×

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

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
PDF BibTeX XML Cite
Full Text: DOI