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Homework Help: Analytic function

  1. Dec 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Let f:ℝ→ℝ an analytic function,i.e, f ∈ C^{∞}(ℝ) and for all a∈ℝ we have that
    Suppose that for all x in ℝ:∃N=N_{x}∈ℕ:f^{(N)}(x)=0.
    Show that F is a polynomial

    2. Relevant equations

    3. The attempt at a solution

    I think that maybe the theorem of Baire's Categories is the key of exercise. So, I said:
    Let A_{n}={x∈ℝ:f⁽ⁿ⁾(x)=0} and I want to show that for some n and for a uncountable x∈ℝ f⁽ⁿ⁾(x)=0...But I don't know how....
    Last edited: Dec 13, 2008
  2. jcsd
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