Moments and cumulants of the multivariate real and complex Gaussian distributions

This paper considers the problem of higher order moments and cumulants for the multivariate normal distribution. An older result of this problem is criticized as far as its practical use. We give an analytical form and a much simpler proof of the central moments and we provide a sequential updating calculation for the general moments. We also consider the central higher order moments of the complex-valued multivariate normal distribution. Key Words: function. Normal distribution; high order moments; characteristic 1.