# New fifth and seventh order mock theta function identities

## TL;DR

This paper provides simple proofs for identities involving fifth and seventh order mock theta functions, revealing unexpected relationships among their coefficients, advancing understanding of Ramanujan's mock theta functions.

## Contribution

It introduces straightforward proofs for complex identities of fifth and seventh order mock theta functions and uncovers surprising coefficient relations among seventh order functions.

## Key findings

- Proofs of identities for fifth and seventh order mock theta functions
- Coefficients of seventh order mock theta functions are surprisingly related
- Enhanced understanding of Ramanujan's mock theta functions

## Abstract

We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan fifth order mock theta functions $\chi_0(q)$ and $\chi_1(q)$ and all three of Ramanujan's seventh order mock theta functions. We find that the coefficients of the three mock theta functions of order 7 are surprisingly related.