FORMULATION OF SOME GAUSSIAN INTEGRALS OVER R(N) VIA GENERATING-FUNCTIONS

This paper deals with the analytic formulation of the integrals over R (n) with the weight function exp(x(T)Cx) where the integrand is the pr oduct of quadratic forms x(T) A(j)x, j = 1,...,p, for arbitrary n x n symmetric matrices A(j). The technique is based on generating function s. First some functions are defined to generate these integrals for th e special case A(j) = A(j) = A...A, and then practical formulas for th e general case are derived.