Tensor expansions of the angular particle distribution

A relation between the class of symmetric spherical tensors and even-odd polynomials is established. The expansions of the scattering operator of photons or neutrons in a series of symmetric spherical tensors are obtained. Among them there are expansions that have a higher speed of uniform convergence in comparison with expansions in the spherical functions and Legendre polynomials. It is shown that in problems of radiation transport in matter with predominant forward or backward scattering, it is advisable to use expansions in the system of Chebyshev polynomials and tensors.