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Homework Help: Integral of complex function

  1. Apr 14, 2012 #1
    I'm looking for a function which has two simple poles, and whose integral along the positive real axis from 0 to infinity is equal to its integral along the positive imaginary axis.

    I don't really know where to start. I'm looking at functions which have symmetry with respect to real/imaginary axes, i.e. if x is real, then f(x) = f(ix), which led me to consider things like f(z) = 1/(z^4) or f(z) = 1/(z^5), but those don't have simple poles and their integrals from 0 to infinity on the axes don't exist since they blow up at the origin. Any help is appreciated!
  2. jcsd
  3. Apr 14, 2012 #2


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    Try locating your poles symmetrically with respect to the two axes. Like along the line x=y.
  4. Apr 15, 2012 #3
    After trying your suggestion with z1 = 1 + i, z2 = -1 - i, and f(z) = 1/((z - z1)*(z-z2)), I ended up with the integral over the imaginary axis being the negative of that over the real axis, so I located my poles on the line y = -x instead, and that solved the problem.
    Thanks for the help!
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