Analytical properties of Einasto dark matter haloes
  Recent high-resolution N-body CDM simulations indicate that nonsingular
three-parameter models such as the Einasto profile perform better than the
singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a
wide range of dark matter haloes. While many of the basic properties of the
Einasto profile have been discussed in previous studies, a number of analytical
properties are still not investigated. In particular, a general analytical
formula for the surface density, an important quantity that defines the lensing
properties of a dark matter halo, is still lacking to date. To this aim, we
used a Mellin integral transform formalism to derive a closed expression for
the Einasto surface density and related properties in terms of the Fox H and
Meijer G functions, which can be written as series expansions. This enables
arbitrary-precision calculations of the surface density and the lensing
properties of realistic dark matter halo models. Furthermore, we compared the
S\'ersic and Einasto surface mass densities and found differences between them,
which implies that the lensing properties for both profiles differ.
