Cauchy Integral Theorem
From ProofWiki
This proof is about Cauchy's Theorem on the value of integrals in complex analysis. For other uses, see Cauchy's Theorem.
Theorem
Let $U$ be a simply connected open subset of the complex plane $\C$.
Let $\gamma : [a,b] \to U$ be a closed path in $U$.
Let $f:U \to \C$ be holomorphic in $U$. Then
- $\displaystyle \oint_\gamma f(z)\ \mathrm dz = 0$
Proof
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Note
This is a special case of the Residue Theorem.
