Analytic function, complex Taylor series and polynomials.

Hi all;
I need the solution of the following question

Suppose f is analytic function defined everywhere in C and such that for each in C at least one coefficient in the expansion

is equal to 0. prove that f is polynomail

Kind regards

Quote:

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Originally Posted by raed

Hi all;
I need the solution of the following question

Suppose f is analytic function defined everywhere in C and such that for each in C at least one coefficient in the expansion

is equal to 0. prove that f is polynomail

Kind regards

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What do you think? You need to show that all but finitely many of those are zero. What if they aren't?