Fourier Series for Functions Related to Chebyshev Polynomials of the First Kind and Lucas Polynomials [PDF]
Mathematics, 2018 In this paper, we derive Fourier series expansions for functions related to sums of finite products of Chebyshev polynomials of the first kind and of Lucas polynomials. From the Fourier series expansions, we are able to express those two kinds of sums of
Taekyun Kim +3 more
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Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials [PDF]
Mathematics, 2018 In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds.
Taekyun Kim +3 more
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Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials [PDF]
Advances in Difference Equations, 2019 In this paper, we investigate sums of finite products of Chebyshev polynomials of the first kind and those of Lucas polynomials. We express each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials ...
Taekyun Kim +3 more
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JTAM (Jurnal Teori dan Aplikasi Matematika), 2021 In this article, we discuss the Chebyshev Polynomial and its characteristics. The second order difference equation and the process obtaining the explicit solution of the Chebyshev polynomial have been given for each real number.
Ikhsan Maulidi +3 more
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Chebyshev polynomials to Volterra-Fredholm integral equations of the first kind
REMATNumerous methods have been studied and discussed for solving ill-posed Volterra integral equations and ill-posed Fredholm integral equations, but rarely for both simultaneously.
Mohamed Nasseh Nadir, Adel Jawahdou
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Chebyshev polynomials of the first kind and the univariate Lommel function: Integral representations
Open MathematicsThis study investigates a number of integrals possessing products of different indices of the univariate Lommel function, sμ,ν(a){s}_{\mu ,\nu }\left(a), with various elementary and special functions.
da Fonseca Carlos M. +2 more
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Approximate solution of a system of singular integral equations of the first kind by using Chebyshev polynomials [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2019 The aim of the present work is to introduce a method based on the Chebyshev polynomials for numerical solution of a system of Cauchy type singular integral equations of the first kind on a finite segment. Moreover, an estimation error is computed for the
S. Ahdiaghdam, S. Shahmorad
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Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 2020 This paper is devoted to the investigation of the Kolmogorov-Wiener filter weight function for continuous fractal processes with a power-law structure function.
Vyacheslav Gorev +2 more
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Chebyshev Polynomials and Spectral Method for Optimal Control Problem [PDF]
Engineering and Technology Journal, 2009 This paper presents efficient algorithms which are based on applying the idea of spectral method using the Chebyshev polynomials: including Chebyshev polynomials of the first kind, Chebyshev polynomials of the second kind and shifted Chebyshev ...
Suha Najeeb Shihab, Jabbar Abed Eleiwy
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Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials [PDF]
Mathematical Problems in Engineering, 2015 We use the combinatorial method and algebraic manipulations to obtain several interesting identities involving the power sums of the derivative of the first kind Chebyshev polynomials. This solved an open problem proposed by Li (2015).
Wang, Tingting, Zhang, Han
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