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Math Help - complex analysis

  1. #1
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    complex analysis

    Let \gamma: [0,1] \rightarrow C be any C^1 curve. Define f(z)=\oint_{\gamma} \frac{1}{\zeta-z}d\zeta
    Prove that f is holomorphic on C\ \tilde{\gamma}, where \tilde{\gamma}=\{ \gamma (t):0\leq t \leq 1\}.
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  2. #2
    Super Member Rebesques's Avatar
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    You can compute the difference quotient [f(z+w)-f(z)]/w as w\rightarrow 0. The limit is (what a surprise) f'(z)=-\int_{\gamma} \frac{1}{(\zeta-z)^2}d\zeta.



    ps. what's with the \oint? I believe that notation is,
    only to signify counter-clockwise integration along a closed curve
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