# Principal Part of a Laurent Series

1. Mar 7, 2013

### ilikegroupreps

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.