Identities About The Special Combinatorial Polynomials Sequences

In this paper,we use the generating function and the coefficient method to study the high order Daehee polynomials,?-Daehee polynomials,Degenerate-Daehee polynomials and ?-Daehee polynomials.We derive a series of combinatorial identities.The main results are as follows:Chapter 1:We state the combinatorial mathematics background and the frontier dynamics of Daehee numbers,and we introduce the generating functions algorithms.Chapter 2:In this chapter,we investigate the generating function of higher-order Daehee polynomials.In particular,by means of the method of coefficients and gener-ating functions,we derive some properties of high order Daehee polynomials.Moreover,we establish some identities involving higher-order Daehee polynomials with generalized Cauchy numbers,Lah numbers,Stirling numbers of the first kind,unsigned Stirling num-bers of the first kind,generalized harmonic polynomials and the numbers P(r,n,k).Chapter 3:we give some properties of ?-Daehee polynomials.Meanwhile,we study the relations of ?-Daehee polynomials generating functions and the other sequences gen-erating functions,and we acquire some new identities involving ?-Daehee polynomials with other polynomials by using the generating function and the method of coefficients.Chapter 4:In this chapter,We study the generating functions of Degenerate-Daehee polynomial and ?-Daehee polynomial,and we generalize the properties of Degenerate-Daehee polynomial.Moreover,we derive a series of combinatorial identities associated with the Degenerate-Daehee polynomial and ?-Daehee polynomial.