Isolated singularities, poles and removable singularities Let $f$ be holomorphic with an isolated singularity at $z_0$. Suppose that $\exists M,m,\epsilon$ positive numbers such that $|f(z)| \leq M|z-z_0|^{-m}$ for $0<|z-z_0|<\epsilon$. Prove that $z_0$ is either a removable singularity or a pole of order $m$.
How should I go about this? Any suggestions, hints, solutions will be deeply appreciated!

Hint: What kind of singularity does $(z - z_0)^m f(z)$ have at $z_0$?
