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Russian Mathematical Surveys, 2008, Volume 63, Issue 3, Pages 405–472
DOI: https://doi.org/10.1070/RM2008v063n03ABEH004533 (Mi rm9197) 		 
This article is cited in 101 scientific papers (total in 101 papers)

Essays on the theory of elliptic hypergeometric functions

V. P. Spiridonov

Joint Institute for Nuclear Research
English version PDF (904 kB) Citations (101)
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DOI: https://doi.org/10.1070/RM2008v063n03ABEH004533
Abstract: This is a brief survey of the main results of the theory of elliptic hypergeometric functions — a new class of special functions of mathematical physics. A proof is given of the most general known univariate exact integration formula generalizing Euler's beta integral. It is called the elliptic beta integral. An elliptic analogue of the Gauss hypergeometric function is constructed together with the elliptic hypergeometric equation for it. Biorthogonality relations for this function and its particular subcases are described. The known elliptic beta integrals on root systems are listed, and symmetry transformations are considered for the corresponding higher-order elliptic hypergeometric functions.
Received: 09.04.2008
Russian version:
Uspekhi Matematicheskikh Nauk, 2008, Volume 63, Issue 3(381), Pages 3–72
DOI: https://doi.org/10.4213/rm9197
Bibliographic databases:
Document Type: Article
UDC: 517.5+517.3
MSC: Primary 33D67; Secondary 33E05
Language: English
Original paper language: Russian
Citation: V. P. Spiridonov, “Essays on the theory of elliptic hypergeometric functions”, Uspekhi Mat. Nauk, 63:3(381) (2008), 3–72; Russian Math. Surveys, 63:3 (2008), 405–472
Citation in format AMSBIB
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    		Успехи математических наук Russian Mathematical Surveys
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    References:144
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