Recurrence Coefficients of a New Generalization of the Meixner Polynomials

Symmetry Integrability and Geometry-Methods and Applications

article

Galina Filipuk¹  Walter Van Assche² 

[1] Faculty of Mathematics, University of Warsaw;Department of Mathematics, Katholieke Universiteit Leuven

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

DOI  :  10.3842/SIGMA.2011.068

来源: National Academy of Science of Ukraine

【 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 .

【 授权许可】

Unknown