Section: New Results

Efficient algorithms for mixed creative telescoping

Creative telescoping is a powerful computer algebra paradigm –initiated by Doron Zeilberger in the 90’s– for dealing with definite integrals and sums with parameters. Alin Bostan and Louis Dumont, together with Bruno Salvy (Inria and ENS Lyon), have addressed in [12] the mixed continuous–discrete case, and have focussed on the integration of bivariate hypergeometric-hyperexponential terms. We have designed a new creative telescoping algorithm operating on this class of inputs, based on a Hermite-like reduction procedure. The new algorithm has two nice features: it is efficient and it delivers, for a suitable representation of the input, a minimal-order telescoper. Its analysis reveals tight bounds on the sizes of the telescoper it produces.