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2025-03-04 16:49:33 -06:00
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We divide the integral into four parts:
![Integral on a disk](https://notenextra.trance-0.com/Math416/Cauchy_disk.png)
![Integral on a disk](https://notenextra.trance-0.com/Math416/Cauchy_theorem_disk.png)
Notice that $\frac{f(\xi)}{\xi-z}$ is holomorphic whenever $f(\xi)\in U$ and $\xi\in \mathbb{C}\setminus\{z\}$.