Basic bilateral very well-poised series and Shukla's -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 -series and -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.