  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.
