English

An extension of the Andrews-Warnaar partial theta function identity

Combinatorics 2019-07-22 v1

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 qq-Jacobi polynomials and the Andrews-Warnaar partial theta function identity.

Keywords

Cite

@article{arxiv.1907.08353,
  title  = {An extension of the Andrews-Warnaar partial theta function identity},
  author = {Lisa Hui Sun},
  journal= {arXiv preprint arXiv:1907.08353},
  year   = {2019}
}