Finding and classifying singularities

Hi. I have to find and classify the isolated singularities for:

So, I've found that

Now, I think I should make the Laurent series for f(z), but I don't know how to handle this function to get it's Laurent series representation.

I also know, of course, that:

Re: Finding and classifying singularities

Quote:

Originally Posted by

**Ulysses** Hi. I have to find and classify the singularities for:

So, I've found that

Now, I think I should make the Laurent series for f(z), but I don't know how to handle this function to get it's Laurent series representation.

I also know, of course, that:

Do you know how to prove that a singularity is a pole **without** finding the Laurent series? (btw the poles are simple).

Re: Finding and classifying singularities

I was looking at my notebook. Should I use a thing called "principle of isolated zeroes" or something like that?

I was trying to determine the order of the pole

EDIT: Alright, I did it this way:

I took

Then it's a pole of order 1.

Re: Finding and classifying singularities

Quote:

Originally Posted by

**Ulysses** I was looking at my notebook. Should I use a thing called "principle of isolated zeroes" or something like that?

I was trying to determine the order of the pole

EDIT: Alright, I did it this way:

I took

Then it's a pole of order 1.

Therefore ....