q-Analogues of the (E.2) and (F.2) supercongruences of Van Hamme

被引：31
|
作者：
Guo, Victor J. W. [1 ]
机构：
[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China
来源：
RAMANUJAN JOURNAL | 2019年 / 49卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Ramanujan; Supercongruences; q-Analogues; Cyclotomic polynomials; q-WZ pair; CONGRUENCES;
D O I：
10.1007/s11139-018-0021-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Motivated by Zudilin's work, we give q-analogues of the Ramanujan-type supercongruences (E.2) and (F.2) of Van Hamme. Our proof utilizes the q-WZ method and properties of cyclotomic polynomials. Using the same q-WZ pair, we also give q-analogues of some similar supercongruences due to He and Swisher. Additionally, we propose several related conjectures on supercongruences or q-supercongruences.
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页码：531 / 544
页数：14
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