Generalized Bernoulli-Euler Polynomials And Their Research

The Bernoulli polynomials and Euler polynomials have important applications in combinatorics,number theory,theory of approximation,computational method,and so on.In this article,we study mainly the following chapters:In the first chapter,we introduce simply definitions of the generalization of Bernoulli polynomials and Euler polynomials,and some related knowledge.In the second chapter,we give several symmetric identities on the generalized Apostol-Bernoulli polynomials by applying the generating functions. These results extend some known identities.In the third chapter,we prove two general symmetric identities involving the generalized degenerate Bernoulli polynomials and sums of generalized falling factorials by applying their generating functions,these results extend some known identities,and give an relationship of the generalized degenerate Bernoulli polynomials.In the fourth chapter,we give some recurrence relations and closed formulas of generalized Bernoulli polynomials B_n(x;a,b,c),generalized Euler polynomials E_k(x;a,b,c).