Recurrence Coefficients of a New Generalization of the Meixner Polynomials

We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N + 1 -β and on the bi-lattice N ∪ (N + 1 -β).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 P V .Initial conditions for different lattices can be transformed to the classical solutions of P V with special values of the parameters.We also study one property of the Bäcklund transformation of P V .