A generalized method of equivalent photon scattering suitable for the
problem of emission from a continuously accelerated charge was success
fully applied to demonstrate that synchrotron radiation is fundamental
ly an inverse-Compton effect. Here we present an improved derivation o
f the classical emissivity and explain in more detail some of the impo
rtant steps in the quantum derivation. Moreover, we extend this method
to derive the emissivity of a charge in arbitrary relativistic motion
, including quantum recoil corrections.