  The Sersic model has become the standard to parametrize the surface
brightness distribution of early-type galaxies and bulges of spiral galaxies. A
major problem is that the deprojection of the Sersic surface brightness profile
to a luminosity density cannot be executed analytically for general values of
the Sersic index. Mazure & Capelato (2002) used the Mathematica computer
package to derive an expression of the Sersic luminosity density in terms of
the Meijer G function for integer values of the Sersic index. We generalize
this work using analytical means and use Mellin integral transforms to derive
an exact, analytical expression for the luminosity density in terms of the Fox
H function for all values of the Sersic index. We derive simplified expressions
for the luminosity density, cumulative luminosity and gravitational potential
in terms of the Meijer G function for all rational values of the Sersic index
and we investigate their asymptotic behaviour at small and large radii. As
implementations of the Meijer G function are nowadays available both in
symbolic computer algebra packages and as high-performance computing code, our
results open up the possibility to calculate the density of the Sersic models
to arbitrary precision.
