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Math Help - Complex analysis

  1. #1
    May 2008

    Complex analysis

    Hey guys.
    I have this question, I took it from a test.
    I need to check if there is an analytic function F(z) in this area (in the pic) that has this derivative (in the pic).

    Well, the derivative is analytic in this area, right?
    If the derivative is analytic, shouldn't F(z) be analytic and even more important, can it be that easy ?
    I'm not sure about the answer, I could really use some help.

    Thanks a lot.
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  2. #2
    MHF Contributor
    Opalg's Avatar
    Aug 2007
    Leeds, UK
    The integral of \frac z{z^2+4} is \tfrac12\ln(z^2+4), and this function cannot be defined globally on the set \mathbb{C}\setminus\{\pm2i\} (logarithm functions can usually only be defined on some kind of cut plane).
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