An Extension of Zeilberger's Fast Algorithm to General Holonomic Functions

Frédéric Chyzak 1
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : We extend Zeilberger's fast algorithm for definite hypergeometric summation to non-hypergeometric holonomic sequences. The algorithm generalizes to the differential case and to q-calculus as well. Its theoretical justification is based on a description by linear operators and on the theory of holonomy.
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Frédéric Chyzak. An Extension of Zeilberger's Fast Algorithm to General Holonomic Functions. Discrete Mathematics, Elsevier, 2000, Formal power series and algebraic combinatorics (Vienna, 1997), 217 (1-3), pp.115-134. ⟨hal-01069235⟩

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