Bailey Pairs With Free Parameters, Mock Theta Functions and Tubular Partitions

Abstract

This study began in an effort to find a simpler derivation of the Bailey pairs associated with the seventh order mock theta functions. It is shown that the introduction of a new parameter independent of both a and q leads to a much simpler treatment. It is noted that a previous treatment of the central fifth order mock theta function inadvertently uses this approach. The paper concludes by applying this method to find new surprising identities and new arithmetic objects, tubular partitions.