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.

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

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