q-hypergeometric double sums as mock theta functions

Abstract

Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums. Additionally, we prove an identity between one of these sums and two classical mock theta functions introduced by Gordon and McIntosh.

12 pages, to appear in Pacific J. Math

References in corpus (1)

• Automorphic properties of generating functions for generalized rank moments and Durfee symbols

Cited by in corpus (2)

• Mock theta double sums
• Higher depth mock theta functions and $q$-hypergeometric series