Finding more divisibility properties of binomial sums via the WZ method

被引：0
作者：
Brian Y. Sun
机构：
[1] Xinjiang University,Department of Mathematics and System Science
来源：
The Ramanujan Journal | 2019年 / 48卷
关键词：
Hypergeometric function; Divisibility; Binomial coefficients; Binomial sums; The WZ method; 11A05; 11A07; 05A10; 11B65;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In recent years, we have witnessed numerous new results on divisibility properties concerning binomial sums. Many conjectures and results were proposed by Z.-W. Sun. Some of these conjectures were proved by himself, and also by some scholars such as V.J.W. Guo, G.S. Mao, B. He, and Y.P. Mu. Motivated by their work, we study the WZ method and its applications to prove divisibility properties of binomial sums. In this paper, we propose a method which can be used to explore more such divisibility properties. Additionally, we give some generalized divisibility properties which can imply those divisibility properties established by Z.-W. Sun and B. He.
引用
收藏
页码：173 / 189
页数：16
相关论文
共 25 条
  • [1] Bober JW(2009)Factorial ratios, hypergeometric series, and a family of step functions J. Lond. Math. Soc. 79 422-444
  • [2] Calkin NJ(1998)Factors of sums of powers of binomial coefficients Acta Arith. 86 17-26
  • [3] Chen YG(2016)On some congruences of certain binomial sums Ramanujan J. 40 237-244
  • [4] Xie XY(1978)Decision procedure for indefinite hypergeometric summation Proc. Natl. Acad. Sci. USA 75 40-42
  • [5] He B(2014)Some divisibility properties of binomial and $q$-binomial coefficients J. Number Theory 135 167-184
  • [6] Gosper RW(2016)Proof of Sun’s conjectures on integer-valued polynomials J. Math. Anal. Appl. 444 182-191
  • [7] Guo VJW(2007)Factors of alternating sums of products of binomial and $q$-binomial coefficients Acta Arith. 127 17-31
  • [8] Krattenthaler C(2010)Factors of binomial sums from the Catalan triangle J. Number Theory. 130 172-186
  • [9] Guo VJW(2015)On the divisibility properties of certain binomial sums J. Number Theory. 147 133-140
  • [10] Guo VJW(2016)On the divisibility properties concerning sums of binomial coefficients Ramanujan J. 43 313-326
123