Bernoulli number

In mathematics, the Bernoulli numbers are a series 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, up to a factor, the values of the Riemann zeta function at negative integers.

Related Topics:
Mathematics - Series - Rational number - Number theory - Riemann zeta function

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They were first studied by Jakob Bernoulli, after whom they were named by Abraham de Moivre. 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.

Related Topics:
Jakob Bernoulli - Abraham de Moivre - Taylor series - Tangent - Hyperbolic tangent - Euler-Maclaurin formula

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Curiously, in note G of Ada Byron's notes on the analytical engine from 1842 an algorithm for computer-generated Bernoulli numbers was described for the first time. This distinguishes the Bernoulli numbers as being the subject of one of the first computer programs ever.

Related Topics:
Ada Byron's notes on the analytical engine - 1842 - Algorithm

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