Lecture Notes, Bernoulli Polynomials and Applications

Abstract

In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications to these polynomials are presented, including a unified approach to the asymptotic expansion of the error term in many numerical quadrature formulae, and many new and sharp inequalities, that bound some trigonometric sums.