A matrix approach to some second-order difference equations with sign-alternating coefficients

被引：19

作者：

Andelic, Milica ^{[1
]}

Du, Zhibin ^{[2
,3
]}

da Fonseca, Carlos M. ^{[4
,5
]}

Kilic, Emrah ^{[6
]}

机构：

[1] Kuwait Univ, Dept Math, Safat, Kuwait

[2] South China Normal Univ, Sch Software, Foshan, Guangdong, Peoples R China

[3] Zhaoqing Univ, Sch Math & Stat, Zhaoqing, Peoples R China

[4] Kuwait Coll Sci & Technol, Dept Math, Safat, Kuwait

[5] Univ Primorska, FAMNIT, Glagoljsaska 8, Koper 6000, Slovenia

[6] TOBB Univ Econ & Technol, Math Dept, Ankara, Turkey

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2020年 / 26卷 / 02期

关键词：

Difference equations; Fibonacci numbers; k-Toeplitz tridiagonal matrices; Chebyshev polynomials of second kind; determinant; FIBONACCI;

D O I：

10.1080/10236198.2019.1709180

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we analyse and unify some recent results on the double sequence {yn, k}, for n, k 1, defined by the second-order difference equation yn, k = (-1) (n-1)/k yn- 1,k - yn- 2,k, with y1, k = 1 and y2, k = 0, in terms of matrix theory and orthogonal polynomials theory. Moreover, we provide a general solution to k = (-1) (n-1)/k zn- 1,k - (-1) (n-2)/a zn- 2,k, using a closely related approach. We discuss briefly other recent problems involving a general recurrence relation of second order and relate them with the existing literature.

引用

页码：149 / 162

页数：14

共 26 条

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