Nucleate boiling

2013-11-11T19:34:32Z

14.139.160.238: /* Mechanism */

{{Calculus|expanded=Fractional calculus}}

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

: <math>\sum_{n=-\infty}^{\infty} a_n e^{in \theta}</math>

with ''a''<sub>0</sub> = 0.

Then the Weyl integral operator of order ''s'' is defined on Fourier series by

: <math>\sum_{n=-\infty}^{\infty} (in)^s a_n e^{in\theta}</math>

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.

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).

==See also==
*[[Sobolev space]]

==References==
*{{springer|first=P.I.|last=Lizorkin|id=f/f041230|title=Fractional integration and differentiation}}

[[Category:Fourier series]]
[[Category:Fractional calculus]]

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Nucleate boiling