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In this paper, by the method of comparing coefficients and the inverse technique, we establish the corresponding variate forms of two identities of Andrews and Yee for mock theta functions, as well as a few allied but unusual $q$-series identities. Among includes a new Bailey pair from which a product formula of two ${}_2phi_1$ series is derived. Further, we focus on two finite $q$-series summations arising from Andrews and Yees mock theta function identities and expound some recurrence relations and transformation formulas behind them.
In this paper we set up a bivariate representation of partial theta functions which not only unifies some famous identities for partial theta functions due to Andrews and Warnaar, et al. but also unveils a new characteristic of such identities. As fu
Ramanujan studied the analytic properties of many $q$-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious $q$-series fit into the theory of automorphic forms.
In this article, we prove a new general identity involving the Theta operators introduced by the first author and his collaborators in [DAdderio, Iraci, Vanden Wyngaerd 2020]. From this result, we can easily deduce several new identities that have co
We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of mock theta functions. By comparing the different evaluations, we deriv
We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the $q$-deformed Pa