Hey guys, I'm having a bit of trouble with the creating Laurent series representations of functions. Specifically, I have no idea what the domain does to the series representation.

Anyways, this is what I'm working on...

for

This is where I go with this?...

No idea where to go from here.

Also, if a function is analytic everywhere in a domain, is the Laurent series representation just the Taylor series?

Thanks for the help in advance.