On the integral of products of higher-order Bernoulli and Euler polynomials

Abstract

In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same method, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials. Moreover, we establish a connection between these results and the generalized Dedekind sums and Hardy--Berndt sums.