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Bernoulli number


A number of the type defined by Jakob Bernouilli in connection with evaluating sums of the form ∑ ik. The sequence B0, B1, B2, ... can be generated using the formula

x/(ex - 1) = ∑(Bn xn)/n!


though various different notations are used for them. The first few Bernoulli numbers are: B0 = 1, B1 = -1/2, B2 = 1/6 , B4 = -1/30 , B6 = 1/42 , ... They crop up in many diverse areas of mathematics including the series expansions of tan x and Fermat's last theorem.


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