1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I need super help on a complex analysis problem.

  1. Dec 28, 2006 #1
    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.
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Dec 28, 2006 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No it isn't. It's not even continuous on the set of all nonzero z.
     
  4. Dec 28, 2006 #3
    I forgot I was looking at the principal branch LOG function, which is not analytic on the negative real axis. Thanx anyways.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: I need super help on a complex analysis problem.
Loading...