[en] In this study methods are introduced that relate to elementary but fairly unknown functional relationships between power sums and coefficients of polynomials. These relationships, also called Waring functions, are derived. They are then used in other applications to give explicit expressions for the generalized Laguerre polynomials in terms of determinant functions. The properties of polynomials generated by a wide class of generating functions are investigated. These relationships are also used to obtain explicit forms for the cumulants of a distribution in terms of its moments. It is pointed out that cumulants (or moments, for that matter) do not determine a distribution function. An application of this is made on the theory of microinstabilities and electromagnetic waves in plasmas