Some new results on Andrews' and Warnaar's q-identities

TL;DR

This paper introduces generalized q-series identities, new Bailey pairs, and related q-identities, expanding on Andrews' and Warnaar's work using inverse relations and coefficient comparison techniques.

Contribution

The paper presents novel generalized q-series identities and two new Bailey pairs, enhancing the understanding of Andrews-Warnaar's sum identity for partial theta functions.

Findings

Established generalized forms of Andrews' q-series identity

Derived two new Bailey pairs and q-identities

Connected new identities to partial theta functions

Abstract

In this paper, by the technique of inverse relations and comparing coefficients, we establish some generalized forms of Andrews' q-series identity and two new Bailey pairs and q-identities closely related to Andrews-Warnaar's sum identity for partial theta functions.