Discrete Orthogonal Polynomials with Hypergeometric Weights and Painleve VI

被引:14
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
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
收藏
页数:19
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