Generalizations of the Andrews-Yee identities associated with the mock theta functions ?(q) and ?(q)

Abstract

George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third order mock theta functions ?(q) and ?(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?(n) and a weighted partition function p?(n) is obtained from one of the special cases of our second theorem.