  The analytical generalization of the classical dynamical friction formula
(derived under the assumption that all the field particles have the same mass)
to the case in which the masses of the field particles are distributed with a
mass spectrum is presented. Two extreme cases are considered: in the first,
energy equipartition is assumed, in the second all the field particles have the
same (Maxwellian) velocity distribution. Three different mass spectra are
studied in detail, namely the exponential, discrete (two components), and
power-law cases. It is found that the dynamical friction deceleration can be
significantly stronger than in the equivalent classical case, with the largest
differences (up to a factor of 10 or more in extreme cases) arising for test
particle velocities comparable to the mass-averaged velocity dispersion of the
field particles. The present results are relevant to our understanding of the
dynamical evolution of globular clusters, in particular in the modelization of
mass segregation and sedimentation of Blue Straggler stars and Neutron stars,
and for the study of binary black holes in galactic nuclei.
