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

Frédéric Chyzak (1)

1 ALGO - Algorithms

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.

Nous étendons l'algorithme rapide de Zeilberger pour la sommation hypergéométrique définie au cas des suites holonomes non hypergéométriques. L'algorithme se généralise aussi au cas différentiel et du q-calcul. Sa justification théorique se fonde sur une description par opérateurs linéaires et sur la théorie de l'holonomie.

Mots clés: $\partial$-finite functions; holonomic functions; symbolic integration; symbolic summation; Zeilberger's algorithm

Domaines: Calcul formel [cs.SC]; Combinatoire [math.CO]

Frédéric Chyzak. An Extension of Zeilberger's Fast Algorithm to General Holonomic Functions. Discrete Mathematics, 2000, Formal power series and algebraic combinatorics (Vienna, 1997), 217 (1-3), pp.115-134. ⟨hal-01069235⟩