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

  • Thread starter IDontKnow1
  • Start date
  • #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]
 

Answers and Replies

  • #2
lurflurf
Homework Helper
2,440
138
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]
 

Related Threads on Theorem connecting the inverse of a holomorphic function to a contour integral

Replies
12
Views
6K
Replies
17
Views
5K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
938
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
918
Replies
11
Views
6K
Replies
1
Views
498
Replies
2
Views
2K
Top