Chebyshev polynomials, Catalan numbers, and tridiagonal matrices

被引：0
|
作者：
Artisevich, A. E. [1 ]
Bychkov, B. S. [2 ]
Shabat, A. B. [3 ]
机构：
[1] Adyghe State Univ, Maykop, Russia
[2] Natl Res Univ Higher Sch Econ, Moscow, Russia
[3] RAS, Landau Inst Theoret Phys, Moscow, Russia
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2020年 / 204卷 / 01期
关键词：
Chebyshev polynomial; tridiagonal matrix;
D O I：
10.1134/S0040577920070016
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We establish a relation between linear second-order difference equations corresponding to Chebyshev polynomials and Catalan numbers. The latter are the limit coefficients of a converging series of rational functions corresponding to the Riccati equation. As the main application, we show a relation between the polynomials phi(n)(mu) that are solutions of the problem of commutation of a tridiagonal matrix with the simplest Vandermonde matrix and Chebyshev polynomials.
引用
收藏
页码：837 / 842
页数：6
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