# Finite Rogers--Ramanujan type identities

## TL;DR

This paper presents polynomial generalizations of all identities in Slater's list of Rogers-Ramanujan type, introduces duality relationships, and provides a Maple package for finitization, expanding the understanding of these identities.

## Contribution

It offers the first complete polynomial generalizations of all 130 identities in Slater's list and introduces duality relationships among them.

## Key findings

- Polynomial generalizations for all Slater identities are provided.
- Many identities are newly discovered, some were previously known.
- A Maple package for finitization is made available for researchers.

## Abstract

Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free download from the author's website.