An extension of the Andrews–Warnaar partial theta function identity

Abstract

In this paper, by applying a range of classic summation and transformation formulas for basic hypergeometric series, we obtain a three-term identity for partial theta functions. It extends the Andrews–Warnaar partial theta function identity, and also unifies several results on partial theta functions due to Ramanujan, Kim and Lovejoy. We also establish a two-term version of the extension, which can be used to derive identities for partial and false theta functions. Finally, we present a relation between the big q-Jacobi polynomials and the Andrews–Warnaar partial theta function identity.