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Winter 2002 On the Rate of Convergence for the Chebyshev Series
Kamel Al-Khaled
Missouri J. Math. Sci. 14(1): 4-10 (Winter 2002). DOI: 10.35834/2002/1401004

Abstract

Let $f(x)$ be a function of bounded variation on $[-1,1]$ and $S_n (f; x)$ the $n$th partial sum of the expansion of $f(x)$ in a Chebyshev series of the second kind. In this note we give the estimate for the rate of convergence of the sequence $S_n (f; x)$ to $f(x)$ in terms of the modulus of continuity of the total variation of $f(x)$.

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Kamel Al-Khaled. "On the Rate of Convergence for the Chebyshev Series." Missouri J. Math. Sci. 14 (1) 4 - 10, Winter 2002. https://doi.org/10.35834/2002/1401004

Information

Published: Winter 2002
First available in Project Euclid: 4 October 2019

zbMATH: 1031.41010
MathSciNet: MR1883603
Digital Object Identifier: 10.35834/2002/1401004

Rights: Copyright © 2002 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.14 • No. 1 • Winter 2002
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