The Gram-Charlier series of type A is discussed in terms of deviants which are related to moments in a way similar to the way Hermite polynomials are related to the powers. Distribution functions are also expressed in terms of the mode and moments (cumulants or deviants), which are useful expansions when the distributions are approximately normal. It is shown that such expansions as well as the Gram-Charlier series are valid asymptotically for discrete distributions defined on the semiinfinite interval [0, ∞].