Show that any analytic function \(\displaystyle f(z)\) on a domain \(\displaystyle D\) can be approximated normally on \(\displaystyle D\) by a sequence of rational functions that are analytic on \(\displaystyle D\).
In this section we have covered Runge's Theorem. It seems clear to me that this would be true. However, I do not see how to prove this. This section mentions Mergelyan's Theorem also. I guess I just need some hints on proving this. Thanks in advance.
In this section we have covered Runge's Theorem. It seems clear to me that this would be true. However, I do not see how to prove this. This section mentions Mergelyan's Theorem also. I guess I just need some hints on proving this. Thanks in advance.