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Analyticity at Infinity

  1. Jul 3, 2008 #1
    How does one define, given a complex function, the following:

    • The function is analytic at infinity.
    • The derivative of the function at infinity.

    It turns out that it's supposed to be quite common to define these terms, however I have never been shown either of them. I have a few guesses, but along with some lecture notes I could put my hands on, it's all become a big mess for me.
     
  2. jcsd
  3. Jul 3, 2008 #2

    matt grime

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    Presumably one replaces z with w=1/z and works w=0.
     
  4. Jul 4, 2008 #3
    O.K., but then if g(z)=f(1/z) do I take f'(\infty)=g'(0)? Just like this?
     
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