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Homework Statement
Find the laurent series about z=-2 for:
f(z) = 1/(z(z+2)3)
Homework Equations
The Attempt at a Solution
Setting t = z+2 yields:
f(t) = 1/(t3(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.