singularities and residues
Consider the function . Find its singularities and compute residues.
I know the denominator vanishes for integer. I first consider , so the function is analytic in $ , and i can write in this punctured disc the following Laurent expansion:
starting from i get Hence
thus i can write where .
So we have higther terms.
Finally, we get + higther terms, fromw which i desume that is a removable singularity for f.
But now i don't knoe hoe to deal with with . I imagine those to be all poles of order 2 for , but how to prove?
A lats question: is it correct to say: the poles accumulates to , hence is not an isolated singularity, thus i cannot compute ?