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Homework Help: Complex integral

  1. Jul 15, 2010 #1
    [tex]\int_{|z|=1}^{nothing } \frac{1}{z}e^{\frac{1}{z}}[/tex]
    in this integral there is no upper bound
    its around |z|=1

    there are no poles here
    only singular significant
    what to do here
    when calclating the residium
  2. jcsd
  3. Jul 15, 2010 #2

    Char. Limit

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    Gold Member

    I believe, and don't trust me on this, that it's asking you to calculate a path integral around the unit circle on the complex plane. There's no "upper bound" because the integral is describing a path, not just a starting point and an ending point. Incidentally, I believe that starting and ending points are the same.
  4. Jul 15, 2010 #3


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    Start by expanding [tex]\exp (1/z)[/tex] as a power series, multiply by 1/z and look for the z^{-1} term. That will be your residue.

  5. Jul 15, 2010 #4


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    Homework Helper

    A change of variables [itex]w = 1/z[/itex] will also do the trick.
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