Some identities for the product of two Bernoulli and Euler polynomials

Let n be the space of polynomials of degree less than or equal to n. In this article, using the Bernoulli basis {B 0 (x), . . . , B n (x)} for n consisting of Bernoulli polynomials, we investigate some new and interesting identities and formulae for the product of two Bernoulli and Euler polynomials like Carlitz did.