Definition of asymptotic relation

  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,

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

    How does this incorporate the idea of asymptoticity?

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

    arildno 12,015
    Science Advisor
    Homework Helper
    Gold Member

    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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