Non-Commutative Elimination in Ore Algebras Proves Multivariate Identities

@article{Chyzak1998NonCommutativeEI,
  title={Non-Commutative Elimination in Ore Algebras Proves Multivariate Identities},
  author={Fr{\'e}d{\'e}ric Chyzak and Bruno Salvy},
  journal={J. Symb. Comput.},
  year={1998},
  volume={26},
  pages={187-227}
}
Many computations involving special functions, combinatorial sequences or theirq-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 ?-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. 

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