Geodesic
Hahn's problem with respect to some perturbations of the raising operator $(X-c)$
Ural mathematical journal, Tome 6 (2020) no. 2, pp. 15-24

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In this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator $X-c$, where $c$ is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the $q$-Hermite (resp. Charlier) polynomial is the only $H_{\alpha,q}$-classical (resp. \linebreak $\mathcal{S}_{\lambda}$-classical) orthogonal polynomial, where $H_{\alpha, q}:=X+\alpha H_q$ and $\mathcal{S}_{\lambda}:=(X+1)-\lambda\tau_{-1}$.
Keywords: linear functional, $\mathcal{O}$-classical polynomials, Raising operators, $q$-Hermite polynomials, Charlier polynomials.
Mots-clés : orthogonal polynomials 
@article{UMJ_2020_6_2_a1,
     author = {Baghdadi Aloui and Jihad Souissi},
     title = {Hahn's problem with respect to some perturbations of the raising operator $(X-c)$},
     journal = {Ural mathematical journal},
     pages = {15--24},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a1/}
}
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Baghdadi Aloui; Jihad Souissi. Hahn's problem with respect to some perturbations of the raising operator $(X-c)$. Ural mathematical journal, Tome 6 (2020) no. 2, pp. 15-24. http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a1/