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

1. Nov 18, 2012

### IDontKnow1

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

$f^{-1}(w) = \frac{1}{2\pi i} \oint_{\partial D(P,r)}{\frac{sf'(s)}{f(s)-w}}ds$

2. Nov 18, 2012

### lurflurf

That is just Cauchy's formula.

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