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Some applications of \(q\)-differential operator. (English) Zbl 1230.05048

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.

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

Citations:

Zbl 1177.33032
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