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Method of residues integration problem

  1. Sep 26, 2009 #1
    Hi all,

    I am trying to determine two Melnikov Integrals (after some manipulation) of the form:
    [tex]\int^{\infty}_{-\infty}cos(at)sech(bt) dt[/tex]
    and
    [tex]\int^{\infty}_{-\infty}cos(at)sech^{3}(bt) dt[/tex]

    The textbook I've been reading (Litchenberg & Libermann), says that the way to integrate similar problems is to use the method of residues. I have a superficial understanding of how that works, but every other time I've used the method of residue I've dealt with rationale functions so that I could find poles and then just apply apply the Cauchy integral formula at the isolated poles.

    Can anyone give me a kick-start on how to begin solving these 2 integrals by the method of residues ?
     
  2. jcsd
  3. Sep 27, 2009 #2
    Hi thrillhouse86,

    I'm not an expert on the "residue Issue" but here's my suggestion:

    1. Note that both integrands are even functions (at least I think so)
    2. Then complexify the cos-functions, i.e. use the e-function

    3. For the Residue Thm. you will need a special contour. I had posted a similar thread a month ago, I'd try with the same contour:

    http://www.mathhelpforum.com/math-h...metry/99385-contour-integral-residue-thm.html


    PS: post the answer when you have it, I'm interested too :)
     
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