On the (K.2) supercongruence of Van Hamme

被引：44

作者：

Osburn, Robert ^{[1
,3
]}

Zudilin, Wadim ^{[2
,3
]}

机构：

[1] Univ Coll Dublin, Sch Math Sci, Dublin 4, Ireland

[2] Univ Newcastle, Sch Math & Phys Sci, Callaghan, NSW 2308, Australia

[3] Max Planck Inst Math, D-53111 Bonn, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 433卷 / 01期

基金：

美国国家科学基金会;

关键词：

Supercongruence; Ramanujan; Wilf-Zeilberger pair;

D O I：

10.1016/j.jmaa.2015.08.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the last remaining case of the original 13 Ramanujan-type supercongruence conjectures due to Van Hamme from 1997. The proof utilizes classical congruences and a WZ pair due to Guillera. Additionally, we mention some future directions concerning this type of supercongruence. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：706 / 711

页数：6

共 16 条

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