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Characterization of \(q\)-Dunkl-classical symmetric orthogonal \(q\)-polynomials. (English) Zbl 1508.33009

Summary: In this paper, we show that, up to a dilatation, the \(q^2\)-analogue of generalized Hermite and \(q^2\)-analogue of generalized Gegenbauer polynomials are the only \(q\)-Dunkl-classical symmetric orthogonal polynomials.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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