高阶Bernoulli数与Stirling数的几个恒等式

Several Identities Between Higher Order Bernoulli Number and Two Types of Stirling Numbers

利用第一、二类高阶Bernoulli数和二类Stirling数S1(n,k),S2(n,k)的定义.研究了二类高阶Bernoulli数母函数的幂级数展开,揭示了二类高阶Bernoulli数之间以及与第一类Stirling数S1(n,k)、第二类Stirling数S2(n,k)之间的内在联系,得到了几个关于二类高阶Bernoulli数和第一类Stirling数S1(n,k)、第二类Stirling数S2(n,k)之间有趣的恒等式.

The author studied the power series expansion of the generating function of two types of higher order Bernoulli numbers by using their definitions and the definitions of the two types of Stirling numbers, S1 （n, k） and S2 （n ,k）; and obtained some inherent relationships between the two types of higher Bernoulli nubers and the two types of Stirling numbers. We also got some interesting identities among the first, the second types of higher Bernoulli numbers, the first and the second types of Stirling numbers.