A q-analogue of the (L.2) supercongruence of Van Hamme

被引：16

作者：

Guo, Victor J. W. ^{[1
]}

机构：

[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 466卷 / 01期

基金：

中国国家自然科学基金;

关键词：

q-Binomial coefficients; q-WZ method; Cyclotomic polynomials; q-Camma function; Jackson's (6)phi(5) summation; CONJECTURES; CONGRUENCES; SUMS;

D O I：

10.1016/j.jmaa.2018.06.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The (L.2) supercongruence of Van Hamme was proved by Swisher recently. In this paper we provide a conjectural q-analogue of the (L.2) supercongruence of Van Hamme and prove a weaker form of it by using the q-WZ method. In the same way, we prove a complete q-analogue of the following congruence Sigma(n)(k=0)(6k + 1)((2k)(k))(3) (-512)(n-k) (math) 0 (mod 4(2n + 1)((2n)(n))), which was conjectured by Z.-W. Sun and confirmed by B. He. We also provide a conjectural q-analogue of another congruence proved by Swisher. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：749 / 761

页数：13

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