On the tenth-order mock theta functions

TL;DR

This paper provides insightful proofs for six of Ramanujan's tenth-order mock theta function identities by leveraging properties of Appell-Lerch functions, enhancing understanding of these complex special functions.

Contribution

It introduces a novel approach using Appell-Lerch functions to prove Ramanujan's tenth-order mock theta identities, offering new insights into their structure.

Findings

Proofs of six Ramanujan identities for tenth-order mock theta functions

Application of Appell-Lerch functions to mock theta identities

Enhanced understanding of mock theta function properties

Abstract

Using properties of Appell-Lerch functions, we give insightful proofs for six of Ramanujan's identities for the tenth-order mock theta functions.