Some new representations of Hikami's second-order mock theta function $\mathfrak{D}_5(q)$

Authors

QIUXIA HU

Abstract

In this paper, a second-order mock theta function $\mathfrak{D}_5(q)$ given by Hikami [11] is studied. By using basic hypergeometric transformation formulae, we attain some new representations of Hikami's mock theta function $\mathfrak{D}_5(q)$. Meanwhile, dual nature of bilateral series associated to mock theta function $\mathfrak{D}_5(q)$ is also discussed.

DOI

10.3906/mat-2106-12

Keywords

Second-order mock theta function, $q$-hypergeometric series, dual nature, Appell-Lerch sums

First Page

2248

Last Page

2259

Recommended Citation

HU, Q (2021). Some new representations of Hikami's second-order mock theta function $\mathfrak{D}_5(q)$. Turkish Journal of Mathematics 45 (5): 2248-2259. https://doi.org/10.3906/mat-2106-12