Multilateral basic hypergeometric summation identities and hyperoctahedral group symmetries

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 $_3ψ_3$ summation formula as an application. We also prove a multiple series analogue of this identity by considering hyperoctahedral group symmetries of higher ranks.

9 pages