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Contour Integral problem

  1. Jun 11, 2007 #1
    I'm trying to find

    [tex]
    \int_{-\infty}^{\infty} \frac{exp(ax)}{cosh(x)} dx
    [/tex]

    where 0<a<1 and x is taken to be real. I'm doing this by contour integration using a contour with corners +- R, +- R + i(pi), and I'm getting an imaginary answer which is

    [tex]\frac{2i\pi}{sin (a \pi)}[/tex].

    I'm thinking this is a problem because my original integral was completely real. Can I just take the real part of my answer, and say the integral = 0 ? That doesn't seem to make any sense, I've drawn a graph of the function and it doesn't look like it's integral should be zero! I'm fairly sure my answer to the contour integral is correct!
     
    Last edited: Jun 11, 2007
  2. jcsd
  3. Jun 11, 2007 #2
    P.s - is there a guide to using tex on physics forums somewhere? Then I could format the above properly!
     
  4. Jun 11, 2007 #3

    malawi_glenn

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    Math & Science Tutorials --> Introducing LaTeX Math Typesetting
     
  5. Jun 11, 2007 #4
    Ah thanks, I knew there was one somewhere!
     
  6. Jun 11, 2007 #5
    Oops, stupid me! The answer is

    [tex]
    \frac{\pi}{cos(\frac{a\pi}{2})}
    [/tex]

    I didn't work out the phase shift the function takes on along the top line of the path properly!
     
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