On the Andrews–Yee Identities Associated with Mock Theta Functions

In this paper, we generalize the Andrews–Yee identities associated with the third-order mock theta functions ω(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega (q)$$\end{document} and ν(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu (q)$$\end{document}. We obtain some q-series transformation formulas, one of which gives a new Bailey pair. Using the classical Bailey lemma, we derive a product formula for two 2ϕ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_2\phi _1$$\end{document} series. We also establish recurrence relations and transformation formulas for two finite sums arising from the Andrews–Yee identities.