A new characterization of the generalized Hermite linear form. (English) Zbl 1220.42017

Ghressi, A.; Khériji, L.

Bull. Belg. Math. Soc. - Simon Stevin 15, No. 3, 561-567 (2008).

Summary: We show that the generalized Hermite linear form \(\mathcal{H}(\mu)\), which is symmetric \(D\)-semiclassical of class one, is the unique \(\mathcal{D}_{\theta}\)-Appell classical character where \(\mathcal{D}_{\theta}\) is the Dunkl operator.

MSC:

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

Keywords:

semiclassical orthogonal polynomials; Dunkl operator; Appell orthogonal polynomials