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Complex residue integral

  1. Jun 7, 2009 #1
    1. The problem statement, all variables and given/known data

    i need to calculate the inverse Mellin transform [tex] \oint ds {x^{-s}}\frac{1}{\Gamma(s)cos(\pi s/2)} [/tex]

    2. Relevant equations

    I can use Cauchy's integral theorem,

    3. The attempt at a solution

    i know that Gamma function has poles at -1,-2,-3, .... and that the cosine term has poles at every integer the question is how could i expand Gamma function and cosine term in order to obtain the complex integral.
  2. jcsd
  3. Jun 7, 2009 #2


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    Science Advisor

    What path is the integral taken over and, in particular, what integers are contained inside that path?
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