# analytic function on open annulus

• Aug 30th 2011, 12:29 AM
Veve
analytic function on open annulus
If f is a non-zero analytic function on the open annulus A= {z in $\mathbb{C}$; 1<|z|<2}, how can I prove that there exists an integer m such that for all r . 1<r<2, 1/ $2\pi$i $\int$_{|z|=r} f '(z)/f(z) dz =m ?

Thanks.
• Aug 30th 2011, 01:09 AM
chisigma
Re: analytic function on open annulus
Quote:

Originally Posted by Veve
If f is a non-zero analytic function on the open annulus A= {z in $\mathbb{C}$; 1<|z|<2}, how can I prove that there exists an integer m such that for all r . 1<r<2, 1/ $2\pi$i $\int$_{|z|=r} f '(z)/f(z) dz =m ?

Thanks.

A proof of the 'argument principle theorem' is here...

http://www.joensuu.fi/matematiikka/k...plex/luku3.pdf

Kind regards

$\chi$ $\sigma$