General properties of collision integral kernels of the nonlinear Boltzmann equation

We consider general properties of kernels of the inverse collision integral, as well as kernels of integral operators appearing in the expansion of the collision integral in spherical harmonics. The recurrent relations between kernels obtained earlier are generalized to the case of interaction of particles with different masses. It is shown that the obtained properties ensure additive invariance of the number of particles, energy, and momentum.