Hello, I am trying to understand the details of the full treatment of synchrotron radiation. I am using Rybicki & Lightman (1979), along with the more detailed treatment given by Longair (1992). For instance, in Longair, chapter 18 (p.240 in the Second Edition), I see that the radiated energy per unit solid angle per unit angular frequency is evaluated at the retarded time, and a change of variable is operated: going from time t to retarded time t', with t' = t - R(t')/c. and R(t') = r - n.r_o(t') (n is the unit vector along the direction joining the particle to the point where the radiation is measured, and r_o(t') is the position vector of the particle at t') In the exponential factor exp(i w t) coming from the Fourier transform, the change of variable leads to exp(i w ( t'+R(t')/c )). It is then said that r_o(t') << r (I agree with that, as the source is at a quite large distance), and finally the exponential factor becomes exp(i w ( t' - n.r_o(t')/c )) I can't understand how to obtain this last result. Probably a first order expansion could be applied somehow but I don't see where and how. Please, could someone give me an explanation for that? Thank you so much in advance for your help. Best regards.