The Bailey chain and 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.