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Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials

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Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300160, China
2
Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
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Department of Mathematics, Sogang University, Seoul 121-742, Korea
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Department of Mathematics Education and ERI, Gyeongsang National University, Jinju, Gyeongsangnamdo 52828, Korea
5
Hanrimwon, Kwangwoon University, Seoul 139-701, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(10), 210; https://doi.org/10.3390/math6100210
Received: 7 September 2018 / Revised: 29 September 2018 / Accepted: 16 October 2018 / Published: 17 October 2018
This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations, each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials, which involve the hypergeometric functions 1 F 1 and 2 F 1 . View Full-Text
Keywords: chebyshev polynomials of second kind; Fibonacci polynomials; sums of finite products; orthogonal polynomials chebyshev polynomials of second kind; Fibonacci polynomials; sums of finite products; orthogonal polynomials
MDPI and ACS Style

Kim, T.; Kim, D.S.; Kwon, J.; Dolgy, D.V. Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials. Mathematics 2018, 6, 210.

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