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