In arithmetic, this idea refers to a selected relationship inside energy collection expansions of trigonometric capabilities, significantly the tangent perform. It includes the Bernoulli numbers and offers 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 thought presents a beneficial instrument for understanding the interaction between seemingly disparate mathematical ideas. Traditionally, its discovery supplied an important hyperlink in creating the speculation of particular capabilities and contributed considerably to developments in quantity principle and evaluation. It continues to be related in trendy arithmetic, showing in areas like complicated evaluation and the examine of particular values of L-functions.
