(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Is there a Laurent Series for Log(z) in the Annulus 0<|z|<1?

2. Relevant equations

Go here for the Theorem. It is theorem 7.8:

www.math.fullerton.edu/mathews/c2003/LaurentSeriesMod.html[/URL]

(copy and paste the link below if you are having problems. Exclude the "[url]" in the link below):

[PLAIN]http://math.fullerton.edu/mathews/c2003/LaurentSeriesMod.html[url] [Broken]

This whole section actually comes right out of my current textbook!

3. The attempt at a solution

From what is stated in the theorem I'm assuming yes because Log(z) is analytic for all z not equal to 0. So for any Annulus A(0,0,R), where R >0, a laurent series should exist.

I calculated a few coefficients out, but I'm not sure it is right for all n. I tried to google this situation to verify that my logic is right, but the only series I'm ever given is the maclaurin series of Log(1+z) which converges in the disk |z|<1.

Any help on this would be most apperciated it.

THanx.

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