Non-commutative Elimination in Ore Algebras Proves Multivariate Identities

F. Chyzak, B. Salvy
1998 Journal of symbolic computation  
Many identities involving special functions can be proved using the theory of @nite or holonomic sequences and functions. This theory applies in particular to numerous combinatorial identities. This work presents a theoretical and algorithmic approach to the multivariate case, together with an implementation. Preuve d'identit es multivari ees par elimination non-commutative dans des alg ebres de Ore R esum e De nombreuses identit es faisant intervenir des fonctions sp eciales peuventêtre prouv
more » ... es par la th eorie des suites et fonctions @nies ou holonomes. Cette th eorie s'applique en particulier a nombre d'identit es combinatoires. Ce travail pr esente une approche th eorique et algorithmique au cas multivari e, ainsi qu'une implantation. Abstract. Many identities involving special functions can be proved using the theory of @-nite or holonomic sequences and functions. This theory applies in particular to numerous combinatorial identities. This work presents a theoretical and algorithmic approach to the multivariate case, together with an implementation.
doi:10.1006/jsco.1998.0207 fatcat:vqifqgc52fe2vgd7xasmqpswxu