The lensing properties of the Einasto profile
  In recent high resolution N-body CDM simulations, it has been had found that
nonsingular three-parameter models, e.g. the Einasto profile has a better
performance better than the singular two-parameter models, e.g. the Navarro,
Frenk and White in the fitting of a wide range of dark matter halos. A problem
with this profile is that the surface mass density is non-analytical for
general values of the Einasto index. Therefore, its other lensing properties
have the same problem. We obtain an exact analytical expression for the surface
mass density of the Einasto profile in terms of the Fox H-function for all
values of the Einasto index. With the idea of facilitate the use of the Einasto
profile in lensing studies, we calculate the surface mass density, deflection
angle, lens equation, deflection potential, magnification, shear and critical
curves of the Einasto profile in terms of the Meijer G-function for all
rational values of the Einasto index. The Meijer G-function have been
implemented in several commercial and open-source computer algebra systems,
thus the use of the lensing properties of the Einasto profile in strong and
weak lensing studies is straighforward. We also compare the S\'ersic and
Einasto surface mass densities profiles and found differences between them.
This implies that the lensing properties are not equal for both profiles.
