Geodesic
A note for the Dunkl-classical polynomials
Problemy analiza, Tome 11 (2022) no. 2, pp. 29-41.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we give a new characterization for the Dunkl-classical orthogonal polynomials. The previous characterization has been illustrated by some examples.
Keywords: Dunkl operator, Dunkl-classical polynomials.
Mots-clés : orthogonal polynomials 
@article{PA_2022_11_2_a2,
     author = {Y. Habbachi and B. Bouras},
     title = {A note for the {Dunkl-classical} polynomials},
     journal = {Problemy analiza},
     pages = {29--41},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2022_11_2_a2/}
}
TY  - JOUR
AU  - Y. Habbachi
AU  - B. Bouras
TI  - A note for the Dunkl-classical polynomials
JO  - Problemy analiza
PY  - 2022
SP  - 29
EP  - 41
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2022_11_2_a2/
LA  - en
ID  - PA_2022_11_2_a2
ER  - 
%0 Journal Article
%A Y. Habbachi
%A B. Bouras
%T A note for the Dunkl-classical polynomials
%J Problemy analiza
%D 2022
%P 29-41
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2022_11_2_a2/
%G en
%F PA_2022_11_2_a2
Y. Habbachi; B. Bouras. A note for the Dunkl-classical polynomials. Problemy analiza, Tome 11 (2022) no. 2, pp. 29-41. http://geodesic.mathdoc.fr/item/PA_2022_11_2_a2/

[1] Alaya J., Maroni P., “Symmetric Laguerre-Hahn forms of class $s=1$”, Int. Transf. and Spc. Funct., 4 (1996), 301–320 | DOI | MR | Zbl

[2] Alfaro M., Álvarez-Nodarse R., “A characterization of the classical orthogonal discrete and $q$-polynomials”, J. Comput. Appl. Math., 201 (2007), 48–54 | DOI | MR | Zbl

[3] Belmehdi S., “Generalized Gegenbauer polynomials”, J. Comput. Appl. Math., 133 (2001), 195–205 | DOI | MR | Zbl

[4] Ben Cheikh Y., Gaied M., “Characterizations of the Dunkl-classical orthogonal polynomials”, App. Math. Comput., 187 (2007), 105–114 | DOI | MR | Zbl

[5] Bouras B., “Some characterizations of Dunkl-classical orthogonal polynomials”, J. Difference Equ. Appl., 20:8 (2014), 1240–1257 | DOI | MR | Zbl

[6] Bouras B., Habbachi Y., “Classification of nonsymmetric Dunkl-classical orthogonal polynomials”, J. Difference Equ. Appl., 23 (2017), 539–556 | DOI | MR | Zbl

[7] Bouras B., Alaya J., Habbachi Y., “A D-Pearson equation for Dunkl-classical orthogonal polynomials”, Facta Univ. Ser. Math. Inform., 31 (2016), 55–71 | MR | Zbl

[8] Chihara T. S., An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978 | MR | Zbl

[9] Dunkl C. F., “Integral kernels reflection group invariance”, Canad. J. Math., 43 (1991), 1213–1227 | DOI | MR | Zbl

[10] Marcellán F., Branquinho A., Petronilho J., “Classical orthogonal polynomials: A functional approach”, Acta. Appl. Math., 34 (1994), 283–303 | DOI | MR | Zbl

[11] Ghressi A, Khériji L., “A new characterization of the generalized Hermite form”, Bull Belg Math Soc Simon Stevin, 15 (2008), 561–567 | DOI | MR | Zbl

[12] Maroni P., “Sur la suite de polynômes orthogonaux associée à la forme $u=\delta_c+\lambda(x - c)^{-1} L$”, Period. Math. Hungar., 21:3 (1990), 223–248 | DOI | MR | Zbl

[13] Maroni P., “Variation around Classical orthogonal polynomials. Connected problems”, J. Comput. Appl. Math., 48 (1993), 133–155 | DOI | MR | Zbl

[14] Sghaier M., “A note on Dunkl-classical orthogonal polynomials”, Integral. Transforms. Spec. Funct., 24 (2012), 753–760 | DOI | MR