A bilateral extension of the q-Selberg integral
Masahiko Ito, Peter J Forrester
Transactions of the American Mathematical Society | American Mathematical Society | Published : 2017
A multi-dimensional bilateral q-series extending the q-Selberg integral is studied using concepts of truncation, regularization and connection formulae. Following Aomoto's method, which involves regarding the q-series as a solution of a q-difference equation fixed by its asymptotic behavior, an infinite product evaluation is obtained. The $ q$-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 q-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.
Related Projects (1)
Awarded by Australian Research Council
Awarded by JSPS KAKENHI
This work was supported by the Australian Research Council (Grant DP110102317) and JSPS KAKENHI Grant Number 25400118.