# Analytic function, complex Taylor series and polynomials.

• May 28th 2010, 01:07 AM
raed
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 $z_{0}$ in C at least one coefficient in the expansion
$f(z)=\sum_{n=0}^{\infty}c_{n}(z-z_{0})^n$
is equal to 0. prove that f is polynomail

Kind regards
• May 28th 2010, 01:09 AM
Drexel28
Quote:

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 $z_{0}$ in C at least one coefficient in the expansion
$f(z)=\sum_{n=0}^{\infty}c_{n}(z-z_{0})^n$
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 $z_0$ are zero. What if they aren't?