Atakishiyeva, Mesuma; Atakishiyev, Natig A non-standard generating function for continuous dual \(q\)-Hahn polynomials. (Spanish. English summary) Zbl 1307.33009 Rev. Mat. Teor. Apl. 18, No. 1, 111-120 (2011). Summary: We study a non-standard form of generating function for the three-parameter continuous dual \(q\)-Hahn polynomials \(p_n(x;a,b,c\,|\,q)\), which has surfaced in a recent work of the present authors on the construction of lifting \(q\)-difference operators in the Askey scheme of basic hypergeometric polynomials. We show that the resulting generating function identity for the continuous dual \(q\)-Hahn polynomials \(p_n(x;a,b,c\,|\,q)\) can be explicitly stated in terms of Jackson’s \(q\)-exponential functions \(e_q(z)\). Cited in 3 Documents MSC: 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 47B39 Linear difference operators Keywords:\(q\)-scheme of Askey; generating function; \(q\)-exponential function of Jackson; dual \(q\)-Hahn polynomials PDFBibTeX XMLCite \textit{M. Atakishiyeva} and \textit{N. Atakishiyev}, Rev. Mat. Teor. Apl. 18, No. 1, 111--120 (2011; Zbl 1307.33009) Full Text: DOI