Hermite Reduction and Creative Telescoping for Hyperexponential Functions

21 Jan 2013  ·  Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li, Guoce Xin ·

We present a reduction algorithm that simultaneously extends Hermite's reduction for rational functions and the Hermite-like reduction for hyperexponential functions. It yields a unique additive decomposition and allows to decide hyperexponential integrability. Based on this reduction algorithm, we design a new method to compute minimal telescopers for bivariate hyperexponential functions. One of its main features is that it can avoid the costly computation of certificates. Its implementation outperforms Maple's function DEtools[Zeilberger]. Moreover, we derive an order bound on minimal telescopers, which is more general and tighter than the known one.

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Symbolic Computation Combinatorics 33F10


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