An algorithm for computing mixed sums of products of Bernoulli polynomials and Euler polynomials

In this paper, by the methods of partial fraction decomposition and generating function, we give an algorithm for computing mixed sums of products of l   Bernoulli polynomials and k−lk−l Euler polynomials, which are of the formTn,kλ(y;l,k−l):=∑j1+⋯+jk=nj1,…,jk⩾0∏i=1kλiji(nj1,…,jk)∏p=1lBjp(xp)∏q=l+1kEjq(xq), where λ=(λ1,…,λk)λ=(λ1,…,λk), and λ1,…,λkλ1,…,λk are nonzero rational numbers. Moreover, some special sums are presented as examples.