This article is cited in 1 paper

Characterization of polynomials via a raising operator

J. Souissi

Faculty of Sciences of Gabes, Department of Mathematics, Gabes University, Street Erriadh 6072 Gabes, Tunisia

Abstract: 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: orthogonal polynomials, СЃlassical polynomials, second-order differential equation, raising operator.

UDC: 517.587, 517.521, 517.538.3

MSC: Primary 33C45; Secondary 42C05

Received: 18.09.2023
Accepted: 12.11.2023

Language: English

DOI: 10.15393/j3.art.2024.14050