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