Results 11 to 20 of about 4,491 (232)
The infinite sums of reciprocals and the partial sums of Chebyshev polynomials
AIMS Mathematics, 2022 In this paper, the infinite sums of reciprocals and the partial sums derived from Chebyshev polynomials are studied. For the infinite sums of reciprocals, we apply the floor function to the reciprocals of these sums to obtain some new and interesting ...
Fan Yang, Yang Li
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Chebyshev series: Derivation and evaluation.
PLoS ONE, 2023 In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial
Robert Reynolds, Allan Stauffer
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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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Sums of finite products of Chebyshev polynomials of two different types
AIMS Mathematics, 2021 In this paper, we consider sums of finite products of the second and third type Chebyshev polynomials, those of the second and fourth type Chebyshev polynomials and those of the third and fourth type Chebyshev polynomials, and represent each of them as ...
Taekyun Kim +3 more
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On Chebyshev Polynomials of Matrices [PDF]
SIAM Journal on Matrix Analysis and Applications, 2010 The $m$th Chebyshev polynomial of a square matrix $A$ is the monic polynomial that minimizes the matrix 2-norm of $p(A)$ over all monic polynomials $p(z)$ of degree $m$. This polynomial is uniquely defined if $m$ is less than the degree of the minimal polynomial of $A$.
Liesen, Jörg +2 more
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The Chebyshev Polynomials of a Matrix [PDF]
SIAM Journal on Matrix Analysis and Applications, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Toh, K.-C., Trefethen, L.N.
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Advances in Difference Equations, 2021 The principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The
Waleed M. Abd-Elhameed +1 more
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Fractal and Fractional, 2021 This paper is concerned with establishing novel expressions that express the derivative of any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in terms of Chebyshev polynomials themselves.
Waleed Mohamed Abd-Elhameed
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Meshless local Petrov-Galerkin method for rotating Rayleigh beam using Chebyshev and Legendre polynomials [PDF]
Archive of Mechanical Engineering, 2022 The numerical solutions are obtained for rotating beams; the inclusion of centrifugal force term makes it difficult to get the analytical solutions. In this paper, we solve the free vibration problem of rotating Rayleigh beam using Chebyshev and Legendre
Vijay Panchore
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Проблемы анализа, 2020 In this paper, we give the generating functions of binary product between 2-orthogonal Chebyshev polynomials and kFibonacci, k-Pell, k-Jacobsthal numbers and the other orthogonal Chebyshev polynomials.
H. Merzouk, B. Aloui, A. Boussayoud
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