- #1
laura_a
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Homework Statement
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
Homework Equations
Well that's 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
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 textbook 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 into where and I'll work on the rest :) any suggestions will make my day (night actually, but who's counting)
Thanks
Laura