Telescoping method and congruences for double sums

被引：11

作者：

Mu, Yan-Ping ^{[1
]}

Sun, Zhi-Wei ^{[2
]}

机构：

[1] Tianjin Univ Technol, Coll Sci, Tianjin 300384, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2018年 / 14卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Telescoping method; double sum; combinatorial sequence; congruence; PROOF; SUN; COMBINATORIAL; CONJECTURES;

D O I：

10.1142/S1793042118500100

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In recent years, Sun proposed several sophisticated conjectures on congruences for finite sums with terms involving combinatorial sequences such as central trinomial coefficients, Domb numbers and Franel numbers. These sums are double summations of hypergeometric terms. Using the telescoping method and certain mathematical software packages, we transform such a double summation into a single sum. With this new approach, we confirm several open conjectures of Sun.

引用

页码：143 / 165

页数：23