k-free recurrences of double hypergeometric terms

AbstractIn their elegant and powerful approaches to automatically proving hypergeometric identities, Wilf and Zeilberger have taken a truly insightful advantage of holonomic hypergeometric terms. Moreover, they have shown that all proper hypergeometric terms are holonomic, and they have conjectured that the converse should hold as well. In this paper, we introduce a canonical representation of double hypergeometric terms, which we call the standard representation. We show that in the case of double hypergeometric terms, the Wilf–Zeilberger conjecture is true. We note that Abramov and Petkovšek [Preprint Series 39 (748) (2001)] has independently obtained the same result