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Applicability of Zeilberger’s Algorithm to Rational Functions

In: Formal Power Series and Algebraic Combinatorics

Author

Listed:
  • S. A. Abramov

    (Computer Center of the Russian Academy of Science)

  • H. Q. Le

    (University of Waterloo, Symbolic Computation Group)

Abstract

We consider the applicability (or terminating condition) of the well-known Zeilberger’s algorithm and give the complete solution to this problem for the case where the original hypergeometric term F(n, k) is a rational function. We specify a class of identities $$\sum\nolimits_{k = 0}^n {F\left( {n,k} \right) = 0} $$ $$F\left( {n,k} \right) \in \mathbb{C}\left( {n,k} \right)$$ that cannot be proven by Zeilberger’s algorithm. Additionally we give examples showing that the set of hypergeometric terms for which Zeilberger’s algorithm terminates is a proper subset of the set of all hypergeometric terms, but a super-set of the set of proper terms.

Suggested Citation

  • S. A. Abramov & H. Q. Le, 2000. "Applicability of Zeilberger’s Algorithm to Rational Functions," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 91-102, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_8
    DOI: 10.1007/978-3-662-04166-6_8
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