The Bernoulli numbers

Bernoulli numbers are a sequence of special numbers that appear in advanced mathematics, particularly in calculus and number theory. They help express the sum of powers of integers and appear in formulas related to the calculus of infinite series and the expansion of functions like the tangent and hyperbolic tangent. Think of them as a set of mathematical tools that simplify complex calculations involving sums and series. Although they originate from abstract concepts, Bernoulli numbers have practical applications in fields like physics, engineering, and computer science, especially when dealing with series expansions and numerical analysis.