# Singularities and Laurent series

## Homework Statement

Classify the singularities of

##\frac{1}{z^{1/4}(1+z)}##

Find the Laurent series for

##\frac{1}{z^2-1}## around z=1 and z=-1

## The Attempt at a Solution

So for the first bit there exists a singularity at ##z=0##, but I'm confused about the order of this since its fractional (I get that its a branch point, but does it 'act' as a singularity as well?)

And there is also a pole at ##z=-1## of order 1.... ?

(My problem with this is if I expand the ##\frac {1}{z^{\frac{1}{4}}}## about z=0 I get ##\frac{e^{\frac{i \pi}{4}}}{1+z} (1+\frac{1}{4}(z+1)+....)## and I don't know why these should be different?/ which one is wrong)

And as for the Laurent series I'm afraid Im completely stuck.

Many thanks- I really appreciate the help as I'm really struggling with these aspects

## Answers and Replies

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?