  We study the totally asymmetric exclusion process (TASEP) on a finite
one-dimensional lattice with open boundaries, i.e., in contact with two
reservoirs at different potentials. The total (time-integrated) current through
the system is a random variable that scales linearly with time in the long time
limit. We give a parametric representation for the generating function of the
cumulants of the current, which is related to the large deviation function by
Laplace transform. This formula is valid for all system sizes and for all
values of the boundary coupling parameters.
