Geodesic
Chebyshev polynomials, Catalan numbers, and tridiagonal matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 3-9

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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
Mots-clés : tridiagonal matrix. 
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     author = {A. E. Artisevich and B. S. Bychkov and A. B. Shabat},
     title = {Chebyshev polynomials, {Catalan} numbers, and tridiagonal matrices},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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A. E. Artisevich; B. S. Bychkov; A. B. Shabat. Chebyshev polynomials, Catalan numbers, and tridiagonal matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a0/