On Chebyshev polynomials, Fibonacci polynomials, and their derivatives. (English) Zbl 1406.11021

Li, Yang

J. Appl. Math. 2014, Article ID 451953, 8 p. (2014).

Summary: We study the relationship of the Chebyshev polynomials, Fibonacci polynomials, and their \(r\)th derivatives. We get the formulas for the \(r\)th derivatives of Chebyshev polynomials being represented by Chebyshev polynomials and Fibonacci polynomials. At last, we get several identities about the Fibonacci numbers and Lucas numbers.

MSC:

11B83	Special sequences and polynomials
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05	Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis