On the integral of the product of four and more Bernoulli polynomials

Abstract

In 1958, L.J. Mordell provided a formula for the integral of the product of two Bernoulli polynomials. He also remarked: "The integrals containing the product of more than two Bernoulli polynomials do not appear to lead to simple results." In this paper, we provide explicit formulas for the integral of the product of r Bernoulli polynomials, where r is any positive integer. Many results in this direction, including those by Norlund, Mordell, Carlitz, Agoh, and Dilcher, are special cases of the formulas given in this paper.