Probabilistic Method And Combinatorial Identities

In this thesis,we apply probabilistic method and generating functions of combina-torial sequences to derive the moment representations of combinatorial sequences which are related to Daehee,Changhee,Changhee-Genocchi numbers and polynomials.In addi-tion,we give identities related to the combinatorial sequences mentioned above and other classic combinatorial sequences.1.Background of combinatorics,domestic and overseas research status about Daehee,Changhee,Changhe-Genocchi numbers and polynomials and basic knowledge of proba-bility theory are introduced.2.The moment representations of higher-order twisted Daehee numbers and poly-nomials,and two kinds of higher-order Changhee polynomials are derived by applying higher-order moment formulae and characteristic functions of uniform distribution and Gamma distribution.Then we give the combinatorial identities related to Daehee num-bers,Cauchy numbers of the second and derangement numbers;as well as higher-order Daehee numbers and Stirling numbers of the first kind.3.Probabilistic method,integral,Weibull distribution and Rayleigh distribution are applyed to derive the moment representations of higher-order Changhee-Genocchi num-bers and polynomials,and modified Changhee-Genocchi polynomials.Besides,we get new identities of higher-order Changhee-Genocchi polynomials,Daehee numbers,Changhee numbers and Stirling numbers of the first kind.At last,we present the relationship between Modified-Changhee-Genocchi polynomials and Changhee polynomials.