摘要
对于复数a1,a2,…,am(m≥1)及整数h1,h2,…,hm,l,n,m,用sln^m及Tln^m分别表示如下两个m次多重和:∑l≤h1≤h2≤…am^hm及∑h1+h2+…hm=n h1,h2,…hm≥l且,m·l≤n首先通过计算探究、猜想分别归纳证明了sln^m(■i,ai≠1的情形)及Tl,n^m(ai≠aj,Ai≠j的情形)的公式;并利用极限运算推导出sl,n^m及Tl,n^m在一般情形下公式.然后通过修改和号下h1,h2,…hm的限制条件,给出了进一步的推广;并将a1,…,am作为变量进行赋值计算,得到了一些推论.最后通过对和式的项a1h2…am^hm进行修改(如添加系数hi等),从而得出sl,n^m及Tl,n^m的求导公式.
Let a1,a2,…,am(m ≥ 1) be plural numbers and h1,h2,…,hm,l,n,m, be integers. Denoted by sl,n^m and Tl,n^m the following two multiple sums of m times, respectively:∑l≤h1≤h2≤…am^hm and ∑h1+h2+…hm=n h1,h2,·a2^h2…am^hm By computational inquiry, conjecture and induction, the case of Ai,ai≠1 when discussing the formula of Ai,ai≠1 is discussed.The general cases of the formula for sl,n^m and Tl,n^m can be deduced by taking the corresponding limits. By modifying the restrictions of h1,h2,…,hm under the sum, further promotion is given respectively. Moreover, by assigning particular values of the variables a1,…,am, some corollaries are obtained. Finally, by modifying the terms a1^h2…am^hm of the sum(e.g.adding the coefficient, etc.), the derivations of sl,n^m and Tl,n^m are obtained respectively.
作者
邢婷文
黄宇飞
XING Ting-wen;HUANG Yu-fei(Guangzhou Civil Aviation College, Guangzhou Guangdong 510403)
出处
《广东技术师范学院学报》
2019年第3期15-21,共7页
Journal of Guangdong Polytechnic Normal University
基金
国家自然科学基金项目(No.11501139)
国家自然科学基金校级重点培育项目(No.18X0429)
关键词
多重和
有序划分
极限
赋值
求导
multiple sum
ordered division
limit
assignment
derivation
