(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write TWO laurent series in powers of z that represent the function

f(z)= \frac{1}{z(1+z^2)}

In certain domains, and specify the domains

2. Relevant equations

Well thats my prob, not sure what the terms in the Laurent series are

The formula I'm looking at is

\sum^{infty}_{n=0} a_n * (z-c)^n

for a complex function f(z) about a point c and a_n is a constant.

I sort of understand that, but do I use it to represent a function? Thats the part I'm not sure about

3. The attempt at a solution

My lame guess is that sub in the f(z) i'm given into the equation. I've seen one example where the fraction is split into two and then the Laurent expansion is applied. I have the answers (because it's a text book question)

They are

\sum^{\infty}_{n=0} (-1)^{n+1} * z^{2n+1} + 1/z (0 < |z| < 1)

and

\sum^{\infty}_{n=0} [(-1)^{n+1}] / z^{2n+1} (1 < |z| < \infty)

All I need to know is what to I plug in to where and I'll work on the rest :) any suggestions will make my day (night actually, but who's counting)

Thanks

Laura

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# Whats a Laurent series? And how do I use one to represent a function?

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