A Generalized Apagodu-Zeilberger Algorithm

The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this algorithm which is applicable to arbitrary \(\partial\)-finite...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Chen, Shaoshi, Kauers, Manuel, Koutschan, Christoph
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 02.08.2014
Subjects:	Algorithms Operators (mathematics)
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this algorithm which is applicable to arbitrary \(\partial\)-finite functions. In analogy to the hypergeometric case, we introduce the notion of proper \(\partial\)-finite functions. We show that the algorithm always succeeds for these functions, and we give a tight a priori bound for the order of the output operator.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1402.2409