On some new Bailey pairs and new expansions for some Mock theta functions

TL;DR

This paper introduces new identities and Bailey pairs related to mock theta functions, enhancing understanding and providing new tools for their study through innovative base-changing techniques.

Contribution

It presents novel Bailey pairs connected to indefinite quadratic forms and new identities for mock theta functions, advancing the analytical methods in this area.

Findings

New Bailey pairs related to indefinite quadratic forms

New identities for mock theta functions

Enhanced methods for analyzing mock theta functions

Abstract

In this paper we offer some new identities associated with mock theta functions and establish new Bailey pairs related to indefinite quadratic forms. We believe our proof is instructive use of changing base of Bailey pairs, and offers new information on some Bailey pairs that have proven important in the study of Mock theta functions.