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Analytic Zeros Proof

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Let f be analytic on a domain D. Prove that if f(z(0))=0 and if f is not identically zero, then z(0) is a zero of f of some finite order m.

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Solution Summary

An analytic zeros proof is provided. Domains of analytic functions for non identical zeros are given.

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Proof: Let f(z) be an analytic complex function on D. That means that (f) can be expanded in a Taylor series around any point (z0) inside D: f(z)=sum(n=0 to inf) of ...

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