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

  • Thread starter IDontKnow1
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  • #1
IDontKnow1
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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]
 

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  • #2
lurflurf
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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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