Geodesic
Characterization of polynomials via a raising operator
Problemy analiza, Tome 13 (2024) no. 1, pp. 71-81

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This paper investigates a first-order linear differential operator $\mathcal{J}_\xi$, where $\xi=(\xi_1, \xi_2) \in \mathbb{C}^2\setminus{(0, 0)}$, and $D:=\frac{d}{dx}$. The operator is defined as $\mathcal{J}_{\xi}:=x(xD+\mathbb{I})+\xi_1\mathbb{I}+\xi_2 D$, with $\mathbb{I}$ representing the identity on the space of polynomials with complex coefficients. The focus is on exploring the $\mathcal{J}_\xi$-classical orthogonal polynomials and analyzing properties of the resulting sequences. This work contributes to the understanding of these polynomials and their characteristics.
Keywords: СЃlassical polynomials, second-order differential equation, raising operator.
Mots-clés : orthogonal polynomials 
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J. Souissi. Characterization of polynomials via a raising operator. Problemy analiza, Tome 13 (2024) no. 1, pp. 71-81. http://geodesic.mathdoc.fr/item/PA_2024_13_1_a4/