2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59144We 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|=1.16 pagesQuantum AlgebraClassical Analysis and ODEstext