Basic bilateral very well-poised series and Shukla's (8)psi(8)-summation formula

摘要

By means of Jackson's q-Dougall-Dixon formula on terminating very well-poised hypergeormetric 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 8 psi 8-series and 10 psi 10-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. (c) 2006 Elsevier Inc. All rights reserved.