Abstract: We give new proofs for certain bilateral basic
hypergeometric summation formulas using the symmetries of the corresponding
series. In particular, wepresentaprooffor Bailey’s summation
formula as an application. We also prove a multiple series analogue of this
identity considering hyperoctahedral group symmetries of higher ranks.
Keywords and phrases: bilateral basic hypergeometric
series, hyperoctahedral group symmetries, Bailey’s summation formula, theta functions.
