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Poles or Removable Singularities

  1. Sep 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Determine the location and nature of singularities in the finite z plane of the follow function and apply Cauchy Integral Formula


    2. Relevant equations

    g(z) =

    sin 2z
    -------
    z^15


    3. The attempt at a solution

    I know there is a pole of order 14 at z = o

    but i'm a bit confuse when i apply the Cauchy Integral Formula

    {sin 2z } / z
    ------------
    ```z^15

    = 2 pi j { d ^13 f(z) / dz}
    ```````-----------------
    `````````````13!

    = 2 pi j / 13! <-- correct ?

    many thanks! :)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 13, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    You'd better take another careful look at the Cauchy integral theorem. I don't know where you got the '13' and what is that f(z) that you are taking the 13th derivative of? Why did it just disappear?
     
  4. Sep 13, 2009 #3
    hi,

    i think i make a mistake...

    sin 2z
    -------
    z^15

    since sin 2z is analytic, f(z) = sin 2 z

    2 pi j { d^14 f(z) / dz }

    = 2 pi j { 0 }

    = 0 <-- correct ?
     
  5. Sep 13, 2009 #4

    Dick

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    Science Advisor
    Homework Helper

    That's better. You are missing a 1/14! But it doesn't matter because the derivative is zero anyway.
     
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