# Singularities and Laurent series

1. Jun 11, 2016

### Physgeek64

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. 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

2. Jun 16, 2016