  Following the success of the explicit construction of the multivariate
Krawtchouk polynomials as the birth and death polynomials, a formulation of
multivariate Hahn polynomials is proposed in the same style. The difference
equations specified by the birth/death rates have polynomial eigenvectors which
form the complete set of orthogonal multivariate Hahn polynomials. Although the
degree one eigenpolynomials are easy to derive, the complete hypergeometric
expressions are yet to be determined. In a certain limit, these Hahn
polynomials reduce to the multivariate Krawtchouk polynomials. The known
limiting procedures to the Meixner and Charlier polynomials produce trivial
results of the direct products of the single variable polynomials.
