Combinatorial Identities' Proof And Research On The Generalized Bernoulli And Euler Polynomials

Researching on combinatorial identities is the important part of combinatorialmathematics. In this paper, we mainly discuss some combinatorial identities which involve Fibonacci number and Lucas number. We also investigatethe 2D Bernoulli polynomials and generalized Euler polynomials by their generating functions and obtain several related conclusions.In the first part of the second chapter, by James Mc Laughlin's:《Combinatorialidentities deriving from the n-th power of a 2×2 matrix》and Sergio Falc(?)n, (?)ngel Plaza's: ((On k-Fibonacci sequences and polynomials and their derivatives)), the author gets some useful results. In the second part, the author uses some special matrices to obtain some combinatorial identities. In the third part, the author gives a few identities about matrices.In the third chapter, making use of the generating functions of Bernoulli polynomials, the author obtains some new results about the 2D Bernoulli polynomials.At last, by the generating functions of Euler polynomials, the author shows some new results about the generalized Euler polynomials.