Bernoulli Polynomials And Power Sum Polynomials

Bernoulli numbers and polynomials have numerous important application innumber theory,combinatorics,and classical numerical analysis.The numbers of Genoc-chi,Stirling and others,as well as the tangent numbers,secant numbers,etc.,are closelyrelated to the Bernoulli numbers.In the seventeenth century,the mathematician Ja-cob Bernoulli discovered these special numbers when he studied the power sumpolynomials.Since then,the mathematicians have studied these special numbers in-volving various methods,and they have gotten many signi?cative results.In this paper,we studied the identities of bernoulli polynomials and power sumpolynomials involving the generating function,matrix and determinant. We alsoobtained some interesting identities,the contents can be summarized as follows:Chapter 1 is the introduction of the background of Bernoulli polynomials andpower sum polynomials, which gives the de?nitions and basic identities of Bernoullipolynomials and power sum polynomials.In chapter 2, we introduced Bernoulli polynomials and power sum polynomi-als involving determinant method,and gave a new approach to the generations ofBernoulli polynomials and power sum polynomials .In chapter 3, we introduced Bernoulli polynomials and power sum polynomialsinvolving matrix method,and got their algebraic properties.