Abel's lemma on summation by parts and basic hypergeometric series

q-extensions of Dougall’s bilateral 2H2-series

“…In a series of papers [8][9][10][11], the author and his collaborators have recently shown that numerous q-series identities can systematically be proved by means of Abel's lemma on summation by parts. For an arbitrary complex sequence {τ k }, define the backward and forward difference operators ∇ and · , respectively, by…”

Bilateral $q$-Watson and $q$-Whipple sums

“…In order to prove Theorem 1, we shall utilize the modified Abel lemma on summation by parts [3,4]. Given an arbitrary complex sequence {τ k }, define the backward and forward difference operators and · , respectively, by…”

Infinite Series Identities on Harmonic Numbers

“…Recently, Abel's lemma on summation by parts has successfully been used to review several identities of hypergeometric series and q-series by Chu [4,5]. This paper aims at its further applications to infinite series identities involving harmonic numbers and their variants.…”