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Aymptotic Series

  1. Mar 17, 2007 #1
    Hi all.
    I am still confued about the definition of an asymptotic series...
    Let says a function f(x) is expanded as a series, Sn, and the remainder is Rn.
    f(x) = Sn +Rn

    so if we divide both sides by Sn, then
    f(x)/Sn = 1+ Rn/Sn
    So f(x)/Sn tends to 1 when Rn/Sn tends to zero as say x tends to c.

    Why not an asymptotic series defined in this way?
    I just can't accept that it is the remainder divided by the "last retained term in the series" say (x-c)^N in Sn, rather than the whole series Sn...

    Could anyone help make this clear to me?
  2. jcsd
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