Bernoulli numbers were defined by Jacob Bernoulli in connection with evaluating sums of the form ∑i^k.
The sequence B0, B1, B2, ... can be generated using the formula
x/(e^x - 1) =∑(Bn x^n)/n!
though various different notations are used for them.
The first few are: B0 = 1 , B1 = -1/2 , B2 = 1/6 , B4 = -1/30 , B6 = 1/42 , ...
They occur in many diverse areas of mathematics including the series expansions of tan(x), Fermat's Last theorem†, etc.
†Fermat's last theorem states that if n > 2 then the equation x^n + y^n = z^n has no positive integer solutions.
(Please note that in the second summation it is B sub-n times x^n, etc.)
It looks like I'll have to start a separate web page just to be able to publish mathematics symbols--this text editor for the blog is rather limited.
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