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Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms

文献类型：期刊论文

作者Chen, Shaoshi1,2; Koutschan, Christoph3
刊名JOURNAL OF SYMBOLIC COMPUTATION
出版日期2019-07-01
卷号93页码:133-147
ISSN号0747-7171
关键词Wilf-Zeilberger conjecture Hypergeometric term Properness Holonomic function D-finite function Ore-Sato theorem
DOI10.1016/j.jsc.2018.06.003
英文摘要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.
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
语种英语
出版者ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
WOS记录号WOS:000457669100008
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/32400]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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