Definition:Bernoulli Numbers/Recurrence Relation
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Separate the 2 definitions out into their own pages and prove equivalence with an equivalence proof
Separate the 2 definitions out into their own pages and prove equivalence with an equivalence proof
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Definition
The Bernoulli numbers $B_n$ are a sequence of rational numbers defined by the recurrence relation:
- $B_n = \begin{cases} 1 & : n = 0 \\ \displaystyle - \sum_{k \mathop = 0}^{n - 1} \binom n k \frac {B_k} {n + 1 - k} & : n > 0 \end{cases}$
or equivalently:
- $B_n = \begin{cases} 1 & : n = 0 \\ \displaystyle - \frac 1 {n+1} \sum_{k \mathop = 0}^{n - 1} \binom {n+1} k B_k & : n > 0 \end{cases}$
Also see
- Results about the Bernoulli Numbers can be found here.
