Discrete Orthogonal Polynomials with Hypergeometric Weights and Painleve VI

被引：13

作者：

Filipuk, Galina ^{[1
]}

Van Assche, Walter ^{[2
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, Banacha 2, PL-02097 Warsaw, Poland

[2] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B,Box 2400, BE-3001 Leuven, Belgium

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

discrete orthogonal polynomials; hypergeometric weights; discrete Painleve equations; Painleve VI; RECURRENCE COEFFICIENTS; EQUATIONS;

D O I：

10.3842/SIGMA.2018.088

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second order differential equation in one of the parameters of the weights. The non-linear difference equations form a pair of discrete Painleve equations and the differential equation is the sigma-form of the sixth Painleve equation. We briefly investigate the asymptotic behavior of the recurrence coefficients as n -> infinity using the discrete Painleve equations.

引用

页数：19

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