Riordan Arrays Method、Combinatorial Sums And Its Asymptotic

In this paper, we use Riordan arrays method and generating functions method to study generalized Harmonic numbers Hn,k,r,(α,β) of properties, and its series of new combinations of identities, and gradually discusses the asymptotic of some sums contain-ing generalized Harmonic numbers Hn,k,r,(α,β) by methods of asymptotic enumeration methods. The main works are as follows:Chapter2:First, we introduce the concept of the generalized Harmonic numbers Hn,k,r,(α,β), using Riordan arrays and generating functions method research its property, we get some identities involving generalized Harmonic numbers Hn,k,r,(α,β) and special combinational numbers (such as:Two kinds of generalized Stirling numbers, two kinds of generalized Cauchy numbers, Cauchy polynomials, generalized Genocchi numbers).Chapter3:In this chapter, we apply the Laplace method, Darboux method, sin-gularity analysis and the method of generating function, obtain some asymptotic values involving generalized Harmonic numbers Hn,k,r,(α,β).