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Help with a troublesome integral

  1. Mar 8, 2015 #1
    We have the integral:
    [tex]I(s)=\int_{0}^{\infty}\log\left(1+\frac{s^{2}}{4\pi^{2}} \log^{2}(1+ix)\right ) e^{-2\pi nx}dx[/tex]
    Where [itex] s [/itex] is a complex parameter, and [itex] n [/itex] is a positive integer.
    Things i tried:
    Set [itex] \log(1+ix)=y [/itex], so that
    [tex] I(s)=-i\int_{c}\log\left(1+\frac{s^{2}}{4\pi^{2}}y^{2} \right )\exp\left(2\pi in e^{y} \right )e^{y}dy [/tex]
    Where the path [itex] c [/itex] has to be defined !!
  2. jcsd
  3. Mar 12, 2015 #2
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