Gauss' mean value theoremGaussMeanValueTheorem2003-04-28 00:17:422004-03-20 09:18:35Theorem% this is the default PlanetMath preamble. as your knowledge
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% define commands hereLet $\Omega$ be a domain in $\mathbb{C}$
and suppose $f$ is an analytic function on $\Omega$.
Furthermore, let $C$ be a circle inside $\Omega$
with center $z_0$ and radius $r$. Then $f(z_0)$
is the mean value of $f$ along $C$, that is,
\begin{displaymath}
f(z_0)=\frac{1}{2\pi}\int_0^{2\pi}f(z_0+re^{i\theta})d\theta.
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