Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials
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
4
Hanrimwon, Kwangwoon University, Seoul 139-701, Korea
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(12), 742; https://doi.org/10.3390/sym10120742
Received: 29 November 2018 / Revised: 8 December 2018 / Accepted: 10 December 2018 / Published: 11 December 2018
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)
In this paper, we consider sums of finite products of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the previously-studied ones. We represent each of them as linear combinations of Chebyshev polynomials of all kinds whose coefficients involve some terminating hypergeometric functions . The results may be viewed as a generalization of the linearization problem, which is concerned with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. These representations are obtained by explicit computations.
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Keywords:
Chebyshev polynomials of the first, second, third, and fourth kinds; sums of finite products; representation
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MDPI and ACS Style
Kim, T.; Kim, D.S.; Jang, L.-C.; Dolgy, D.V. Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials. Symmetry 2018, 10, 742. https://doi.org/10.3390/sym10120742
AMA Style
Kim T, Kim DS, Jang L-C, Dolgy DV. Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials. Symmetry. 2018; 10(12):742. https://doi.org/10.3390/sym10120742
Chicago/Turabian StyleKim, Taekyun; Kim, Dae S.; Jang, Lee-Chae; Dolgy, Dmitry V. 2018. "Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials" Symmetry 10, no. 12: 742. https://doi.org/10.3390/sym10120742
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