I have to find the Laurent series of the function $f(z)=\frac{\sin z}{z^2}$ in these open annulus $0 < |z|< 3$ and $|z|>3$. Is anyone able to give me the difference between these two series? Can I use the Laurent theorem? Does there exist an easy way to compute those without using Laurent theorem?
I am usually able to find the Laurent series when it includes $0$, but now it is a bit different.