Four identities related to third-order mock theta functions

@article{Cui2020FourIR,
title={Four identities related to third-order mock theta functions},
author={Su-Ping Cui and Nancy S. S. Gu and Chen-Yang Su},
journal={The Ramanujan Journal},
year={2020}
}
• Published 1 December 2018
• Mathematics
• The Ramanujan Journal
Ramanujan presented four identities for third order mock theta functions in his Lost Notebook. In 2005, with the aid of complex analysis, Yesilyurt first proved these four identities. Recently, Andrews et al. provided different proofs by using $q$-series. In this paper, in view of some identities of a universal mock theta function \begin{align*} g(x;q)=x^{-1}\left(-1+\sum_{n=0}^{\infty}\frac{q^{n^{2}}}{(x;q)_{n+1}(qx^{-1};q)_{n}}\right), \end{align*} we establish new proofs of these four…

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