The inverse Compton (IC) scattering of relativistic electrons is one of themajor gamma-ray production mechanisms in different environments. Often thetarget photons for the IC scattering are dominated by black (or grey) bodyradiation. In this case, the precise treatment of the characteristics of ICradiation requires numerical integrations over the Planckian distribution.Formally, analytical integrations are also possible but they result in seriesof several special functions; this limits the efficiency of usage of theseexpressions. The aim of this work is the derivation of approximate analyticalpresentations which would provide adequate accuracy for the calculations of theenergy spectra of up-scattered radiation, the rate of electron energy losses,and the mean energy of emitted photons. Such formulae have been obtained bymerging the analytical asymptotic limits. The coefficients in these expressionsare calculated via the least square fitting of the results of numericalintegrations. The simple analytical presentations, obtained for both theisotropic and anisotropic target radiation fields, provide adequate (as good as$1\%$) accuracy for broad astrophysical applications.
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