# Laurent Series - when do singularities on the boundary of an annulus require a Laurent series instead of Taylor?

I need to find the Laurent Expansion of $F(z) = \dfrac{1}{(z-1)^2(z+2)}$ in the regions $A_1 = D(0,1)$ and $A_2 = \{z: 1 < |z| < 2 \}$.

After doing partial fractions on $F(z)$, how do I know whether I need to work out a regular Taylor series or one of those fancy Laurent series, since the singularities aren't actually in the annulus but on the (open) boundary?

Thanks

If the summand is regular in the point (no $1/0$), has a Taylor series.