- #1

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I still didn't fully understand how to get the residues of a complex function. For example the function [tex]f(z)=\frac{1}{(z^{2}-1)^{2}}[/tex] in the region [tex]0<|z-1|<2[/tex] has a pole of order 2. So the residue of f(z) in 1 should be given by the limit:

[tex]\lim_{z \to 1}(z-1)^{2}f(z)=1/4 [/tex]

But when I get the Laurent serie:

[tex] \sum_{n=1}^{+\infty} (-1)^{n+1}n\frac{(z-1)^{n-3}}{2^{n+1}}[/tex]

i don't know how to get the residue directly from it.