Semi-automated proof of supercongruences on partial sums of hypergeometric series

被引：23

作者：

Liu, Ji-Cai ^{[1
]}

机构：

[1] Wenzhou Univ, Dept Math, Wenzhou 325035, Peoples R China

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2019年 / 93卷

关键词：

Combinatorial identities; Supercongruences; Euler numbers; Harmonic numbers;

D O I：

10.1016/j.jsc.2018.06.004

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Using the software package sigma developed by Schneider, we automatically discover and prove some combinatorial identities involving harmonic numbers, from which we deduce some supercongruences on partial sums of hypergeometric series. These results confirm some conjectural generalizations of van Hamme's super congruences in some special cases, which were recently proposed by Guo (2017). (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：221 / 229

页数：9

共 12 条

[1]

Amdeberhan T., 2017, CONGRUENCE DOUBLE HA

[2]

[Anonymous], 1914, Quarterly Journal of Mathematics

[3] Some generalizations of a supercongruence of van Hamme [J].

Guo, Victor J. W. .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2017, 28 (12) :888-899

[4] HYPERGEOMETRIC EVALUATION IDENTITIES AND SUPERCONGRUENCES [J].

Long, Ling .

PACIFIC JOURNAL OF MATHEMATICS, 2011, 249 (02) :405-418

[5] A p-adic supercongruence conjecture of van Hamme [J].

Mortenson, Eric .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (12) :4321-4328

[6] GAUSSIAN HYPERGEOMETRIC SERIES AND SUPERCONGRUENCES [J].

Osburn, Robert ;

Schneider, Carsten .

MATHEMATICS OF COMPUTATION, 2009, 78 (265) :275-292

[7]

Schneider C., 2007, SEM LOTHAR COMBIN, V56, pB56b

[8] A REFINEMENT OF A CONGRUENCE RESULT BY VAN HAMME AND MORTENSON [J].

Sun, Zhi-Wei .

ILLINOIS JOURNAL OF MATHEMATICS, 2012, 56 (03) :967-979

[9] Super congruences and Euler numbers [J].

Sun Zhi-Wei .

SCIENCE CHINA-MATHEMATICS, 2011, 54 (12) :2509-2535

[10]

vanHamme L, 1997, LECT NOTES PURE APPL, V192, P223

← 1 2 →