\(q\)-derivative operators and basic hypergeometric series (Q860128)

The author obtains formal series expansions in terms of \(q\)-derivative operators. This generalizes some results due to \textit{L. Carlitz} [Glas. Mat. 28, 205--214 (1973; Zbl 0267.33010)] and \textit{Z.-G. Liu} [Ramanujan J. 6, 429--447 (2002; Zbl 1044.05012)]. As applications, he gets a non-termining summation formula for \({}_6\phi_5\)-series, at Watson's \(q\)-analogue transformation for \({}_8\phi_7\)-series, a basic hypergeometric transformation for \({}_8\phi_7\)-series and a reduction formula for the very-well-poised basic hypergeometric \({}_{10}\phi_9\)-series.