A fast algorithm for proving terminating hypergeometric identities
Discrete Mathematics
The method of differentiating under the integral sign
Journal of Symbolic Computation
The method of creative telescoping
Journal of Symbolic Computation
A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
Solving systems of strict polynomial inequalities
Journal of Symbolic Computation
An extension of Zeilberger's fast algorithm to general holonomic functions
Discrete Mathematics
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Picard--Vessiot extensions for linear functional systems
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Computing the rank and a small nullspace basis of a polynomial matrix
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
The automatic construction of pure recurrence relations
ACM SIGSAM Bulletin
Differential equations for algebraic functions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
A non-holonomic systems approach to special function identities
Proceedings of the 2009 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
Order-degree curves for hypergeometric creative telescoping
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Desingularization explains order-degree curves for ore operators
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Hermite reduction and creative telescoping for hyperexponential functions
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We analyze the differential equations produced by the method of creative telescoping applied to a hyperexponential term in two variables. We show that equations of low order have high degree, and that higher order equations have lower degree. More precisely, we derive degree bounding formulas which allow to estimate the degree of the output equations from creative telescoping as a function of the order. As an application, we show how the knowledge of these formulas can be used to improve, at least in principle, the performance of creative telescoping implementations, and we deduce bounds on the asymptotic complexity of creative telescoping for hyperexponential terms.