CVR17

From Exampleproblems

Find the residues of $f(z)\,$ at all its isolated singular points and at infinity (if infinity is not a limit point of singular points), where $f(z)\,$ is given by $\frac{(Log(z))2}{z^2+1}\,$

The poles are at $z=\pm i\,$ .

$\lim_{z\to i} \frac{(Log (z))^2}{z+i} = \frac{(Log(i))^2}{2i} = \frac{(i\pi/2)^2}{2i} = \frac{i\pi^2}{8}\,$

$\lim_{z\to -i} \frac{(Log (z))^2}{z-i} = \frac{(\log -i)^2}{-2i} = \frac{(-i\pi/2)^2}{-2i} = \frac{-i\pi^2}{8}\,$

Main Page : Complex Variables : Residues

CVR17

From Exampleproblems

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