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

2012/06/18 by Su Hu, Daeyeoul Kim, Hu, Su +3
Mathematics · #11B68 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1206.3826

openalex publication_date 2012/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Nörlund, Mordell, Carlitz, Agoh and Dilcher are special cases of the formulas given in this paper.

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