Andrey Ryabichev, Konstantin Shcherbakov
Published 2024-03-07Version 1
The main result of the article says that the formal power series equal to the ratio of two neighboring Chebyshev polynomials, after some renormalization, approximates the generating function of the Catalan numbers. We present a proof of this result using continued fractions. Also, for completeness of the presentation, we recall the basic properties of Chebyshev polynomials and formal power series that we use.
Comments: 8 pages, in Russian. Comments are welcome!
The Limiting Distribution of the Coefficients of the $q$-Catalan Numbers
The freeness of Ish arrangements
A derivation of the Catalan numbers from a bijection between permutations and labeled trees
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