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Open AccessArticle

Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds

1
Institute of National Sciences, Far Eastern Federal University, 690950 Vladivostok, Russia
2
Department of Mathematics, Sogang University, Seoul 04107, Korea
3
Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300160, China
4
Department of Mathematics, Kwangwoon University, Seoul 01897, Korea
5
Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Gyeongsangnamdo, Korea
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(11), 617; https://doi.org/10.3390/sym10110617
Received: 8 October 2018 / Revised: 3 November 2018 / Accepted: 5 November 2018 / Published: 9 November 2018
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)
This paper treats the connection problem of expressing sums of finite products of Chebyshev polynomials of the third and fourth kinds in terms of five classical orthogonal polynomials. In fact, by carrying out explicit computations each of them are expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer, and Jacobi polynomials which involve some terminating hypergeometric functions F 0 2 , F 1 2 , and F 2 3 . View Full-Text
Keywords: sums of finite products of Chebyshev polynomials of the third and fourth kinds; Hermite; generalized Laguerre; Legendre; Gegenbauer; Jacobi sums of finite products of Chebyshev polynomials of the third and fourth kinds; Hermite; generalized Laguerre; Legendre; Gegenbauer; Jacobi
MDPI and ACS Style

Dolgy, D.V.; Kim, D.S.; Kim, T.; Kwon, J. Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds. Symmetry 2018, 10, 617.

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