Calculation of density for the multivariate Poisson distribution (Q1098478)

It is known that a density function of Poisson distribution p(k,l) in the bivariate case satisfies two main recurrence relations (r.r.). Conversely, if we need to calculate the density using the r.r.'s, not using the direct calculation, one of the relations would be meaningless except in the usage of its reduced relations. It is also known that in the trivariate case, the density function satisfies three main r.r.'s. But to calculate the density from r.r.'s we need one of the relations and their reduced relations. The author has obtained the r.r.'s for the multivariate case and shown that only one of the n main r.r.'s and their reduced relations are used to calculate the density function.