Artículos de revistas
Elliptic beta integrals and modular hypergeometric sums: An overview
Registro en:
Rocky Mountain Journal of Mathematics 32 (2): 639-656
0035-7596
Autor
Van Diejen, J.F.
Spiridonov, V.P.
Institución
Resumen
Van Diejen, J.F. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile. 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.