CVR8
From Exampleproblems
Find the residues of 
at all its isolated singular points and at infinity (if infinity is not a limit point of singular points), where is given by
This has poles at 
of multiplicity 
.
Use the formula ![\mathrm{Res}_{z=z_0} f(z) = \frac{1}{(k-1)!}\lim_{z\to z_0} \frac{d^{k-1}}{{dz}^{k-1}}\left[(z-z_0)^k f(z)\right]\,](/wiki/images/math/f/d/e/fded86bdbecf9ea9fc9c85714763d2fa.png)
![\mathrm{Res}_{z=n\pi} =\frac{1}{2} \lim_{z\to n\pi} \frac{d^2}{{dz}^2} (z-n\pi)^3 f(z) = \frac{1}{2} \lim_{z\to n\pi} \frac{d^2}{{dz}^2} \left[ \frac{(z-n\pi)\cos z}{\sin z} \right]^3 = ... = -1\,](/wiki/images/math/7/3/1/7315233972abd56fc83eea49be33fcb8.png)
In this case infinity is a limit point of singular points, so there is no residue at infinity.
