In arithmetic, this idea refers to a selected relationship inside energy collection expansions of trigonometric features, notably the tangent perform. It entails the Bernoulli numbers and gives a connection between these numbers and particular values of the Riemann zeta perform. As an example, it permits one to precise /6 because the infinite sum of the reciprocals of the squares of pure numbers.
This mathematical concept affords a precious instrument for understanding the interaction between seemingly disparate mathematical ideas. Traditionally, its discovery offered a vital hyperlink in growing the speculation of particular features and contributed considerably to developments in quantity principle and evaluation. It continues to be related in trendy arithmetic, showing in areas like advanced evaluation and the examine of particular values of L-functions.
