On the structure of multivariate hypergeometric terms

In 1992, Wilf and Zeilberger conjectured that every multivariate holonomic hypergeometric term is a proper term (i.e., a product of a polynomial, exponentials, and factorials of linear forms with integer coefficients). We show that every multivariate hypergeometric term is equivalent to the product of a nonzero rational function and a nontrivial proper term. Then we use this structure theorem to prove a slightly modified version of the above conjecture, namely that every multivariate holonomic hypergeometric term is equivalent to a nontrivial proper term. (This is joint work with Sergeď A. Abramov.)