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 -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}
}