The method of creative telescoping
Journal of Symbolic Computation
Desingularization of linear difference operators with polynomial coefficients
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Applicability of Zeilberger's algorithm to hypergeometric terms
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
When does Zeilberger's algorithm succeed?
Advances in Applied Mathematics
Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
On the summation of P-recursive sequences
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Dimensions of solution spaces of H-systems
Journal of Symbolic Computation
Power series and linear difference equations
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Analytic solutions of linear difference equations, formal series, and bottom summation
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Solving recurrence relations using local invariants
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
A definite summation of hypergeometric terms of special kind
Programming and Computing Software
Linear differential and difference systems: EGδ- and EGσ- eliminations
Programming and Computing Software
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We consider linear difference equations with polynomial coefficients over C and their solutions in the form of sequences indexed by the integers (sequential solutions). We investigate the C-linear space of subanalytic solutions, i.e., those sequential solutions that are the restrictions to Z of some analytic solutions of the original equation. It is shown that this space coincides with the space of the restrictions to Z of entire solutions and that the dimension of this space is equal to the order of the original equation. We also consider d-dimensional (d=1) hypergeometric sequences, i.e., sequential and subanalytic solutions of consistent systems of first-order difference equations for a single unknown function. We show that the dimension of the space of subanalytic solutions is always at most 1, and that this dimension may be equal to 0 for some systems (although the dimension of the space of all sequential solutions is always positive). Subanalytic solutions have applications in computer algebra. We show that some implementations of certain well-known summation algorithms in existing computer algebra systems work correctly when the input sequence is a subanalytic solution of an equation or a system, but can give incorrect results for some sequential solutions.