Complex Numbers (Laurent Series)

[jojosg]

Homework Statement

Am attempting a Laurent Series question but I'm not confident in my answers. would appreciate any corrections.

Relevant Equations

f(z) = sigma (cnz^n)

see attached.

 

[FactChecker]

Are you sure this problem is valid? The domains of the two expansions would make more sense to me if the function was
$\frac {z+1}{z^3(z^2-1)}$
or if the domains were $0\lt z \lt \sqrt 2$ and $\sqrt 2 \lt z \lt \infty$

PS. I can not read your work.