The <em>q</em>-twisted Cohomology and the <em>q</em>-hypergeometric Function at |<em>q</em>|=1

Abstract

We construct the q-twisted cohomology associated with the q-multiplicative function of Jordan–Pochhammer type at |q|=1. In this framework, we prove the Heine's relations and a connection formula for the q-hypergeometric function of the Barnes type. We also prove an orthogonality relation of the q-little Jacobi polynomials at |q|=1.