Appell function proofs of recent and old mock theta function identities

TL;DR

This paper introduces new proofs for recent and old mock theta function identities using Appell function properties, highlighting similarities with Ramanujan's identities and suggesting potential for discovering more such identities.

Contribution

It provides a novel proof approach for mock theta identities based on Appell functions, connecting recent findings with classical identities and opening avenues for further discoveries.

Findings

New proofs for two recent mock theta identities by Garvan and Mukhopadhyay

A new proof of Watson's old mock theta identity

Identification of similarities with Ramanujan's sixth and tenth-order identities

Abstract

In this note we give new proofs of two recent mock theta function identities discovered by Garvan and Mukhopadhyay. We also give a new proof of an old mock theta function identity of Watson. Using the setting of Appell function properties as first introduced and developed by Hickerson and Mortenson, we demonstrate that the identities are similar to certain tenth-order and sixth-order mock theta function identities found in Ramanujan's lost notebook. Our approach suggests more identities like those of Garvan and Mukhopadhyay.