A CHARACTERIZATION OF MEIXNER ORTHOGONAL POLYNOMIALS VIA A CERTAIN TRANSFERT OPERATOR
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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