一种新颖的第二类Stirling数公式证明

A new way to prove the second Stirling formula

现有的Stirling数公式证明过程繁杂且难以掌握,文中根据满射函数定义和排列组合基础理论,结合逐步淘汰原理给出了第二类Stirling数公式的一个既简单又易接受的证明过程。该证明过程不仅给出了第二类Stirling数公式的来源,而且从满射函数特性方面回答了其正确性。

The current methods to prove the Stirling formula are complicated. Here we present a new way to simplify the proving process for the Second Stirling Formula based on the surjective function definition, permutation and combination and the gradual phase-out principle. Not only the source of Stirling formula is revealed but the correctness is proven from the aspect of surjective function.