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Math Help - complex analysis evaluation

  1. #1
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    complex analysis evaluation

    Evaluate \int_{C(0,e)}\frac{1-cosz}{(e^z-1)sinz}dz.
    This function has an isolated singularity at z=0.
    I tried this so many times, but still can't get it. Can I get some help please?
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  2. #2
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    Quote Originally Posted by dori1123 View Post
    Evaluate \int_{C(0,e)}\frac{1-cosz}{(e^z-1)sinz}dz.
    This function has an isolated singularity at z=0.
    I tried this so many times, but still can't get it. Can I get some help please?
    When z = 0, the function \frac{1-cosz}{(e^z-1)sinz} has a zero of order 2 in the numerator, and also a zero of order 2 in the denominator. Therefore this singularity is removable. There are no other singularities inside the contour, so the integral must be 0.
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