Generalizations of the Andrews–Yee identities associated with the mock theta functions ω(q) and ν(q)

Bruce C. Berndt, Atul Dixit, Rajat Gupta

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
JournalJournal of Algebraic Combinatorics
DOIs
StateAccepted/In press - 2021

Keywords

  • 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

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