The Bailey chain and mock theta functions

TL;DR

This paper explores the Bailey chain's role in mock theta functions, demonstrating how to construct and prove identities for these functions using Bailey pairs and q-hypergeometric multisums.

Contribution

It introduces a method to explicitly construct mock theta functions via a change of base in Bailey pairs, expanding the toolkit for studying mock modularity.

Findings

Standard Bailey chain preserves mixed mock modularity but not pure mock modularity.

Explicit constructions of mock theta functions using Bailey pairs.

Proved identities linking multisums to classical mock theta functions.

Abstract

Standard applications of the Bailey chain preserve mixed mock modularity but not mock modularity. After illustrating this with some examples, we show how to use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to explicitly construct families of q-hypergeometric multisums which are mock theta functions. We also prove identities involving some of these multisums and certain classical mock theta functions.