Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds: Explicit and inversion formulas for Chebyshev polynomials

Feng Qi, Da-Wei Niu, and Dongkyu Lim, Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds, Miskolc Mathematical Notes 20 (2019), no. 2, 1129--1137; available online at https://doi.org/10.18514/MMN.2019.2976.International audienceIn the paper, starting from the Rodrigues formulas for the Chebyshev polynomials of the first and second kinds, by virtue of the Fa\`a di Bruno formula, with the help of two identities for the Bell polynomials of the second kind, and making use of a new inversion theorem for combinatorial coefficients, the authors derive two nice explicit formulas and their corresponding inversion formulas for the Chebyshev polynomials of the first and second kinds