关联Bernoulli数与Stirling数、Eulerian数的恒等式  

Identities Involving Bernoulli Numbers,Stirling Numbers and Eulerian Numbers

作　　者：唐军强[1] TANG Junqiang(Basic Course Department of Jiaozuo College,Jiaozuo 454000,Henan,China)

机构地区：[1]焦作大学基础部,河南焦作454000

出　　处：《山西师范大学学报（自然科学版）》2024年第4期1-5,共5页Journal of Shanxi Normal University(Natural Science Edition)

摘　　要：自然数的幂和公式可以用Bernoulli数、两类Stirling数和Eulerian数分别表示.这些常数之间一定存在着某种关联,将后两者公式中关于n的组合数用第一类Stirling数的升阶乘定义展开,将所得结果与雅各布·伯努利公式中关于n的各幂次的系数进行比较,得到了关联Bernoulli数和两类Stirling数及Eulerian数的恒等式.Sums of powers of integers can be expressed in specific expressions with Bernoulli numbers,two kinds of Stirling numbers and Eulerian numbers.By expanding the combinatorial in the latter two formulae with the first kind Stirling numbers and comparing the coefficients of the powers of n,some identities are obtained involving the Bernoulli numbers,Stirling numbers and Eulerian numbers.

关 键 词：自然数方幂和 BERNOULLI数 第一类STIRLING数 第二类STIRLING数 Eulerian数 

分 类 号：O156[理学—数学]