On recursions for coefficients of mock theta functions

TL;DR

This paper employs a generalized Lambert series identity to derive recursive formulas for coefficients of third-order mock theta functions, providing new proofs and exploring broader applications within mock theta function theory.

Contribution

It introduces a novel approach using Lambert series identities to prove recursive formulas for mock theta function coefficients, expanding understanding of their structure.

Findings

Derived recursive formulas for third-order mock theta coefficients

Provided q-series proofs for recent results by Imamoglu, Raum, and Richter

Discussed applications of the identity to other mock theta functions

Abstract

We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoglu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions. Additionally, we discuss an application of this identity to other mock theta functions.