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The identity theroem complex analysis

  1. Apr 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that there is no holomorphic function f in the open unit disk such that f(1/n)=((-1)^n)/(n^2) for n=2,3,4....


    2. Relevant equations
    The identity theorem: Let f and g be holomorphic functions in the connected open subset of C, G. If f(z)=g(z) for all z in a subset of G that has a limit point in G, then f=g.



    3. The attempt at a solution

    We proved in an earlier example that there is not holomorphic function f in the open unit disk such that f(1/n)=2^(-n) n=2,3,4... Is the above function identical to this? I thought this was the route to go but i am not sure anymore. I know we have to somehow use the identity theorem.
     
  2. jcsd
  3. Apr 1, 2008 #2
    Maybe it helps to consider the function [itex]g(z)=(-1)^{\frac{1}{z}}z^2[/itex]
     
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