Non-commutative Elimination in Ore Algebras Proves Multivariate Identities

Frédéric Chyzak (1) , Bruno Salvy (1)

1 ALGORITHMS - Algorithms

Many computations involving special functions, combinatorial sequences or their $q$-analogues can be performed using linear operators and simple arguments on the dimension of related vector spaces. In this article, we develop a theory of~$\partial$-finite sequences and functions which provides a unified framework to express algorithms for computing sums and integrals and for the proof or discovery of multivariate identities. This approach is vindicated by an implementation.

Domaines: Calcul formel [cs.SC]

Frédéric Chyzak, Bruno Salvy. Non-commutative Elimination in Ore Algebras Proves Multivariate Identities. Journal of Symbolic Computation, 1998, 26 (2), pp.187-227. ⟨hal-01069833⟩