Hermite Reduction and Creative Telescoping for Hyperexponential Functions

Abstract

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.

8 pages

References in corpus (3)

• Proof of Ira Gessel's Lattice Path Conjecture
• Proof of George Andrews's and David Robbins's q-TSPP Conjecture
• Enumeration of bilaterally symmetric 3-noncrossing partitions

Cited by in corpus (6)

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• Parallel Telescoping and Parameterized Picard--Vessiot Theory
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• Reduction-Based Creative Telescoping for Fuchsian D-finite Functions
• Additive Decompositions in Primitive Extensions
• Reduction-Based Creative Telescoping for Algebraic Functions