  Three types of integral representations for the cumulative distribution
functions of convolutions of non-central p-variate gamma distributions are
given by integration of elementary complex functions over the p-cube Cp =
(-pi,pi]x...x(-pi,pi]. In particular, the joint distribution of the diagonal
elements of a generalized quadratic form XAX' with n independent normally
distributed column vectors in X is obtained. For a single p-variate gamma
distribution function (p-1)-variate integrals over Cp-1 are derived. The
integrals are numerically more favourable than integrals obtained from the
Fourier or laplace inversion formula.
