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cbarker1

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MHB

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I am wondering how to use the integral formula for a holomorphic function at all points except a point that does not exist in function's analyticity. For instance, Let $f$ be defined as $$f(z)=\frac{z}{e^z-i}$$. $f$ is holomorphic everywhere except for $z_n=i\pi/2+2ni\pi$ for all $n$ in the integers. Let curve $C$ be closed positively oriented simple curve. \[ f(z_0)=\frac{1}{2i\pi}\int_C\frac{f(z)}{z-z_0}dz \], I want to find $z_0=i$, if it is possible.Thanks,

Cbarker1