Hey guys.
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 $\displaystyle \frac{z^2-3z+2}{(z-2)(z-4)}$
2 annulates the denominator, so you can think that it's a pole. But (z-2) also divides z²-3z+2 (because z²-3z+2=(z-1)(z-2))
So the limit when z goes to 2 is defined. It's a removable singularity.
No you don't, because $\displaystyle z^2+z-1=\left(z-\frac{-1+\sqrt{5}}{2}\right)\left(z-\frac{-1-\sqrt{5}}{2}\right)$
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.
http://en.wikipedia.org/wiki/Mathema...mplex_analysis