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Math Help - complex integral..

  1. #1
    MHF Contributor
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    complex integral..

    \int_{|z|=1}^{nothing } \frac{1}{z}e^{\frac{1}{z}}
    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
    ??
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Champaign, Illinois
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    Quote Originally Posted by transgalactic View Post
    \int_{|z|=1}^{nothing } \frac{1}{z}e^{\frac{1}{z}}
    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
    ??
     \frac1ze^{1/z}=\frac1z\left(1+\frac1z+\frac{1}{2z^2}+\cdots\ri  ght) = \frac1z+\frac{1}{z^2}+\frac{1}{2z^3}+\cdots

    Thus  \text{Res}_{z=0}\left(\frac1ze^{1/z}\right)=1
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