Help: Laurent Series

May 2018
11
0
south africa
I need urgent help with the following:

Find the Laurent series of the function 1/(z^3-z^4)
with center z0=0
for
(i) 0<|z|<1 and
(ii) |z|>1

Any assistance will be great.
 
Last edited by a moderator:

romsek

Math Team
Sep 2015
2,958
1,673
USA
$\dfrac{1}{z^3 - z^4} = \dfrac{1}{z^3(1-z)}$

Now use partial fractions and find $A,~B$ such that

$\dfrac{1}{z^3(1-z)} = \dfrac{A}{z^3} + \dfrac{B}{1-z}$

And use standard results to finish the problem.
 
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skipjack

Forum Staff
Dec 2006
21,473
2,466
Expand 1/(1 - $z$), then divide each term by $z^3$.