Calculating the residue of a complex function

  • #1
Robin04
260
16
Homework 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 occur 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?
 
Physics news on Phys.org
  • #2
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:
243694
 

Similar threads

Replies
3
Views
901
Replies
14
Views
3K
Replies
2
Views
1K
Replies
3
Views
1K
Replies
2
Views
2K
Replies
5
Views
1K
Replies
8
Views
2K
Back
Top