# Calculating the residue of a complex function

#### Robin04

Problem Statement
Calculate the residue of the following function at its singularities: $f(z)=\frac{e^{i\omega z}\lambda z}{(z^2+\lambda^2)^2}$
Relevant Equations
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The singularities occure at $z = \pm i\lambda$. As $\frac{d}{dz}(z^2+\lambda^2)^2|_{z=\pm i\lambda}=0$, these singularities aren't first order and the residues cannot be calculated with differentiating the denominator and evaluating it at the singularities. What is the general method to determine the Laurent series?

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#### fresh_42

Mentor
2018 Award
Wikipedia has your example, https://de.wikipedia.org/wiki/Residuensatz, but I'm too lazy to translate and adapt it to your exact situation. I suggest to use the translation functionality in chrome. It worked quite well here: ### Want to reply to this thread?

"Calculating the residue of a complex function"

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