Development of the nonlinear moment method for solving the Boltzmann equation in axially symmetric case

A new computation algorithm is advanced being an essential part of the moment method to solve the Boltzmann equation. The treatment is based on an invariance principle of the collision integral concerning a choice of the basic system of functions over which the distribution function expansion is accomplished. The relations between the matrix elements of an interaction matrix are systematically studied in details. The recurrent relationships between the matrix elements are deduced for the axially symmetric case.