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Math Help - Holomorphic function

  1. #1
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    Holomorphic function

    Hey who can help me with this:
    Let f be holomorphic in a neighborhood of a closed disk \bar{D}. Then g(z) = \int_{\delta  D}\frac{f(\zeta)d\zeta}{\zeta -z} is a holomorphic function on \mathbb{C}-\bar{D}.
    Why, and which one?
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  2. #2
    Super Member girdav's Avatar
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    Did you compute \frac{g(z)-g(z_0)}{z-z_0} for z,z_0\in\mathbb C\setminus \overline D ?
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  3. #3
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    Why do I do this, to check whether its holomorphic?
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  4. #4
    Super Member girdav's Avatar
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    Yes, we try to check the definition of holomorphic.
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  5. #5
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    Im somehow lost, when I compute the quotient I just get f'(z) multiplied by a constant. And I dont really use the fact that z is outside D.
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