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Math Help - normal convergence, meromorphic function

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    normal convergence, meromorphic function

    Let \{ z_k \} be a sequence of distinct points such that |z_k| \rightarrow \infty and \sum_{k=1}^{\infty} |z_k|^{-m-1}< \infty. Show that z^m \sum_{k=1}^{\infty} \frac{1}{z_k^m(z-z_k)} converges normally to a meromorphic function with principal part \frac{1}{z-z_k} at z_k. (If z_k=0, we replace the corresponding summand by \frac{1}{z}.)


    In this section, we covered the Mittag-Leffler Theorem. I am not sure if we need to apply that result here though. I am not sure what this sequence would converge to. I would appreciate some help with this. Thank you.
    Last edited by zelda2139; April 19th 2010 at 10:45 AM.
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