Indefinite sums of rational functions
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Greatest factorial factorization and symbolic summation
Journal of Symbolic Computation
A criterion for the applicability of Zeilberger's algorithm to rational functions
Discrete Mathematics
A direct algorithm to construct the minimal Z-pairs for rational functions
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Computing the rank and a small nullspace basis of a polynomial matrix
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Differential equations for algebraic functions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Complexity of creative telescoping for bivariate rational functions
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Trading order for degree in creative telescoping
Journal of Symbolic Computation
Desingularization explains order-degree curves for ore operators
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators. Our bounds are expressed as curves in the (r, d)-plane which assign to every order r a bound on the degree d of the telescopers. These curves are hyperbolas, which reflect the phenomenon that higher order telescopers tend to have lower degree, and vice versa.