Lorentzian line shape profile

Carnot

Hi

I hope some one can help me with this one:

I have a Lorentzian line profile

L(√_L) = 1 / ((√_L - √₀ )^2 + ([itex]\Gamma[/itex]²/4))

for v = 0.

For v [itex]\neq[/itex] 0 I have

[itex]\int[/itex](1 / ((√_L - √₀ - kv_z)^2 + ([itex]\Gamma[/itex]²/4)) * g(v_z) dv_z)

I suppose the factor g(v_z) dv_z is a velocity factor, but how do I calculate it or where can I read more about the Lorentzian line shape profile with this velocity factor. I can only find descriptions about the Lorentzian without this velocity factor.

Hope someone can give me a hint or an explanation to this as I do not understand it.

Thanks :-)