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

Su Hu, Daeyeoul Kim, Min-Soo Kim

Published 2012-06-18, updated 2013-09-02Version 2

In 1958, L.J. Mordell provided the 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 authors' results in this direction, including N\"orlund, Mordell, Carlitz, Agoh and Dilcher are special cases of the formulas given in this paper.