q-hypergeometric double sums as mock theta functions

TL;DR

This paper introduces new mock theta functions expressed as q-hypergeometric double sums derived from Bailey pairs, connecting them to real quadratic fields and classical mock theta functions.

Contribution

It presents novel mock theta functions from Bailey pairs and establishes an identity linking these to classical mock theta functions.

Findings

New mock theta functions as q-hypergeometric double sums

Connection to real quadratic fields via Bailey pairs

Identity relating new sums to classical 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.