In this paper, we utilize exponential generating function to establish an identical formula describing the relationship between Bernoulli number and Stirling number of the second kind. 应用灰色系统理论对玻璃钢抽油杆的疲劳性能进行研究,建立了不同交变应力与对数循环次数之间的生成函数。
Several precise expressions involving Stirling numbers as coefficients for the power sum of natural numbers are given. Some new properties of the Stirling number and counting formulae of the Bernoulli number are obtained. 给出了自然数方幂和的包含Stirling数的几种精确表示式,得到了Stirling数的一些新的性质和Bernouli数的计数式。
A recurrence formula of the coefficient of the sum of natural numbers power and the calculating formula of Bernoulli Number(BN) 自然数幂和公式系数的递推公式和有关Bernoulli数的计算公式
The Relation Between Euler Number and Bernoulli Number(BN) and Their Application 欧拉数与伯努利数(BN)的关系及应用
The uniform expression for two kinds of Stirling number and Bernoulli number 两类Stirling数和Bernoulli数的统一表示