Chebyshev polynomials, Catalan numbers, and tridiagonal matrices
Abstract
We establish a relation between linear secondorder 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 that are solutions of the problem of commutation of a tridiagonal matrix with the simplest Vandermonde matrix and Chebyshev polynomials.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 July 2020
 DOI:
 10.1134/S0040577920070016
 Bibcode:
 2020TMP...204..837A
 Keywords:

 Chebyshev polynomial;
 tridiagonal matrix