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arXiv · 1605.05082

Efficient Algorithms for Mixed Creative Telescoping

Alin Bostan·Louis Dumont·Bruno Salvy
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Abstract

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. We address the mixed continuous-discrete case, and focus on the integration of bivariate hypergeometric-hyperexponential terms. We design 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.

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Alin Bostan, Louis Dumont, Bruno Salvy. 2016-05-17. Efficient Algorithms for Mixed Creative Telescoping. https://doi.org/10.1145/2930889.2930907

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