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George Andrews and Ae Ja Yee recently established beautiful results involvingbivariate 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 thesemock theta functions remained a mystery, as pointed out by Li and Yang in theirrecent work. We partially solve this problem and generalize these identities.Several new as well as well-known results are derived. For example, one of ourtwo main theorems gives, as a corollary, a special case of Soon-Yi Kang'sthree-variable reciprocity theorem. A relation between a new restrictedoverpartition function $p^{*}(n)$ and a weighted partition function $p_*(n)$ isobtained from one of the special cases of our second theorem.

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