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Calculating a Residue

  1. Oct 18, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the residue of ##\frac{1-cos2z}{z^3}## at ##z=0##

    2. Relevant equations

    ##Res=\frac{1}{n!}\frac{d^n}{dz^n}[f(z)(z-z_0)^{n+1}]## Where the order of the pole is ##n+1##

    3. The attempt at a solution

    Differentiating ##(1-cos2z)z^3## twice, leaves me with zeros against every term giving me ##0## for a residue which is incorrect. Mathematica gives me 2 for a residue. Since ##z_0=0## I am only left multiplying the top function by z. I have no idea what I am missing here.

    What am I doing incorrectly?

    Thanks
    Chris
     
  2. jcsd
  3. Oct 18, 2014 #2

    mfb

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    Staff: Mentor

    What is the order of your pole?
     
  4. Oct 18, 2014 #3
    3rd order. I think I made a mistake that the 1/z^3 factor was not included in f(x). If I include it, it cancels out the z's outside of the cos2z function altogether. In that case, the part that gets differentiated and evaluated is just 1-cos2x.

    Thanks,
    Chris
     
  5. Oct 19, 2014 #4

    mfb

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    Staff: Mentor

    It is not. Don't forget the numerator.
     
  6. Oct 19, 2014 #5
    I got it. I having trouble with a different problem now. A new thread is in order for that one.

    Thanks,
    Chris
     
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