How can I get Mathematica to simplify the following expressions, with
Element[n,Integers], n > 0, and
FullSimplify simplifies the above expressions.
Context for this question: I am frequently implementing new Bayesian statistical models that automated tools such as OpenBUGS can't handle, and so I need to work out expressions for various full conditional probability densities from the (large and complex) joint probability distribution. These expressions need to be simplified as much as possible, for computational efficiency. I want to see if I can use Mathematica to do this more quickly and reliably, instead of always doing it by hand. One of my needs is to be able to manipulate and/or simplify various linear algebra expressions that often arise; the dimensionality of these matrices and vectors is itself a parameter of the problem, not a fixed number.