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Journal of Applied Mathematics
Volume 2014, Article ID 451953, 8 pages
http://dx.doi.org/10.1155/2014/451953
Research Article

On Chebyshev Polynomials, Fibonacci Polynomials, and Their Derivatives

Department of Mathematics, Northwest University, Xi’an, Shaanxi 710127, China

Received 6 June 2013; Revised 19 November 2013; Accepted 7 February 2014; Published 13 March 2014

Academic Editor: Vijay Gupta

Copyright © 2014 Yang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the relationship of the Chebyshev polynomials, Fibonacci polynomials, and their rth derivatives. We get the formulas for the rth 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.