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arXiv · 1309.0001

A bilateral extension of the $q$-Selberg integral

Masahiko Ito·Peter J. Forrester
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Abstract

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.

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Masahiko Ito, Peter J. Forrester. 2016-10-29. A bilateral extension of the $q$-Selberg integral. https://doi.org/10.1090/tran%2F6851

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