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Homework Help: 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
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