Deduction of a symmetric tensor formulation of the PN method for the linear transport equation

In the paper, a new formulation of the classic spherical harmonics method for the study of the linear transport equation is proposed. The method makes use of an expansion of the angular flux in terms of symmetric spherical harmonics and therefore it does not present privileged directions in its formulation. In the paper, the symmetric spherical harmonics are introduced in a simple way and their properties are presented in order to deduce the new equations for the moments of the flux.