# 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
-
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?

Related Calculus and Beyond Homework News on Phys.org

#### 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:

"Calculating the residue of a complex function"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving