George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third-order mock theta functions ω(q) and ν(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.
- Andrews–Yee identities
- Partial theta function
- Reciprocity theorem
- Third-order mock theta functions
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics