Further results on Andrews--Yee's two identities for mock theta functions $\omega(z;q)$ and $v(z;q)$

TL;DR

This paper extends Andrews and Yee's identities for mock theta functions by deriving variate forms, new Bailey pairs, and exploring related finite q-series summations, recurrence relations, and transformations.

Contribution

It introduces variate forms of existing identities, a new Bailey pair, and analyzes finite q-series summations related to mock theta functions.

Findings

Derived variate forms of Andrews--Yee identities

Established a new Bailey pair and product formula

Analyzed recurrence relations and transformation formulas

Abstract

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 ${}_2\phi_1$ series is derived. Further, we focus on two finite $q$-series summations arising from Andrews and Yee's mock theta function identities and expound some recurrence relations and transformation formulas behind them.