Solving difference equations whose coefficients are not transcendental

Authors:
Manuel Kauers
Affiliations:
Research Institute for Symbolic Computation, Johannes Kepler Universität, Altenberger Straβe 69, A-4040 Linz, Austria
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

We consider a large class of sequences which are defined by systems of (possibly nonlinear) difference equations. A procedure for recursively enumerating the algebraic dependencies of such sequences is presented. Also a procedure for solving linear difference equations with such sequences as coefficients is proposed. The methods are illustrated on some problems arising in the literature on special functions and combinatorial sequences.