Dirichlet–Jordan test: Difference between revisions
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Deleted unnecessary condition f(x) be single-valued, as this is in the definition of a function. |
these are for Fourier _series_ |
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In [[mathematics]], the '''Dirichlet conditions''' are the conditions that must be met for a function |
In [[mathematics]], the '''Dirichlet conditions''' are the conditions that must be met for a [[periodic function]] ''f''(''x''), to have a [[Fourier series]]. These conditions are named after [[Johann Peter Gustav Lejeune Dirichlet]]. |
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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 [[extrema]] in any given interval |
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*''f''(''x'') must have a finite number of [[discontinuity|discontinuities]] in any given interval |
*''f''(''x'') must have a finite number of [[discontinuity|discontinuities]] in any given interval |
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*''f''(''x'') must be absolutely integrable |
*''f''(''x'') must be [[absolutely integrable]] over a period. |
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==External link== |
==External link== |
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*{{planetmath reference|id=3891|title=Dirichlet conditions}} |
*{{planetmath reference|id=3891|title=Dirichlet conditions}} |
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[[Category:Fourier |
[[Category:Fourier series]] |
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Revision as of 11:24, 25 September 2006
In mathematics, the Dirichlet conditions are the conditions that must be met for a periodic function f(x), to have a Fourier series. 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.