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Math Help - sequence, analytic function

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    sequence, analytic function

    Let \{ z_k \} be a sequence of distinct points in a domain D that accumulates on \partial D. Let \{ m_k \} be a sequence of positive integers, and for each k, let a_{k0}, \ldots, a_{km_k} be complex numbers. Show that there is an analytic function f(z) on D such that f^{(j)}(z_k)=a_{kj} for 0 \leq j \leq m_k and for all k.

    In this section we have covered Runge's Theorem. However, I am still not sure how to prove this. I need some hints on doing this. Thanks in advance.
    Last edited by eskimo343; April 19th 2010 at 01:40 PM.
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