Classification of nonsymmetric Dunkl-classical orthogonal polynomials

Abstract

In this paper, we classify nonsymmetric Dunkl-classical linear functionals. Firstly, we reduce the characterization of a Dunkl-classical linear functional given by the first author in a previous work to a $T_{\mathit{\mu }}$-distributional equation of Pearson’s type. Secondly, after rescaling the parameters, we prove that the unique nonsymmetric Dunkl-classical linear functional is the perturbed generalized Gegenbauer form.

Keywords:

• Orthogonal polynomials
• Dunkl-classical polynomials
• regular forms
• semiclassical polynomials

AMS Subject Classifications:

• 33C45
• 42C05

Notes

No potential conflict of interest was reported by the authors.