Extended Thermodynamics is a very important theory: for example, it predicts
hyperbolicity, finite speeds of propagation waves as well as continuous
dependence on initial data. Therefore, it constitutes a significative
improvement of ordinary thermodynamics. Here its methods are applied to the
case of an arbitrary, but fixed, number of moments. The kinetic approach has
already been developed in literature; then, the macroscopic approach is here
considered and the constitutive functions appearing in the balance equations
are determined up to whatever order with respect to thermodynamical
equilibrium. The results of the kinetic approach are a particular case of the
present ones
