# Please help me to solve this contour integral

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1. Apr 22, 2015

### Ana2015

• 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. Apr 25, 2015

### 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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