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Definition of asymptotic relation

  1. Jul 19, 2006 #1
    Hi all!

    Can anyone explain to me why the asymptotic relation between a function and a power series is defined in such a way:

    For all N,

    f(x) - \sum_{n=0}^N a_n(x-x_0)^n << (x-x_0)^N

    How does this incorporate the idea of asymptoticity?

    Please kindly help.
    Last edited: Jul 19, 2006
  2. jcsd
  3. Jul 19, 2006 #2


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    It means that:
    [tex]\lim_{x\to{x}_{0}}\frac{f(x) - \sum_{n=0}^N a_n(x-x_0)^n}{(x-x_{0})^{N}}=0[/tex]
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