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What does the residue theorem state?
in Mathematics by Platinum (142,760 points) | 99 views

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Suppose that \(C\) is a simple closed contour contained in the interior of a simply connected domain \(D\). If \(f\) is analytic everywhere on and within \(C\), except possibly for at a finite number of isolated singularities (call them \(\left.z_{1}, \ldots, z_{n}\right)\) inside \(C\), then
\[
\oint_{C} f(z) d z=2 \pi i \sum_{k=1}^{n} \operatorname{Res}\left(f(z), z_{k}\right)
\]
by Platinum (142,760 points)

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