An algorithm for computing mixed sums of products of Bernoulli polynomials and Euler polynomials. (January 2015) - Feng, Lei; Wang, Weiping
Abstract: 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 − l Euler polynomials, which are of the form T n, k λ ( y ; l, k − l ) : = ∑ j 1 + ⋯ + j k = n j 1, …, j k ⩾ 0 ∏ i = 1 k λ i j i ( n j 1, …, j k ) ∏ p = 1 l B j p ( x p ) ∏ q = l + 1 k E j q ( x q ), where λ = ( λ 1, …, λ k ), and λ 1, …, λ k are nonzero rational numbers. Moreover, some special sums are presented as examples.