A possible confortable way is the complex variable subsitution so that is...
(1)
... and we have...
(2)
Now for is...
(3)
... so that is...
(4)
... and therefore...
(5)
The series (5) converges for ...
Kind regards
I must find the Laurent series of the function for 3 different regions: , and .
My attempt: I've found out that g has 3 singularities (at and ) and is I think otherwise analytic.
So for the first region, there is 1 singularity inside it (just at the center of the region).
So I think I should write the Laurent series centered at the singularity .
I've tried many things like rewriting but I realized it was better to keep it as it was. I was thinking about writing as an infinite series (now I realize that as it should be centered in i, I should have factored out by (z-i)...) and then divide by z the whole series. I'm going into circles and I don't click yet on how to get it. I'd like a tip.