Question: Suppose that g ( z ) is an entire function that never vanishes. What are all the possible values of the integrals C 1 z

Suppose that g(z) is an entire function that never vanishes. What are all the possible values of the integrals C1zg(z)dz, where C is any smooth curve that does not pass through 0 and goes from z=1 to z=z0.
Suppose that g ( z ) is an entire function that

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