Multilateral basic hypergeometric summation identities and hyperoctahedral group symmetries

TL;DR

This paper introduces new proofs for bilateral basic hypergeometric summation formulas leveraging hyperoctahedral group symmetries, including a multiple series analogue of Bailey's $_3\psi_3$ summation, expanding understanding of these identities.

Contribution

The paper provides novel symmetry-based proofs for hypergeometric identities and extends Bailey's $_3\psi_3$ summation to higher-rank multiple series using hyperoctahedral group symmetries.

Findings

New symmetry-based proofs for hypergeometric summations

Extension of Bailey's $_3\psi_3$ to higher ranks

Identification of hyperoctahedral group symmetries in series

Abstract

We give new proofs for certain bilateral basic hypergeometric summation formulas using the symmetries of the corresponding series. In particular, we present a proof for Bailey's $_3\psi_3$ summation formula as an application. We also prove a multiple series analogue of this identity by considering hyperoctahedral group symmetries of higher ranks.