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Non analytic function?

  1. Dec 26, 2006 #1
    Non analytic function???

    1. The problem statement, all variables and given/known data

    I was set this question as part of an extra problem sheet by my maths teacher, and i dont know where to start. He said its like first year university maths standard, and gave me hints to use the maclaurins and binomial series. Im just a bit stuck... PLEASE HELP... I found an example of a non analytical function on this forum, but just confused me!

    the question...

    Consider the function
    f(x) = "e− 1
    x2 if x "= 0
    0 if x = 0
    Calculate the Maclaurin series of f and show that it does not converge to f(x) for x "= 0. In
    particular f is not an analytic function.

    2. Relevant equations

    Maclaurins series
    Binomial expansion

    3. The attempt at a solution

    I dont know where to start
  2. jcsd
  3. Dec 26, 2006 #2


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    Staff: Mentor

  4. Dec 28, 2006 #3
    woops... cant copy and paste!

    Yes sorry it is an e^x....

    Thanks for yuor reply, but im still really stuck. I emailed my teacher the other day and he said to try find an example, and just understand it (or try to understand it).

    Does anyone know where i could find a worked solution of this... preferablely with quotations as it goes along...

  5. Jan 11, 2007 #4


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    Staff: Mentor

    This page has some good examples regarding convergence of a series.

    Think about the purpose of expanding using a series and then think about the criterion for convergence.
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