Recurrence Coefficients of a New Generalization of the Meixner Polynomials

[摘要] 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 .

[关键词] Painlev´e equations;B¨acklund transformations;classical solutions;orthogonal polynomials;recurrence coef ficients