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!

Principal Part of a Laurent Series

  1. Mar 7, 2013 #1
    1. The problem statement, all variables and given/known data
    It f is a meromorphic function with finite number of singularities, prove that the the principal part of the laurent series centered at a singularity has infinite convergence radius.


    2. Relevant equations
    f(z)=Ʃ(a_n)(z-z_j) where z_j is the singularity.
    Principal part = Ʃ(a_n)(z-z_j) where the sum goes from -1 to -infinity


    3. The attempt at a solution
    I see that the principal part is a power series in (z-z_j)^-1 but I'm not sure what else I'm supposed to be looking for.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Principal Part of a Laurent Series
  1. Laurent series part 2 (Replies: 7)

  2. Laurent series (Replies: 3)

  3. Laurent series (Replies: 3)

  4. Laurent series (Replies: 3)

Loading...