Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms

doi:10.1016/j.jsc.2018.06.003

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	Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms
	Chen, Shaoshi1,2 ; Koutschan, Christoph 3
	2019-07-01
发表期刊	JOURNAL OF SYMBOLIC COMPUTATION
ISSN	0747-7171
卷号	93 页码:133-147
摘要	In 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.
关键词	Wilf-Zeilberger conjecture Hypergeometric term Properness Holonomic function D-finite function Ore-Sato theorem
DOI	10.1016/j.jsc.2018.06.003
语种	英语
资助项目	NSFC[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研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000457669100008
出版者	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32401
专题	系统科学研究所
通讯作者	Chen, Shaoshi
作者单位	1.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
推荐引用方式 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.