第二类Stirling数与多重自然数方幂和

The Stirling Numbers of the Second Kind and Multiple Sums of Powers of Natural Numbers

本文讨论多重自然数方幂和的计算问题,应用多重和算符理论,得到这种和的包含第二类Stirling数的一般公式,并进一步证明了一系列含有第二类Stirling数的恒等式。

In this article, we discuss calculating problem for multiple sums of powers of natural numbers. We obtain general formulae involving stirling numbers of the second kind about the sums by making use of multiple sum symbol. Furthermore, we prove that several new identities involving stirling numbers of the second kind.