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Gauss's Mean-Value Theorem

Let $f(z)$ be an Analytic Function in $\vert z-a\vert<R$. Then

\begin{displaymath}
f(z) = {1\over 2\pi} \int^{2\pi}_0 f(z+re^{i\theta})\,d\theta
\end{displaymath}

for $0 < r < R$.




© 1996-9 Eric W. Weisstein
1999-05-25