The method of creative telescoping
Journal of Symbolic Computation
Some questions concerning computer-generated proofs of a binomial double-sum identity
Journal of Symbolic Computation
Binomial identities: combinatorial and algorithmic aspects
Discrete Mathematics - Special issue: trends in discrete mathematics
Non-commmutative elimination in ore algebras proves multivariate identities
Journal of Symbolic Computation
An extension of Zeilberger's fast algorithm to general holonomic functions
Discrete Mathematics
Concrete Math
Rational normal forms and minimal decompositions of hypergeometric terms
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
On the structure of multivariate hypergeometric terms
Advances in Applied Mathematics
Hi-index | 7.29 |
We present a method to prove hypergeometric double summation identities. Given a hypergeometric term F(n, i, j), we aim to find a difference operator L = a0(n)N0 + a1(n)N1 +...+ ar(n)Nr and rational functions R1 (n, i, j), R2(n, i, j) such that LF = Δi(R1F)+Δj(R2F). Based on simple divisibility considerations, we show that the denominators of R1 and R2 must possess certain factors which can be computed from F(n, i, j). Using these factors as estimates, we may find the numerators of R1 and R2 by guessing the upper bounds of the degrees and solving systems of linear equations. Our method is valid for the Andrews-Paule identity, Carlitz's identities, the Apéry-Schmidt-Strehl identity, the Graham-Knuth-Patashnik identity, and the Petkovšek-Wilf-Zeilberger identity.