Generalizations of the Andrews-Yee identities associated with the mock theta functions $\omega (q)$ and $\nu (q)$

Abstract

George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third order mock theta functions $\omega (q)$ and $\nu (q)$, thereby extending their earlier results with the second author. Generalizing the Andrews-Yee identities for trivariate generalizations of these mock theta functions remained a mystery, as pointed out by Li and Yang in their recent work. We partially solve this problem and generalize these identities. Several new as well as well-known results are derived. For example, one of our two main theorems gives, as a corollary, a special case of Soon-Yi Kang's three-variable reciprocity theorem. A relation between a new restricted overpartition function $p^{\ast }(n)$ and a weighted partition function $p_{\ast }(n)$ is obtained from one of the special cases of our second theorem.

25 pages, submitted for publication