Abstract: The molecular velocity distribution function and Boltzmann equation in the kinetic theory of gases are expanded in basis of the orthogonal Burnett functions. Hence it is shown that the calculation of Boltzmann collision matrix elements can be realized by computing the reduced integrals, Clebsch-Gordan coefficients and Brody-Moshinsky coefficients. Finally the computatimal mathod of high efficiency and numerical examples are given.

Key words: expansion of velocity distribution function in Burnett functions, Boltzmann collision matrix element, reduced integral, Clebsch-Gordan coefficient, Brody-Moshinsky coefficient