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Calculation residues at z=1 of order 4

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the residue of the following function at z=1

    2. Relevant equations
    f(z)=z^2/(z-1)^4(z-2)(z-3)


    3. The attempt at a solution
    lim z→2 z^2/(z-1)^4(z-3)=-4

    limz→3 z^2/(z-1)^4(z-2)=9/16

    at z=1 of order 4?? using formula 1/m-1! d/dz{(z-a)^m f(z)}
     
  2. jcsd
  3. Jan 30, 2013 #2
    Looks good, except that you need to take m-1 derivatives (why?).
     
  4. Jan 31, 2013 #3
    Thanks for your reply. Please can you solve it and show me, sir.
     
  5. Jan 31, 2013 #4
    I think it would be better if you did your homework yourself.

    Remember the definition of a residue -- there's an easier way to calculate it in this case, than differentiating the function three times. Expand it into a Laurent series around z=1 by multiplying a couple of geometric series together.
     
  6. Jan 31, 2013 #5
    You are correct. I will try this method.
     
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