In this paper, we find an expression for the density of the sum of two independent d-dimensional

Student t-random vectors X and Y with arbitrary degrees of freedom. As a

byproduct we also obtain an expression for the density of the sum N+X, where N is normal

and X is an independent Student t-vector. In both cases the density is given as an infinite

series $\sum_{n=0}^\infty c_nf_n$

where f_n is a sequence of probability densities on R^d and c_n is a sequence of positive

numbers of sum 1, i.e. the distribution of a non-negative integer-valued random variable

C, which turns out to be infinitely divisible for d=1 and d=2.  When d=1 and the

degrees of freedom of the Student variables are equal, we recover an old result of Ruben.