This article is cited in 3 papers

Chebyshev polynomials, Catalan numbers, and tridiagonal matrices

A. E. Artisevich^a, B. S. Bychkov^b, A. B. Shabat<sup>c

a</sup> Adyghe State University, Maykop, Russia
^b National Research University "Higher School of Economics", Moscow, Russia
^c Landau Institute for Theoretical Physics of Russian Academy of Sciences, Moscow, Russia

Abstract: 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 $\varphi_n(\mu)$ that are solutions of the problem of commutation of a tridiagonal matrix with the simplest Vandermonde matrix and Chebyshev polynomials.

Keywords: Chebyshev polynomial, tridiagonal matrix.

Received: 27.01.2020
Revised: 27.01.2020

DOI: 10.4213/tmf9885

 English version: Theoretical and Mathematical Physics, 2020, 204:1, 837–842

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