A CHARACTERIZATION OF MEIXNER ORTHOGONAL POLYNOMIALS VIA A CERTAIN TRANSFERT OPERATOR

Emna Abassi     (Faculté des Sciences de Tunis, Université de Tunis El Manar, Rommana 1068, Tunisia)
Lotfi Khériji     (Institut Préparatoire aux Etudes d’Ingénieur El Manar, Université de Tunis El Manar, Rommana 1068, Tunisia)

Abstract


Here we consider a certain transfert operator \(\mathrm{M}_{(c,\omega)}=I_{\mathcal{P}}-c \, \tau_{\omega},\) \(\omega\neq0,\) \({c \in \mathbb{R}-\{0,1\},}\) and we prove the following statement: up to an affine transformation, the only orthogonal sequence that remains orthogonal after application of this transfert operator is the Meixner polynomials of the first kind.


Keywords


Orthogonal polynomials, Regular form, Meixner polynomials, Divided-difference operator, Transfert operator, Hahn property

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DOI: http://dx.doi.org/10.15826/umj.2024.1.001

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