Results 41 to 50 of about 4,491 (232)
Distribution of values of Hardy sums over Chebyshev polynomials
AIMS MathematicsThis paper mainly studied the distribution of values of Hardy sums involving Chebyshev polynomials. By using the method of analysis and the arithmetic properties of Hardy sums and Chebyshev polynomials of the first kind, we obtained a sharp asymptotic ...
Jiankang Wang, Zhefeng Xu, Minmin Jia
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Some identities involving the bi-periodic Fibonacci and Lucas polynomials
AIMS Mathematics, 2023 In this paper, by using generating functions for the Chebyshev polynomials, we have obtained the convolution formulas involving the bi-periodic Fibonacci and Lucas polynomials.
Tingting Du, Zhengang Wu
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On the Gaussian integration of Chebyshev polynomials [PDF]
Mathematics of Computation, 1972 It is shown that as m m tends to infinity, the error in the integration of the Chebyshev polynomial of the first kind, T ( 4 m + 2 ) j ± 2 l
A. R. Curtis, Philip Rabinowitz
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Properties of the second-kind Chebyshev polynomials of complex variable
Researches in Mathematics, 2020 We construct a system of functions biorthogonal with Chebyshev polynomials of the second kind on closed contours in the complex plane. Properties of these functions and sufficient conditions of expansion of analytic functions into series in Chebyshev ...
O.V. Veselovska +2 more
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Gaussian quadrature of Chebyshev polynomials
Journal of Computational and Applied Mathematics, 1998 Let \(f\) be a bounded integrable function on the interval \((-1,1)\) and \(I(f)={\int_{-1}^1 w(x)f(x) dx}\), where \(w\) is a weight function. Let further \(\varepsilon _{n}(f)=J(f)-K_{n}\), where \(J(f)=I(f):I(1)\) and\(K_{n}(f)\) is the Gaussian quadrature for \(J(f)\) with the \(n\)-knots on \((-1,1)\).
David B. Hunter, Geno Nikolov
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An approximate solution of the Blasius problem using spectral method
Partial Differential Equations in Applied MathematicsThis paper aims at finding the numerical approximation of a classical Blasius flat plate problem using spectral collocation method. This technique is based on Chebyshev pseudospectral approach that involves the solution is approximated using Chebyshev ...
Zunera Shoukat +6 more
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Chebyshev polynomials are not always optimal [PDF]
Journal of Approximation Theory, 1991 The problem of finding the polynomial with minimal uniform norm on \({\mathcal E}_ r\) among all polynomials of degree at most \(n\) and normalized to be 1 at \(c\) is considered. Here \({\mathcal E}_ r\) is a given ellipse with both foci on the real axis and \(c\) is a given real point not contained in \({\mathcal E}_ r\). \textit{A. J.
Roland W. Freund +2 more
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Advanced Theory and Simulations, EarlyView.This study develops a superconvergent meshless method to analyze and control vibrations in twisted, bidirectional functionally graded Terfenol‐D beams. By optimizing magnetostrictive patch placement, it demonstrates effective vibration suppression under dynamic loads, highlighting the design potential of strategically graded materials in complex ...
Mukund A. Patil +2 more
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Resultants of Chebyshev Polynomials
Zeitschrift für Analysis und ihre Anwendungen, 2008 Recently, K. Dillcher and K. B. Stolarsky [ Trans. Amer. Math. Soc. 357 (2004), 965–981] used algebraic methods to evaluate the resultant of two linear combinations of Chebyshev polynomials of the second kind. In this paper we give an alternative method of computing the same resultant and resultants of more general
Jemal Gishe, Mourad E. H. Ismail
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Advanced Energy and Sustainability Research, EarlyView.A novel polylactic acid/wax electret composite is developed, combining biodegradability with long‐term charge stability. The study investigates charge storage behavior, structural morphology, and thermal performance. Results reveal a notable charge retention recovery after thermal stress and exhibit stable surface potential over 2 kV. This eco‐friendly
Gabriele Perna +6 more
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