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The Gibbs Phenomenon for Taylor Means and for [F, Dn] Means

Published online by Cambridge University Press:  20 November 2018

Chester L. Miracle
Chester L. Miracle*
Affiliation:
University of Minnesota
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The Gibbs phenomenon may be described, quite generally, as follows. Let a sequence {fn(x)} (n = 0, 1, 2, … ,) converge to a function f(x) for x in the interval x0 < x < x0+ h. We say that {fn(x)} displays the Gibbs phenomenon in a right-hand neighbourhood of the point X0, if

A similar definition holds for a left-hand neighbourhood. If {fn(x)} displays the Gibbs phenomenon at both sides of x0, we say simply that {fn(x)} displays Gibbs phenomenon at the point X0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 660 - 673
Copyright
Copyright © Canadian Mathematical Society 1960

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