Recurrence Coefficients of a New Generalization of the Meixner Polynomials

被引：16

作者：

Filipuk, Galina ^{[1
]}

Van Assche, Walter ^{[2
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, PL-02097 Warsaw, Poland

[2] Katholieke Univ Leuven, Dept Math, BE-3001 Louvain, Belgium

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2011年 / 7卷

关键词：

Painleve equations; Backlund transformations; classical solutions; orthogonal polynomials; recurrence coefficients;

D O I：

10.3842/SIGMA.2011.068

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N + 1 - beta and on the bi-lattice N boolean OR (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 Painleve 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 Backlund transformation of P-V.

引用

页数：11

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