I'm trying to solve the following problem from one of the past qualifying exams.
Find an explicit formula for all meromorphic functions $g$ on $\mathbb{C}$ such that $$|g(z)|\leq \frac{\log(2+|z|^2)}{|z|}$$ for all $z\neq 0$.
I am completely stumped on how to start on this problem. I tried using Laurent expansion, but it's not getting me anywhere. Any hint/help will be appreciated.
Thanks in advance.