# Hint for Complex Analysis Proof of $f = \frac{g'}{g}$

I am working on some Complex Analysis problems and am stuck on the following from Lang 3rd edition. I understand all the homework up to this point but don't even know where to begin here! I have attached a screenshot but the question is as follows:

Let f be analytic on an open disc centered at a point $$z_o$$, except at the point itself where f has a simple pole with residue equal to an integer n. Show that there is an analytic function g on the disc such that $$f=\frac{g'}{g}$$, and $$g(z) = (z-z_o)^n h(z)$$ where $$h$$ is analytic and $$h(z_0)≠ 0$$ We can assume that $$z_0=0$$ for simplicity.

Anything would be appreciated! Lang VI.1.22

Note that $$g \longmapsto \frac{g’}{g}$$ maps products to sums, so you can split $$f$$ into a holomorphic part and $$\frac{n}{z}$$, so you can treat each part separately.