Relativistic extended thermodynamics is a very interesting theory which is widely appreciated. here its methods are applied to ultrarelativistic gases, and an arbitrary, but fixed number of moments is considered. 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.
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