- #1
cathode-ray
- 50
- 0
Hi everyone!
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:
But when I get the Laurent serie:
i don't know how to get the residue directly from it.
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.