# Math Help - sequence, analytic function

1. ## 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.