Difference equations related to Jacobi-type pencils

被引：2

作者：

Zagorodnyuk, Sergey Mihaylovich ^{[1
]}

机构：

[1] Kharkov Natl Univ, Sch Math & Comp Sci, Kharkov, Ukraine

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2018年 / 24卷 / 10期

关键词：

Orthogonal polynomials; difference equation; basic set of solutions; differential equation; POLYNOMIALS;

D O I：

10.1080/10236198.2018.1515929

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study various difference equations related to Jacobi-type pencils. By a Jacobi-type pencil one means the following pencil: is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the second subdiagonal. The basic set of solutions for the corresponding 4th order difference equation is constructed. Spectral properties of the truncated pencil and some special matrix orthogonality relations are investigated. Classical type orthogonal polynomials satisfying a 4th order differential equation are constructed.

引用

页码：1664 / 1684

页数：21

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