# Generalising the Wallis Product

## TL;DR

This paper explores generalizations of Wallis' Product for pi using Gamma Function techniques, presenting new results on related infinite products and expanding understanding of these mathematical formulas.

## Contribution

It introduces new findings on classes of infinite products related to Wallis' Product using Gamma Function methods.

## Key findings

- New formulas for generalized Wallis products
- Connections between infinite products and Gamma Function
- Enhanced understanding of pi-related infinite products

## Abstract

In 1655, John Wallis whilst at the University of Oxford discovered the famous and beautiful formula for pi, now known as Wallis' Product. Since then, several analogous formulae have been discovered generalising the original. One more modern proof of the Wallis Product and its relatives directly uses the Gamma Function. This short paper will use similar techniques to understand certain related classes of infinite products. Almost all results within this paper are new findings made by myself; when I should be revising or completing assignment work I find myself always going back to this.