The spectral shape of radiation due to inverse Compton scattering is analyzed in the Thomson and the Klein-Nishina regime for electron distributions with exponential cutoff. We derive analytical, asymptotic expressions for the spectrum close to the maximum cutoff region. We consider monoenergetic, Planckian, and synchrotron photons as target photon fields. These approximations provide a direct link between the distribution of parent electrons and the upscattered spectrum at the cutoff region.
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