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

Find the laurent series about z=-2 for:

f(z) = 1/(z(z+2)^{3})

2. Relevant equations

3. The attempt at a solution

Setting t = z+2 yields:

f(t) = 1/(t^{3}(t-2))

= 1/t (-1/(2(1-t/2))) = (1/t)^{3}* (-1/2) * Ʃ(t/2)^{n}which can be put together in a sum, but I can't be bothered due to my poor Latex skills.

My question is however: In what region will this sum converge? Am I right at saying that the expansion will only be valid in the region described by the circle lz+2l<2? If not please tell me, because the term 1/(t-2) should wreak havoc according to me if we go outside this circle.

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# Homework Help: Find laurent series about z=-2

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