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Please help me to solve this contour integral

  1. Apr 22, 2015 #1
    • New member warned about not using the homework template
    I want to solve this contour integral
    $$J(\omega)= \frac{1}{2\pi}\frac{\gamma_i\lambda^2}{(\lambda^2+(\omega_i-\Delta-\omega)^2)} $$
    $$N(\omega)=\frac{1}{e^{\frac{-\omega t}{T}}-1}$$

    $$\int_0^\infty J(\omega)N(\omega)$$



    there are three poles I don't know how I get rid of pole on zero (pole in N(w))
    would you please help me?
    Thanks
     
  2. jcsd
  3. Apr 25, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    Doesn't look like a convergent integral to me.

    For small ω,
    $$N(\omega)=\frac{1}{e^{\frac{-\omega t}{T}}-1} \approx \frac{-T}{\omega t}$$

    While J(ω) quickly approaches some constant.
     
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