Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T07:27:27.257Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on the Gibbs Phenomenon

Published online by Cambridge University Press:  24 October 2008

S. Verblunsky
S. Verblunsky
Affiliation:
Magdalene College
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.