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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