用无穷矩阵方程求解第二类Stirling数表示的自然数幂和  

Power sum of natural numbers expressed by Stirling numbers of second kind by solving infinite matrix equation

作　　者：唐军强[1] 艾英[1] TANG Junqiang;AI Ying(Department of Basic Courses,Jiaozuo College,Jiaozuo 454000,China)

机构地区：[1]焦作大学基础部,河南焦作454000

出　　处：《高师理科学刊》2023年第1期20-23,共4页Journal of Science of Teachers＇College and University

基　　金：河南省自然科学基金项目(222300420579)。

摘　　要：讨论了4个用第二类Stirling数表示的自然数的幂和公式.利用升阶乘和降阶乘的定义式,得到关于各阶幂和的递推关系,用求解无穷矩阵方程的方法给出用第二类Stirling数表示的幂和公式,并证明了它们之间的等价性.Four power sum formulas of natural numbers expressed by Stirling numbers of second kind are discussed.By means of the definition of rising factorial and falling factorial,the recursive relation of the power sum of each order is obtained,and the formula of the power sum expressed by the Stirling numbers of second kind is given by means of solving the infinite matrix equation,and the equivalence between them is proved.

关 键 词：无穷矩阵方程 自然数 幂和 第一类STIRLING数 第二类STIRLING数 

分 类 号：O156[理学—数学]