# Math Help - Complex Analysis: Laurent series

1. ## Complex Analysis: Laurent series

Hello,

I m stuck with the following exercise:

Find the Laurent series expansion about the origin of the following function:

f(z)= cos z/ z^4

What type of singularity does this function has at the origin?

I can't find the laurent series.. I need help.

Richard

2. Just take the Taylor series of cos z and divide by z^4.

3. Okay I was not sure..

So it's $f(z)=1/z^4 -1/2!z^2 + 1/4! ....$??

And what about the fact that f is analytic on the punctured disc D={z \in C : 0<|z|< ? }