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Homework Help: Residue Calculus

  1. Mar 12, 2010 #1
    [tex]\int[/tex]u^-B sin(u) du, 0<B<2 integrating from 0 to infinity. What is really throwing me off is the condition, I'm not sure why it's there or really what to do with it. Can I just solve this the same way I'd solve sin(x)/x?
     
  2. jcsd
  3. Mar 12, 2010 #2
    Had I not something strange like u^B, I'd solve the problem as follows.
    [tex]\frac{1}{u^B}[/tex](u-[tex]\frac{z^3}{6}[/tex]+...)
    I'd then look for C_-1, the residue. Then it's just a simple matter of 2pi(i)*res. But again, having u^B does not allow me to do this. There is a systematic formula I can apply to find the residue, but it does not allow me to eliminate i.
     
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