  In this paper, we propose a general way of computing expectation values in
the zero-range process, using an exact form of the partition function. As an
example, we provide the fundamental diagram (the flux-density plot) of the
asymmetric exclusion process corresponding to the zero-range process.We express
the partition function for the steady state by the Lauricella hypergeometric
function, and thereby have two exact fundamental diagrams each for the parallel
and random sequential update rules. Meanwhile, from the viewpoint of
equilibrium statistical mechanics, we work within the canonical ensemble but
the result obtained is certainly in agreement with previous works done in the
grand canonical ensemble.
