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| {{Calculus|expanded=Fractional calculus}}
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| In [[mathematics]], the '''Weyl integral''' is an operator defined, as an example of [[fractional calculus]], on functions ''f'' on the [[unit circle]] having integral 0 and a [[Fourier series]]. In other words there is a Fourier series for ''f'' of the form
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| : <math>\sum_{n=-\infty}^{\infty} a_n e^{in \theta}</math>
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| with ''a''<sub>0</sub> = 0.
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| Then the Weyl integral operator of order ''s'' is defined on Fourier series by
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| : <math>\sum_{n=-\infty}^{\infty} (in)^s a_n e^{in\theta}</math>
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| where this is defined. Here ''s'' can take any real value, and for integer values ''k'' of ''s'' the series expansion is the expected ''k''-th derivative, if ''k'' > 0, or (−''k'')th indefinite integral normalized by integration from ''θ'' = 0.
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| The condition ''a''<sub>0</sub> = 0 here plays the obvious role of excluding the need to consider division by zero. The definition is due to [[Hermann Weyl]] (1917).
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| ==See also==
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| *[[Sobolev space]]
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| ==References==
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| *{{springer|first=P.I.|last=Lizorkin|id=f/f041230|title=Fractional integration and differentiation}}
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| [[Category:Fourier series]]
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| [[Category:Fractional calculus]]
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Latest revision as of 17:19, 22 May 2014
Andrew Berryhill is what his spouse enjoys to call him and he totally digs that title. I've always cherished residing in Kentucky but now I'm considering other choices. He works as a bookkeeper. It's not a common thing but what I like doing is to climb but I don't have the time recently.
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