Series Expansions for Quadratic Forms in Normal Variables

A differential operator is defined and applied to the gamma density function. By formal mathematical manipulation the resulting function can be identified with linear combinations of independent gamma variates and central and noncentral definite quadratic forms in independent normal variates. Laguerre series expansions in which the choice of parameters is of a general nature are given. These Laguerre series and chi-square, power and Edgeworth series are then compared in the effectiveness in evaluating the distribution function of quadratic forms.