2 papers
math.CO2024
Chebyshev polynomials, their remarkable properties and connection with Catalan numbers
Andrey Ryabichev, Konstantin Shcherbakov
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 generatin…
math.CA2024
Roots of polynomials and tangents of circles
Andrey Ryabichev, Konstantin Shcherbakov
Given a real cubic function with three roots, take an equilateral triangle , the projections of which vertices are the roots of . There is a folklore fact that th…