Next Article in Journal
The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F-Contractions
Next Article in Special Issue
Generalized Tepper’s Identity and Its Application
Previous Article in Journal
An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization
Previous Article in Special Issue
Some Identities Involving Certain Hardy Sums and General Kloosterman Sums
Open AccessArticle

Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials

1
School of Science, Xi’an Technological University, Xi’an 710021, China
2
Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
3
Department of Mathematics, Sogang University, Seoul 121-742, Korea
4
Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Korea
*
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(2), 210; https://doi.org/10.3390/math8020210
Received: 2 January 2020 / Revised: 28 January 2020 / Accepted: 4 February 2020 / Published: 7 February 2020
(This article belongs to the Special Issue Special Polynomials)
In this paper, we consider three sums of finite products of Chebyshev polynomials of two different kinds, namely sums of finite products of the second and third kind Chebyshev polynomials, those of the second and fourth kind Chebyshev polynomials, and those of the third and fourth kind Chebyshev polynomials. As a generalization of the classical linearization problem, we represent each of such sums of finite products as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer, and Jacobi polynomials. These are done by explicit computations and the coefficients involve terminating hypergeometric functions 2 F 1 , 1 F 1 , 2 F 2 , and 4 F 3 . View Full-Text
Keywords: sums of finite products; Chebyshev polynomials of the second; third and fourth kinds; terminating hypergeometric functions sums of finite products; Chebyshev polynomials of the second; third and fourth kinds; terminating hypergeometric functions
MDPI and ACS Style

Kim, T.; Kim, D.S.; Lee, H.; Kwon, J. Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials. Mathematics 2020, 8, 210.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop