Geodesic
Second structure relation for the Dunkl-classical orthogonal polynomials
Problemy analiza, Tome 12 (2023) no. 3, pp. 86-104.

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

In this paper, we characterize the Dunkl-classical orthogonal polynomials by a second structure relation.
Keywords: Dunkl-classical polynomials, regular forms, second structure relation.
Mots-clés : orthogonal polynomials 
@article{PA_2023_12_3_a5,
     author = {Y. Habbachi},
     title = {Second structure relation for the {Dunkl-classical} orthogonal polynomials},
     journal = {Problemy analiza},
     pages = {86--104},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2023_12_3_a5/}
}
TY  - JOUR
AU  - Y. Habbachi
TI  - Second structure relation for the Dunkl-classical orthogonal polynomials
JO  - Problemy analiza
PY  - 2023
SP  - 86
EP  - 104
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2023_12_3_a5/
LA  - en
ID  - PA_2023_12_3_a5
ER  - 
%0 Journal Article
%A Y. Habbachi
%T Second structure relation for the Dunkl-classical orthogonal polynomials
%J Problemy analiza
%D 2023
%P 86-104
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2023_12_3_a5/
%G en
%F PA_2023_12_3_a5
Y. Habbachi. Second structure relation for the Dunkl-classical orthogonal polynomials. Problemy analiza, Tome 12 (2023) no. 3, pp. 86-104. http://geodesic.mathdoc.fr/item/PA_2023_12_3_a5/

[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] Al-Salam W. A., Chihara T. S., “Another characterization of the classical orthogonal polynomials”, SIAM J. Math. Anal., 3 (1972), 65–70 | 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] Ben Salah I., Ghressi A., Khériji L., “A characterization of symmetric $T_\mu$-classical monic orthogonal polynomials by a structure relation”, Integral Transforms Spec. Funct., 25 (2014), 423–432 | DOI | MR | Zbl

[6] Bochner S., “Über Sturm-Liouvillesche polynomsysteme”, Math. Z., 29 (1929), 730–736 | DOI | MR

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

[8] 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

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

[10] Bouras B., Habbachi Y., Marcellán F., “Rodrigues formula and recurrence coefficients for non-symmetric Dunkl-classical orthogonal polynomials”, The Ramanujan Journal, 56 (2021), 451–466 | DOI | MR | Zbl

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

[12] Chihara T. S., Generalized Hermite polynomials, PhD thesis, Purdue, 1955 | MR

[13] Cryer C. W., “Rodrigues' formula and the classical orthogonal polynomials”, Boll. Un. Mat. Ital., 3 (1970), 1–11 | MR | Zbl

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

[15] Geronimus J. L., “On polynomials orthogonal with respect to numerical sequences and on Hahn's theorem”, Izv. Akad. Mauk, 4 (1940), 215–228 | MR | Zbl

[16] Habbachi Y., “Moments and an integral representation for the non-symmetric Dunkl-classical form”, MFAT, 28:2 (2022), 119–126 | DOI | MR

[17] Habbachi Y., Bouras B., “A note for the Dunkl-classical polynomials”, Probl. Anal. Issues Anal., 11(29):2 (2022), 29–41 | DOI | MR

[18] Hahn W., “Über die Jacobischen Polynome und zwei verwandte Polynomklassen”, Math. Z., 1935, 634–638 | DOI | MR | Zbl

[19] Hildebrandt E. H., “Systems of polynomials connected with the Charlier expansions and the Pearson differential and difference equation”, Math. Nachr., 2 (1949), 4–34 | DOI | MR

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

[21] Maroni P., “Fonctions eulériennes. Polynômes orthogonaux classiques”, Techniques de l'ingénieur, A, 154 (1994), 1–30

[22] Maroni P., “Une théorie algébrique des polynômes orthogonaux. Application aux polynômes orthogonaux semi-classiques”, Orthogonal Polynomials and Their Applications, IMACS Ann. Comput. Appl. Math., 9, 1991, 95–130 | MR | Zbl

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

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

[25] Sghaier M., “Rodrigues formula for the Dunkl-classical symmetric orthogonal polynomials”, Filomat, 27 (2013), 1285–1290 | DOI | MR | Zbl