The q-twisted cohomology and the q-hypergeometric function at |q|=1

摘要

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