On the expectation of a ratio of quadratic forms in normal variables

Using relatively recent results from multivariate distribution theory, the expectation of a ratio of quadratic forms in normal variables is obtained. Infinite series expressions involving the invariant polynomials of matrix argument are derived. Convergence of the solution depends upon the choice made for two positive, but upper bounded, constants. The same methodology is used to obtain the expectation of multiple ratios of quadratic forms in normal variables.