How can I calculate the residues of this function (in the pic) in all of its singularity points?
I'm kind of a newbie in this this residues stuff and I can really use an example.
Thanks in advance.
Also, be careful of the removable singularities !
Poles are points where the limit is undefined.
But removable singularities are points where the limit exists. For example
2 annulates the denominator, so you can think that it's a pole. But (z-2) also divides zē-3z+2 (because zē-3z+2=(z-1)(z-2))
So the limit when z goes to 2 is defined. It's a removable singularity.
it was just in case...because you might meet some in the future :P
There are also essential singularities, which are singularities that are neither poles nor removable singularities.