Certain q-series identities and applications to Lecture hall type partitions

Abstract

In this work, we found certain new q summation formulae and some recurrence relations for q-Jacobi polynomials using generalization of the contiguous relations for basic hypergeometric series. Some of these results are new and the proof of remaining are shorter than the one that exist in the literature. As an application, certain identities related to Lecture hall type partitions are also exhibited.