Question

Laurent series expansion of
f(z) =z^2-4/(z+1)(z+4).valid in the region 1< |z|<4​

Answer 1

Answer:

We have f(z)=1z2−4+16−z. I want to expand this as a Laurent series in z0=2 on {4<|z−2|<∞}.

The partial decomposition is:

f(z)=141z−2−141z+2+16−z

In my reference, they expand 1z+2 and 16−z with the help of the geometric series, but they leave 1z−2 as it is.