Published electronically: July 21, 2009
MathSciNet review: 2492363
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Abstract | References | Similar Articles | Additional Information

Abstract: A family of continuous biorthogonal functions related to an elliptic analog of the Gauss hypergeometric function is constructed. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. The relationship with the Sklyanin algebra and elliptic analogs of the Faddeev modular double are discussed in detail.


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Additional Information

V. P. Spiridonov
Affiliation: Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980 Moscow Region, Russia
Email: spiridon@theor.jinr.ru

DOI: https://doi.org/10.1090/S1061-0022-09-01073-5
Keywords: Completely integrable systems, special functions, Sklyanin algebra, Faddeev modular double
Received by editor(s): December 17, 2007
Published electronically: July 21, 2009
Article copyright: © Copyright 2009 American Mathematical Society

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