The Integrals of Products of Bernoulli Polynomials

Abstract

In this thesis, the concept of the integrals of products of Bernoulli polynomials will be introduced. ”The integrals containing the product of more than two Bernoulli polynomials do not appear to lead to simple results.” Let r be any positive integer. In this paper, we provide the explicit formulas for the integrals of the products of r Bernoulli polynomials. Many authors results in this direction, including Norlund, Mordell, Carlitz, Agoh and Dilcher are special cases of the formulas given in this paper. The study provides propositions and examples in support of this study results.The study obtained some consequences of integrals of products of certain cubic, quadratic and more Bernoulli polynomials.