# Analytic function, complex Taylor series and polynomials.

#### 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 $$\displaystyle z_{0}$$ in C at least one coefficient in the expansion
$$\displaystyle f(z)=\sum_{n=0}^{\infty}c_{n}(z-z_{0})^n$$
is equal to 0. prove that f is polynomail

Kind regards

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#### Drexel28

MHF Hall of Honor
Hi all;
I need the solution of the following question

Suppose f is analytic function defined everywhere in C and such that for each $$\displaystyle z_{0}$$ in C at least one coefficient in the expansion
$$\displaystyle f(z)=\sum_{n=0}^{\infty}c_{n}(z-z_{0})^n$$
is equal to 0. prove that f is polynomail

Kind regards
What do you think? You need to show that all but finitely many of those $$\displaystyle z_0$$ are zero. What if they aren't?

mr fantastic