Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials

In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds. Here, the coefficients involve terminating hypergeometric functions...

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Main Authors:	Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, Jongkyum Kwon
Format:	Article
Language:	English
Published:	MDPI AG 2018-12-01
Series:	Mathematics
Subjects:	sums of finite products Chebyshev polynomials of the first kind Lucas polynomials Chebyshev polynomials of all kinds
Online Access:	http://www.mdpi.com/2227-7390/7/1/26

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spelling	doaj-c71cb8f45dbe42a8a27d51ca9495c4f32020-11-24T21:47:48ZengMDPI AGMathematics2227-73902018-12-01712610.3390/math7010026math7010026Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev PolynomialsTaekyun Kim0Dae San Kim1Dmitry V. Dolgy2Jongkyum Kwon3Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300160, ChinaDepartment of Mathematics, Sogang University, Seoul 121-742, KoreaHanrimwon, Kwangwoon University, Seoul 139-701, KoreaDepartment of Mathematics Education and ERI, Gyeongsang National University, Jinju, Gyeongsangnamdo 52828, KoreaIn this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds. Here, the coefficients involve terminating hypergeometric functions 2 F 1 and these representations are obtained by explicit computations.http://www.mdpi.com/2227-7390/7/1/26sums of finite productsChebyshev polynomials of the first kindLucas polynomialsChebyshev polynomials of all kinds
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Taekyun Kim Dae San Kim Dmitry V. Dolgy Jongkyum Kwon
spellingShingle	Taekyun Kim Dae San Kim Dmitry V. Dolgy Jongkyum Kwon Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials Mathematics sums of finite products Chebyshev polynomials of the first kind Lucas polynomials Chebyshev polynomials of all kinds
author_facet	Taekyun Kim Dae San Kim Dmitry V. Dolgy Jongkyum Kwon
author_sort	Taekyun Kim
title	Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials
title_short	Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials
title_full	Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials
title_fullStr	Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials
title_full_unstemmed	Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials
title_sort	representing sums of finite products of chebyshev polynomials of the first kind and lucas polynomials by chebyshev polynomials
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2018-12-01
description	In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds. Here, the coefficients involve terminating hypergeometric functions 2 F 1 and these representations are obtained by explicit computations.
topic	sums of finite products Chebyshev polynomials of the first kind Lucas polynomials Chebyshev polynomials of all kinds
url	http://www.mdpi.com/2227-7390/7/1/26
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Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials

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