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Calculating the residue of a complex function

  • Thread starter Robin04
  • Start date
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?

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