I am having trouble understanding when a function might have a removable singularity over a pole.
For example: $f(z)=\frac{\sin^2 z}{z}$
I believe the pole is at $z=0$. However, if we take the taylor expansion of $f(z)$ apparently the pole vanishes. I do not understand how and where does the pole vanish that it becomes a removable singularity.