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

Taekyun Kim, Dae San Kim, Jongkyum Kwon and Dmitry V. Dolgy
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Taekyun Kim: Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300160, China
Dae San Kim: Department of Mathematics, Sogang University, Seoul 121-742, Korea
Jongkyum Kwon: Department of Mathematics Education and ERI, Gyeongsang National University, Jinju, Gyeongsangnamdo 52828, Korea
Dmitry V. Dolgy: Hanrimwon, Kwangwoon University, Seoul 139-701, Korea

Mathematics, 2018, vol. 6, issue 10, 1-14

Abstract: 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 .

Keywords: chebyshev polynomials of second kind; Fibonacci polynomials; sums of finite products; orthogonal polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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