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Open AccessArticle

Fourier Series for Functions Related to Chebyshev Polynomials of the First Kind and Lucas Polynomials

by Taekyun Kim 1,†, Dae San Kim 2,†, Lee-Chae Jang 3,*,† and Gwan-Woo Jang 1,†
1
Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
2
Department of Mathematics, Sogang University, Seoul 121-742, Korea
3
Graduate School of Education, Konkuk University, Seoul 139-701, Korea
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2018, 6(12), 276; https://doi.org/10.3390/math6120276
Received: 23 October 2018 / Revised: 19 November 2018 / Accepted: 20 November 2018 / Published: 23 November 2018
(This article belongs to the Special Issue Special Functions and Applications)
In this paper, we derive Fourier series expansions for functions related to sums of finite products of Chebyshev polynomials of the first kind and of Lucas polynomials. From the Fourier series expansions, we are able to express those two kinds of sums of finite products of polynomials as linear combinations of Bernoulli polynomials. View Full-Text
Keywords: Fourier series; Chebyshev polynomials of the first kind; Lucas polynomials; Bernoulli polynomials Fourier series; Chebyshev polynomials of the first kind; Lucas polynomials; Bernoulli polynomials
MDPI and ACS Style

Kim, T.; Kim, D.S.; Jang, L.-C.; Jang, G.-W. Fourier Series for Functions Related to Chebyshev Polynomials of the First Kind and Lucas Polynomials. Mathematics 2018, 6, 276.

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