论文标题
整数和超谐音数的力量总和
Sums of powers of integers and hyperharmonic numbers
论文作者
论文摘要
在本文中，我们得出了一个涉及超声谐波数字和第二类的stirling数字的第一个$ n $正整数（$ s_k（n）$的权力之和）的公式。然后，使用对超谐音数的明确表示，我们将此公式推广到任意算术进程的幂之和。此外，我们用第二种的超声多项式和stirling数字来表达Bernoulli多项式。最后，我们将$ s_k（n）$的获得的公式扩展到$ n $的负值。
In this paper, we derive a formula for the sums of powers of the first $n$ positive integers, $S_k(n)$, that involves the hyperharmonic numbers and the Stirling numbers of the second kind. Then, using an explicit representation for the hyperharmonic numbers, we generalize this formula to the sums of powers of an arbitrary arithmetic progression. Moreover, we express the Bernoulli polynomials in terms of hyperharmonic polynomials and Stirling numbers of the second kind. Finally, we extend the obtained formula for $S_k(n)$ to negative values of $n$.
