A q-product tutorial for a q-series MAPLE package

TL;DR

This paper introduces a Maple package for q-series that facilitates conversion between q-series and q-products, enabling algebraic relation discovery and finite q-product factorizations, with applications to theta functions and eta products.

Contribution

It provides the first implementation of Andrews' algorithm for converting q-series into products and demonstrates its effectiveness in finding factorizations.

Findings

Successfully converts q-series to q-products using the package.

Finds finite q-product factorizations effectively.

Applies to factorisations involving theta functions and eta products.

Abstract

This is a tutorial for using a new q-series Maple package. The package includes facilities for conversion between q-series and q-products and finding algebraic relations between q-series. Andrews found an algorithm for converting a q-series into a product. We provide an implementation. As an application we are able to effectively find finite q-product factorisations when they exist thus answering a question of Andrews. We provide other applications involving factorisations into theta functions and eta products.