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Theorem connecting the inverse of a holomorphic function to a contour integral

  1. Nov 18, 2012 #1
    I tried posting this at stack exchange but it never got the question answered. I want to prove this:

    If f:U→C is holomorphic in U and invertible, P∈U and if D(P,r) is a sufficently small disc about P, then


    [itex]f^{-1}(w) = \frac{1}{2\pi i} \oint_{\partial D(P,r)}{\frac{sf'(s)}{f(s)-w}}ds[/itex]
     
  2. jcsd
  3. Nov 18, 2012 #2

    lurflurf

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    Homework Helper

    That is just Cauchy's formula.

    [tex]f^{-1}(w)=\frac{1}{2\pi\imath}\oint_{\partial D(P,r)} \frac{s}{f(s)-w}d(f(s))[/tex]
     
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