1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted