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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/4320

Title: Elliptic beta integrals and modular hypergeometric sums: An overview
Authors: Van Diejen, J.F.
Spiridonov, V.P.
Keywords: Rational Functions; bailey transform; series; polynomials; formulas
Issue Date: 2002
Citation: Rocky Mountain Journal of Mathematics 32 (2): 639-656
Abstract: Recent results on elliptic generalizations of various beta integrals are reviewed. Firstly, a single variable Askey-Wilson type integral describing an elliptic extension of the Nassrallah-Rahman integral is presented. Then a multiple Selberg-type integral defining an elliptic extension of the Macdonald-Morris constant term identities for nonreduced root systems is described. The Frenkel-Turaevsu m and its multivariable generalization, conjectured recently by Warnaar, follow from these integrals through residue calculus. A new elliptic Selberg-type integral, from which the previous one can be derived via a technique due to Gustafson, is defined. Residue calculus applied to this integral yields an elliptic generalization of the Denis-Gustafson sum a modular extension of the Milne-type multiple basic hypergeometric sums.
Description: Van Diejen, J.F. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile.
URI: http://dspace.utalca.cl/handle/1950/4320
ISSN: 0035-7596
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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