Variants of the Andrews-Gordon Identities

TL;DR

This paper introduces a new generalization of the Andrews-Gordon identities, extending recent results and providing combinatorial insights into their finite forms, enriching the understanding of these mathematical identities.

Contribution

The paper proposes and proves a novel generalization of the Andrews-Gordon identities, building on recent work and offering combinatorial analysis of finite forms.

Findings

New generalization of Andrews-Gordon identities proved

Combinatorial discussion of finite forms provided

Extension of recent results by Garrett, Ismail, and Stanton

Abstract

The object of this paper is to propose and prove a new generalization of the Andrews-Gordon identities, extending a recent result of Garrett, Ismail and Stanton. We also give a combinatorial discussion of the finite form of their result, which appeared in the work of Andrews, Knopfmacher, and Paule.