An Algorithm for the calculation of non-isotropic collision integral matrix elements of the non-linear Boltzmann equation by the use of recurrence relations

An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we believe are known, are starting ones. The procedure is valid for any interaction law and any mass ratio of the colliding particles.