Shifted versions of the Bailey and well-poised Bailey lemmas

TL;DR

This paper introduces shifted Bailey lemmas to derive new Rogers-Ramanujan type identities, extending classical results and providing novel multisum identities through innovative applications of well-poised variants.

Contribution

It develops shifted versions of the Bailey and Well-Poised Bailey lemmas to produce new identities, extending the classical Rogers-Ramanujan framework.

Findings

Derived m-versions of multisum Rogers-Ramanujan identities

Extended Rogers-Ramanujan identities using Well-Poised Bailey lemma

Provided new proofs and extensions of classical identities

Abstract

The Bailey lemma is a famous tool to prove Rogers-Ramanujan type identities. We use shifted versions of the Bailey lemma to derive $m$-versions of multisum Rogers-Ramanujan type identities. We also apply this method to the Well-Poised Bailey lemma and obtain a new extension of the Rogers-Ramanujan identities.