The generalized Krawtchouk polynomials and the fifth Painleve equation

被引：6

作者：

Boelen, Lies ^{[1
]}

Filipuk, Galina ^{[2
]}

Smet, Christophe ^{[1
]}

Van Assche, Walter ^{[1
]}

Zhang, Lun ^{[1
]}

机构：

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

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

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2013年 / 19卷 / 09期

关键词：

discrete orthogonal polynomials; semi-classical extension of the Krawtchouk weight; recurrence coefficients; Painleve equations; RECURRENCE COEFFICIENTS; RATIONAL SOLUTIONS;

D O I：

10.1080/10236198.2012.755522

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the recurrence coefficients of the orthogonal polynomials with respect to a semi-classical extension of the Krawtchouk weight. We derive a coupled discrete system for these coefficients and show that they satisfy the fifth Painleve equation when viewed as functions of one of the parameters in the weight.

引用

页码：1437 / 1451

页数：15

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