Definition:Bernoulli Numbers/Sequence

Definition

The sequence of Bernoulli numbers begins:

 $\displaystyle B_0$ $=$ $\displaystyle 1$ $\displaystyle B_1$ $=$ $\, \displaystyle - \,$ $\displaystyle \dfrac 1 2$ $\displaystyle B_2$ $=$ $\displaystyle \dfrac 1 6$ $\displaystyle B_4$ $=$ $\, \displaystyle - \,$ $\displaystyle \dfrac 1 {30}$ $\displaystyle B_6$ $=$ $\displaystyle \dfrac 1 {42}$ $\displaystyle B_8$ $=$ $\, \displaystyle - \,$ $\displaystyle \dfrac 1 {30}$ $\displaystyle B_{10}$ $=$ $\displaystyle \dfrac 5 {66}$ $\displaystyle B_{12}$ $=$ $\, \displaystyle - \,$ $\displaystyle \dfrac {691} {2730}$

The odd index Bernoulli numbers, apart from $B_1$, are all equal to $0$.