Canonical Representations of Hypergeometric Terms

Sergei A. Abramov Marko Petkovsek

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors. Using this normal form we construct a minimal representation of hypergeometric terms in one variable. Our main result concerns hypergeometric terms in two variables: every such term is the quotient of a proper term by a polynomial. This may open the way to prove a conjecture of Wilf and Zeilberger which states that a hypergeometric term is proper if and only if it is holonomic.

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