How to obtain higher-order multivariate Hermite expansion of Maxwell-Boltzmann distribution by using Taylor expansion? (Q2375804)

The Maxwell-Boltzmann distribution is expressed in terms of the Gauss distribution and is used in kinetic theory of gases to describe the equilibrium state of the molecular velocity with respect to the macroscopic velocity and temperature. This paper shows how can be obtained, for practical purposes, the multivariate Hermite expansion of the Maxwell-Boltzmann distribution up to any order. For doing this, the authors introduce a new operator and a compact tensorial notation that generalizes the one due to \textit{H. Grad} [Commun. Pure Appl. Math. 2, 325--330 (1949; Zbl 0036.04102)]. It is also shown how make a proper selection of variables in the Taylor expansion to give the same result as that obtained using the Hermite representation.