  The Landau distribution as well as its first and second momenta are well
suited for describing the energy loss of charged particles traversing a thin
layer of matter. At present, just rational approximations and asymptotic
expressions for these functions were obtained. In this paper we present a
direct calculation of the integral representation of these functions obtaining
perturbative and nonperturvative solutions expressed in terms of fast
convergent series. We also provide a simple numerical algorithm which allows to
control speed and precision of the results. The testing runs have provided, in
reasonable computing times, correct results up to 13-14 significant digits on
the density and distribution functions and 9-10 on the first and second
momenta. If necessary, this accuracy could be improved by adding more
coefficients to the algorithm.
