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Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms
Chen, Shaoshi1,2; Koutschan, Christoph3
2019-07-01
Source PublicationJOURNAL OF SYMBOLIC COMPUTATION
ISSN0747-7171
Volume93Pages:133-147
AbstractIn 1992, Wilf and Zeilberger conjectured that a hypergeometric term in several discrete and continuous variables is holonomic if and only if it is proper. Strictly speaking the conjecture does not hold, but it is true when reformulated properly: Payne proved a piecewise interpretation in 1997, and independently, Abramov and Petkovsek in 2002 proved a conjugate interpretation. Both results address the pure discrete case of the conjecture. In this paper we extend their work to hypergeometric terms in several discrete and continuous variables and prove the conjugate interpretation of the Wilf-Zeilberger conjecture in this mixed setting. (C) 2018 Elsevier Ltd. All rights reserved.
KeywordWilf-Zeilberger conjecture Hypergeometric term Properness Holonomic function D-finite function Ore-Sato theorem
DOI10.1016/j.jsc.2018.06.003
Language英语
Funding ProjectNSFC[11501552] ; NSFC[11688101] ; Frontier Key Project[QYZDJ-SSW-SYS022] ; Fund of the Youth Innovation Promotion Association, CAS ; Austrian Science Fund (FWF)[W1214] ; Austrian Science Fund (FWF)[P29467-N32] ; Fields Institute's 2015 Thematic Program on Computer Algebra in Toronto, Canada
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Theory & Methods ; Mathematics, Applied
WOS IDWOS:000457669100008
PublisherACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32401
Collection系统科学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Austrian Acad Sci, Johann Radon Inst Computat & Appl Math RICAM, Altenberger Str 69, A-4040 Linz, Austria
Recommended Citation
GB/T 7714
Chen, Shaoshi,Koutschan, Christoph. Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms[J]. JOURNAL OF SYMBOLIC COMPUTATION,2019,93:133-147.
APA Chen, Shaoshi,&Koutschan, Christoph.(2019).Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms.JOURNAL OF SYMBOLIC COMPUTATION,93,133-147.
MLA Chen, Shaoshi,et al."Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms".JOURNAL OF SYMBOLIC COMPUTATION 93(2019):133-147.
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