A Note on Explicit Formulas for Bernoulli Polynomials

Abstract

For r 2 { 1; - 1; 1 2 } , we prove several explicit formulas for the n-th Bernoulli polynomial Bn (x), in which Bn (x) is equal to a linear combination of the polynomials xn, (x + r)n ; : : : ; (x + rm)n, where m is any fixed positive integer greater than or equal to n