A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
Selected papers of the conference on Formal power series and algebraic combinatorics
Solving difference equations in finite terms
Journal of Symbolic Computation
An extension of Zeilberger's fast algorithm to general holonomic functions
Discrete Mathematics
A procedure for proving special function inequalities involving a discrete parameter
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Solving third order linear differential equations in terms of second order equations
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Liouvillian solutions of irreducible linear difference equations
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
When can we detect that a P-finite sequence is positive?
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Liouvillian solutions of irreducible second order linear difference equations
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Solving recurrence relations using local invariants
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
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In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence equations and a counterpart to existing results on differential equations. As motivation and application for this work, we discuss the problem of proving positivity of sequences given merely in terms of their defining recurrence relation. The main advantage of the present approach to earlier methods attacking the same problem is that our algorithm provides human-readable and verifiable, i.e., certified proofs.