Application Of Riordan Array And Generating Function In Combinatorial Identity

Combinatorial identity is widely utilized in discrete mathematics,algebra and prob-ability theory.It requires special skills to prove the identical equations.There are flexible ways to prove them.The paper utilizes Riordan array and generating functions to study high order Changhee polynomial,generalized Apostol Changhee polynomial and gener-alized Apostol Daehee polynomial in combinatorial enumeration.It also obtains combi-natorial identities related to other classical combinatorial sequences.Primary steps are stated as follows:1.We briefly introduce the research background of combinatorics and the research status at home and abroad.Moreover,we also introduce the Riordan array and the generating functions algorithms.2.We mainly use the classical method of Riordan arrays and generating function to establish some new identities involving two kinds of higher-order Changhee numbers and polynomials,which are related to Stirling number,Lah number and Harmonic number.3.we establish several elementary properties and provide some explict relationships with the generalized Apostol Changhee polynomials and the generalized Apostol Daehee polynomials,and derive some new identities involving the generalized Apostol Changhee polynomials and other special polynomials.