Summary: On the Structure of Multivariate Hypergeometric Terms
S. A. Abramov \Lambda
Computer Center of
the Russian Academy of Science,
Vavilova 40, Moscow 117967, Russia
abramov@ccas.ru
M. PetkovŸsek y
Faculty of Mathematics and Physics,
University of Ljubljana,
Jadranska 19, SI­1000 Ljubljana, Slovenia
marko.petkovsek@uni­lj.si
Abstract
Wilf and Zeilberger conjectured in 1992 that a hypergeometric term is proper­hypergeometric if and
only if it is holonomic. We prove a slightly modified version of this conjecture in the case of several
discrete variables.
1 Introduction
Let K be a field of characteristic zero, n 1 ; : : : ; n d variables ranging over the nonnegative integers, and E i the
corresponding shift operators, acting on functions of n 1 ; : : : ; n d by E i f(n 1 ; : : : ; n i ; : : : ; n d ) = f(n 1 ; : : : ; n i +
1; : : : ; n d ). A K­valued function T (n 1 ; : : : ; n d ) is a hypergeometric term if there are rational functions F i 2
K(n 1 ; : : : ; n d ) (called the certificates of T ) such that E i T = F i T , for i = 1; : : : ; d. T (n 1 ; : : : ; n d ) is holonomic

Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences
Petkovsek, Marko - Department of Mathematics, University of Ljubljana

Collections: Computer Technologies and Information Sciences; Mathematics