2011/08/23 by Shaoshi Chen, Manuel Kauers, Chen, Shaoshi +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #FOS: Computer and information sciences #Numerical Methods and Algorithms #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC
paper · pdf · doi:10.48550/arxiv.1108.4508
openalex publication_date 2011/08/23 · arxiv created 2012/01/31 · arxiv updated 2012/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.