Question about non essential singulariy

Question

When reading Ahlfor's Complex Analysis book, I came across the notion of non essential singularity. I know that for a function $f(z)$ an element $a\in\mathbb C$ is a non essential singularity iff there exists $m\in\mathbb Z$ such that $g(z)=(z-a)^mf(z)$ has a removable singularity at $a$. The question is this: is a non essential singularity at $\infty$ removable or is it necessarily non removable, which would imply that it is a pole? Thanks.

Answer 1

It could be either. For example, $z^2$ has a pole at $\infty$, $1/z$ has a removable singularity there.