Basic bilateral very well-poised series and Shukla’s 8ψ8-summation formula

By means of Jackson’s q-Dougall–Dixon formula on terminating very well-poised hypergeometric series, the linearization lemma on the factorial fractions with well-poised parameter-pairs will be established. It will be applied to prove the generalized well-poised 8ψ8-series and 10ψ10-series identities. The linearization method will further be employed to present a constructive proof of Milne’s transformation formula from nonterminating very well-poised bilateral series to terminating multiple unilateral series. © 2006 Elsevier Inc. All rights reserved