  In calculations of transport quantities, such as the electrical conductivity,
thermal conductivity, Seebeck, Peltier, Nernst, Ettingshausen, Righi-Leduc, or
Hall coefficients, sums over the Brillouin zone of wave-vector derivatives of
the dispersion relation commonly appear. When the self-energy depends only on
frequency, as in single-site dynamical mean-field theory, it is advantageous to
perform these sums once and for all. We show here that in the case of a
hypercubic lattice in d dimensions, the sums needed for any of the transport
coefficients can be expressed as integrals over powers of the energy weighted
by the energy-dependent non-interacting density of states. It is also shown
that our exact expressions for the transport functions can be obtained from
differential equations that follow from sum rules. By substituting the Bethe
lattice density of states, one can obtain the previously unknown transport
function for the electrical or thermal Hall coefficients and for the Nernst
coefficient of the Bethe lattice.
