Redirected from Bernoulli numbers
Sometimes the lower-case bn is used in order to distinguish these from the Bell numbers.
The first eleven Bernoulli numbers are listed below.
n | Bn |
---|---|
0 | 1 |
1 | -1/2 |
2 | 1/6 |
3 | 0 |
4 | -1/30 |
5 | 0 |
6 | 1/42 |
7 | 0 |
8 | -1/30 |
9 | 0 |
10 | 5/66 |
One can calculate the Bernoulli numbers using the following recursive formula.
It turns out that Bn = 0 whenever n is odd and n ≥ 3.
The Bernoulli numbers 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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