Analytic function, complex Taylor series and polynomials.

Sep 2009
173
0
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
Nov 2009
4,563
1,566
Berkeley, California
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?
 
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