An extension of the Andrews-Warnaar partial theta function identity

2019/07/19 by Sun, Lisa Hui
#05A30 #33D15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.08353

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, Lovejoy and Kim. 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.

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