Title: Recurrence coefficients of a new generalization of the Meixner polynomials Authors: Filipuk, Galina ×Van Assche, Walter # Issue Date: Jul-2011 Series Title: Symmetry, Integrability and Geometry: Methods and Applications vol:7 issue:068 pages:11 Abstract: 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 Painlevé equation. Initial conditions for different lattices can be transformed to the classical solutions of Painlevé V with special values of the parameters. We also study one property of the Bäcklund transformation of PV. ISSN: 1815-0659 Publication status: published KU Leuven publication type: IT Appears in Collections: Analysis Section