Ok, another last thing, the exercise was at the beginning: Laurent series of for ,
then I wrote partial fractions: and then I wrote the Laurent Series for every fraction:
At this point my question is: I can leave and as they are?
So the final result will be:
... is a Laurent expansion. The (1) converges for but with a procedure called 'analytic extension' the analyticity of can be 'extended' to the region . Of course a spontaneous question is: what's the practical utility of all that?...
That way, you get a constant term 1 for the Laurent series, plus a single series arising from the z-1 denominator.