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Laurent series / residual theorem

  1. Aug 17, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img243.imageshack.us/img243/4339/69855059.jpg [Broken]

    2. Relevant equations
    i've heard that the solution requires the use of the exponential taylor series:
    http://img31.imageshack.us/img31/6163/37267605.jpg [Broken]

    3. The attempt at a solution

    i know that the first step is to convert cos(1/z) into it's complex number form which is:
    cos(1/z) = 0.5 (e^(i/z) + e^(-i/z))
    I've tried manipulating 1/z and z^5 into the exp.taylor series but it gets messy (might be doing it wrong). any ideas would be great!
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 17, 2009 #2
    I would say you don't have to convert the cosine to exponential form if you already know the Maclauren series of cosine.
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