IJPAM: Volume 39, No. 1 (2007)

ON THE $q$-ANALOGUE OF DUNKL OPERATOR AND
ITS APPELL CLASSICAL ORTHOGONAL POLYNOMIALS

A. Ghressi$^1$, L. Khériji$^2$
$^1$Faculté des Sciences de Gabès
Route de Mednine, Gabès, 6029, TUNISIA
e-mail: Abdallah.Ghrissi@fsg.rnu.tn
$^2$Institut Supérieur des Sciences Appliquées et de Technologie de Gabès
Rue Omar Ibn El Khattab, Gabès, 6072, TUNISIA
e-mail: kheriji@yahoo.fr


Abstract.We introduce an operator $\mathcal{D}(\theta,q)$ giving a connection with $H_{q}$-semiclassical orthogonal polynomials and we investigate it to characterize a well known symmetric (MOPS) related to the Wall's one, us the unique $\mathcal{D}(\theta,q)$-Appell classical. This (MOPS) is also $H_{\sqrt{q}}$ -semiclassical of class one. The moments and integral representation of the corresponding linear form are given.

Received: March 8, 2007

AMS Subject Classification: 42C05, 33C45

Key Words and Phrases: $q$-semiclassical orthogonal polynomials, $q$-Dunkl operator, $q$-Appell orthogonal polynomials, moments and integral representation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 1