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Mathematical Problems in Engineering
Volume 2015, Article ID 950695, 5 pages
http://dx.doi.org/10.1155/2015/950695
Research Article

Some Identities Involving Chebyshev Polynomials

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

Received 18 December 2014; Accepted 18 March 2015

Academic Editor: Fabio Tramontana

Copyright © 2015 Xiaoxue 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

The main purpose of this paper is using the combinatorial method and algebraic manipulations to study some sums of powers of Chebyshev polynomials and give several interesting identities. As some applications of these results, we obtained several divisibility properties involving Chebyshev polynomials.