Dirichlet–Jordan test: Difference between revisions
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The conditions are: |
The conditions are: |
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*''f''(''x'') must have a finite number of [[extrema]] in any given interval |
*''f''(''x'') must have a finite number of [[Maxima_and_minima|extrema]] in any given interval |
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*''f''(''x'') must have a finite number of [[Classification_of_discontinuities|discontinuities]] in any given interval |
*''f''(''x'') must have a finite number of [[Classification_of_discontinuities|discontinuities]] in any given interval |
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*''f''(''x'') must be [[absolutely integrable]] over a period. |
*''f''(''x'') must be [[absolutely integrable]] over a period. |
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Revision as of 16:38, 10 January 2008
In mathematics, the Dirichlet conditions are sufficient condition for a periodic function f(x), to have a Fourier series representation or to possess a Fourier Transform. These conditions are named after Johann Peter Gustav Lejeune Dirichlet.
The conditions are:
- f(x) must have a finite number of extrema in any given interval
- f(x) must have a finite number of discontinuities in any given interval
- f(x) must be absolutely integrable over a period.