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Singularity and residue theorem

  1. Jul 23, 2014 #1
    Hello.
    Can someone check if I got the answer right?

    Find the singularity and the residue.

    ##f(z)=\frac{e^{-2z}}{(z+1)^2}##

    My solution:

    ##f(z)=\frac{e^{-2z}}{(z+1)^2}##
    $$Resf(z)_{|z=-1|}=\lim_{{z}\to{-1}}\frac{d}{dz}((z+1)^2\frac{e^{-2z}}{(z+1)^2})$$

    $$\lim_{{z}\to{-1}}-2e^{-2z}=-2e^{2}$$
     

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    Last edited: Jul 23, 2014
  2. jcsd
  3. Jul 23, 2014 #2

    vanhees71

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    Science Advisor
    2016 Award

    A check with Mathematica tells me that your solution is correct :-).
     
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