Explicit formulae for sums of products of Bernoulli polynomials, including poly-Bernoulli polynomials

摘要

We study sums of products of Bernoulli polynomials, including poly- Bernoulli polynomials. As a main result, for any positive integer m, explicit expressions of sums of m products are given. This result extends that of the first author, as well as the famous Euler formula about sums of two products of Bernoulli numbers.