Recurrence Coefficients of a New Generalization of the Meixner Polynomials
Recurrence Coefficients of a New Generalization of the Meixner Polynomials
We investigate new generalizations of the Meixner polynomials on the lattice $\mathbb{N}$, on the shifted lattice $\mathbb{N}+1-\beta$ and on the bi-lattice $\mathbb{N}\cup (\mathbb{N}+1-\beta)$. We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlev\'e equation P$_{\textup V}$. Initial …