Bernoulli number

In mathematics, the Bernoulli numbers are a sequence of rational numbers with deep connections in number theory. Although easy to calculate, the values of the Bernoulli numbers have no elementary description; they are closely related to the values of the Riemann zeta function at negative integers.In Europe, they were first studied by Jakob Bernoulli, after whom they were named by Abraham de Moivre, and independently discovered, perhaps earlier, by Seki Takakazu. They appear in the Taylor series expansion of the tangent and hyperbolic tangent functions, in the Euler-Maclaurin formula, and in expressions of certain values of the Riemann zeta function.
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