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We analyze the differential equations produced by the method of creativetelescoping applied to a hyperexponential term in two variables. We show thatequations of low order have high degree, and that higher order equations havelower degree. More precisely, we derive degree bounding formulas which allow toestimate the degree of the output equations from creative telescoping as afunction of the order. As an application, we show how the knowledge of theseformulas can be used to improve, at least in principle, the performance ofcreative telescoping implementations, and we deduce bounds on the asymptoticcomplexity of creative telescoping for hyperexponential terms.

Trading Order for Degree in Creative Telescoping