Abstract
The Abel method on summation by parts is reformulated to present new and elementary proofs of several classical identities of terminating well-poised basic hypergeometric series, mainly discovered by [F H. Jackson, Certain q-identities, Quart. J. Math. Oxford Ser. 12 (1941) 167–172]. This strengthens further our conviction that as a traditional analytical instrument, the revised Abel method on summation by parts is indeed a very natural choice for working with basic hypergeometric series.
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