Exact Formulas for Additional Terms in Some Important Series Expansions.

An investigation into previous work dealing with various series expansions about the normal distribution revealed little in the way of exact formulas for the terms in these expansions. In fact, for the univariate case, no more than the first terms in any of the expansions have been published, with the exception of the Cornish-Fisher expansion, for which the first six terms are given in the Cornish-Fisher 1960 paper. In order to use the expansions in other problems, the authors first needed the exact formulas for some higher order terms. The paper is devoted to the presentation of these new terms and to the techniques used to obtain them. Exact formulas for, at least, the first eight terms in four important expansions are given. Author