The method of creative telescoping
Journal of Symbolic Computation
D'Alembertian solutions of linear differential and difference equations
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Greatest factorial factorization and symbolic summation
Journal of Symbolic Computation
A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Discrete Mathematics
Journal of the ACM (JACM)
On solutions of linear ordinary difference equations in their coefficient field
Journal of Symbolic Computation
Computer proofs for polynomial identities in arbitrary many variables
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Degree Bounds to Find Polynomial Solutions of Parameterized Linear Difference Equations in ΠΣ-Fields
Applicable Algebra in Engineering, Communication and Computing
Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Finding telescopers with minimal depth for indefinite nested sum and product expressions
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Symbolic summation with radical expressions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
A refined difference field theory for symbolic summation
Journal of Symbolic Computation
Reasoning with Generic Cases in the Arithmetic of Abstract Matrices
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Computing with abstract matrix structures
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Summation in finite terms using sage
ACM Communications in Computer Algebra
Integration of unspecified functions and families of iterated integrals
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We consider symbolic sums which contain subexpressions representing unspecified sequences. Existing symbolic summation technology is extended to sums of this kind. We show how this can be applied in the systematic search for general summation identities. Both, results about the non-existence of identities of a certain form, and examples of general families of identities which we have discovered automatically are included in the paper.