Differential equations for families of semi-classical orthogonal polynomials within class one

被引：2

作者：

Filipuk, G. ^{[1
,2
]}

Rebocho, M. N. ^{[3
,4
]}

机构：

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

[2] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00656 Warsaw, Poland

[3] Univ Beira Interior, Dept Matemat, P-6201001 Covilha, Portugal

[4] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra, Portugal

来源：

APPLIED NUMERICAL MATHEMATICS | 2018年 / 124卷

关键词：

Painleve equations; Semi-classical orthogonal polynomials; Stieltjes function;

D O I：

10.1016/j.apnum.2017.10.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study families of semi-classical orthogonal polynomials within class one. We derive general second or third order ordinary differential equations (with respect to certain parameters) for the recurrence coefficients of the three-term recurrence relation of these polynomials and show that in particular well-known cases, e.g. related to the modified Airy and Laguerre weights, these equations can be reduced to the second and the fourth Painleve equations. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：76 / 88

页数：13

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