Fang, Jian-Ping Some applications of \(q\)-differential operator. (English) Zbl 1230.05048 J. Korean Math. Soc. 47, No. 2, 223-233 (2010). Summary: We use \(q\)-differential operator to recover the finite Heine \( _2\Phi_1\) transformations given in [G. E. Andrews, “The finite Heine transformation”, in: B. Landman, (ed.) et al., Combinatorial number theory. Proceedings of the 3rd ‘Integers Conference 2007’, Carrollton, GA, USA, October 24–27, 2007. Berlin: Walter de Gruyter, Integers 9, Suppl., Article A1, 1–6 (2009; Zbl 1177.33032)]. Applying that, we also obtain some terminating \(q\)-series transformation formulas. Cited in 8 Documents MSC: 05A30 \(q\)-calculus and related topics 33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\) 33D60 Basic hypergeometric integrals and functions defined by them 33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals Keywords:\(q\)-series; \(q\)-differential operator; Rogers-Ramanujan type identity Citations:Zbl 1177.33032 PDFBibTeX XMLCite \textit{J.-P. Fang}, J. Korean Math. Soc. 47, No. 2, 223--233 (2010; Zbl 1230.05048) Full Text: DOI