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Math Help - Analytic function, complex Taylor series and polynomials.

  1. #1
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    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
    Last edited by mr fantastic; July 3rd 2010 at 05:15 AM. Reason: Re-titled.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by raed View Post
    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?
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