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This is just a small question about Cauchys theorem.

If there is a function f(z) such that int f(z)dz = 0 can you conclude f is analytic in and on the region of integration?

What I mean is can you work the theorem in reverse?

For example if the above is true over a region C which is a simple closed curve, is f(z) analytic both inside and on C?

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# Cauchys theorem

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