NOTES ON THE RODRIGUES FORMULAS FOR TWO KINDS OF THE CHEBYSHEV POLYNOMIALS

Feng Qi (1, 2, 3) , Da-Wei Niu (4) , Dongkyu Lim (5)

1 Tianjin Polytechnic University
2 Henan Polytechnic University
3 Inner Mongolia University for Nationalities
4 ECNU - East China Normal University [Shangaï]
5 SKKU - Sungkyunkwan University [Suwon]

In the paper, the authors derive, from the Rodrigues formulas for the Chebyshev polynomials of the first and second kinds and by virtue of the Fàa di Bruno formula and two identities for the Bell polynomials of the second kind, two explicit formulas for the Chebyshev polynomials of the first and second kinds, find, by virtue of an inversion formula for combinatorial coefficients, two inversion formulas for explicit formulas of the Chebyshev polynomials of the first and second kinds, and collect variants of the Rodrigues formulas for the Chebyshev polynomials of the first and second kinds.

Mots clés: Chebyshev polynomial of the first kind; Faà di Bruno formula; explicit formula; Rodrigues formula; Chebyshev polynomial of the second kind; Bell polynomial of the second kind; inversion formula for combinatorial coefficients; variant

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]; Analyse classique [math.CA]

Feng Qi, Da-Wei Niu, Dongkyu Lim. NOTES ON THE RODRIGUES FORMULAS FOR TWO KINDS OF THE CHEBYSHEV POLYNOMIALS: Rodrigues formulas for Chebyshev polynomials. 2018. ⟨hal-01705040v1⟩