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Homework Help: Very easy and quick residue calculus question.

  1. Apr 27, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\oint_{\left|z\right|=3/2} \frac{e^{\frac{1}{z-1}}}{z} dz

    2. Relevant equations

    Using residue theorem, since there are two singularities withing the domain, evaluate residues at each singularity, and multiply by [tex]2\pi i[/tex]

    3. The attempt at a solution

    Here is the problem. The answer is [tex]2 \pi i[/tex] instead of [tex]2 \pi i + \frac{2\pi i}{e}[/tex]
    I don't understand why singularity at zero is ignored.
    FYI, if the domain it |z| = 1/2, the answer is 2pi*i/e.
  2. jcsd
  3. Apr 28, 2009 #2


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    Homework Helper

    They didn't ignore the singularity at 0. The singularity at z=1 is not what you think it is. Try putting w=z-1 and expanding the power series around w=0. You'll find an infinite number of 1/w terms. Sum them.
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