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## 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

## Homework Equations

## 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 I am completely stuck.

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