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A non-standard generating function for continuous dual \(q\)-Hahn polynomials. (Spanish. English summary) Zbl 1307.33009

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 \(e_q(z)\).

MSC:

33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
47B39 Linear difference operators
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