A multilateral Bailey Lemma and multiple Andrews--Gordon identities

TL;DR

This paper introduces a multilateral Bailey Lemma, enabling the derivation of multiple Andrews--Gordon identities and generalizations of classical theorems using determinant expressions of theta functions.

Contribution

It presents a new multilateral Bailey Lemma and applies it to generalize key identities like Rogers--Ramanujan and Euler's Pentagonal Theorem.

Findings

Established a multilateral Bailey Lemma.

Derived multiple analogues of Rogers--Ramanujan identities.

Generalized Andrews--Gordon identities using determinants of theta functions.

Abstract

A multilateral Bailey Lemma is proved, and multiple analogues of the Rogers--Ramanujan identities and Euler's Pentagonal Theorem are constructed as applications. The extreme cases of the Andrews--Gordon identities are also generalized using the multilateral Bailey Lemma where their final form is written in terms of determinants of theta functions.