关于差分算子Δ的一些算子恒等式及其应用

Some identities related to difference operator and their applications

利用发生函数得到了关于差分算子Δ的一些算子恒等式,并且讨论了它们在组合恒等式中的应用;给出了关于Bernoulli多项式、Bernoulli数、Stirling数等特殊组合数的一些递推关系和组合恒等式.

In this paper,some operator identities concerning difference operator are given in terms of generating function,and the applications are discussed in combinatorial identities.We also obtain some recurrence relations and identities about the special combinatorial numbers,such as Bernoulli polynomials,Bernoulli numbers,Stirling numbers and so on.