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Note on the Gibbs Phenomenon

Published online by Cambridge University Press:  24 October 2008

S. Verblunsky
S. Verblunsky
Affiliation:
Magdalene College
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Extract

The Fourier series of the function defined by

is

and if

then

while

The expression (1) exceeds (2); this is the Gibbs phenomenon.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 26 , Issue 2 , April 1930 , pp. 158 - 169
Copyright
Copyright © Cambridge Philosophical Society 1930

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References

* I owe this remark to a referee.

† Szegö, , Acta Scient. Univ. Hung. Szeged, 3 (1927), 17–24.Google Scholar

* The formal proof of this statement follows in a simple manner from the result of lemma 3.