A New Identity Involving the Chebyshev Polynomials

Yixue Zhang and Zhuoyu Chen
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Yixue Zhang: School of Mathematics, Northwest University, Xi’an 710127, China
Zhuoyu Chen: School of Mathematics, Northwest University, Xi’an 710127, China

Mathematics, 2018, vol. 6, issue 11, 1-8

Abstract: In this paper, firstly, we introduced a second order non-linear recursive sequence, then we use this sequence and the combinatorial methods to perform a deep study on the computational problem concerning one kind sums, which includes the Chebyshev polynomials. This makes it possible to simplify a class of complex computations involving the second type Chebyshev polynomials into a very simple problem. Finally, we give a new and interesting identity for it.

Keywords: Chebyshev polynomials; recursive sequence; convolution sums; combinatorial method; identity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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