A bilateral extension of the -Selberg integral
arXiv:1309.0001 · doi:10.1090/tran/6851
Abstract
A multi-dimensional bilateral -series extending the -Selberg integral is studied using concepts of truncation, regularization and connection formulae. Following Aomoto's method, which involves regarding the -series as a solution of a -difference equation fixed by its asymptotic behavior, an infinite product evaluation is obtained. The -difference equation is derived applying the shifted symmetric polynomials introduced by Knop and Sahi. As a special case of the infinite product formula, Askey--Evans's -Selberg integral evaluation and its generalization by Tarasov--Varchenko and Stokman is reclaimed, and an explanation in the context of Aomoto's setting is thus provided.
36 pages. V6: minor corrections. arXiv admin note: text overlap with arXiv:1308.6650