## 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
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