 Bernoulli polynomials

Bernoulli polynomials are a sequence of classical orthogonal polynomials that arise in various areas of mathematics, particularly in number theory, combinatorics, and approximation theory. They are defined using the following generating function: \[ \frac{t}{e^t - 1} = \sum_{n=0}^{\infty} B_n \frac{t^n}{n!