Category:Bernoulli Numbers

From ProofWiki
Jump to navigation Jump to search

This category contains results about Bernoulli Numbers.
Definitions specific to this category can be found in Definitions/Bernoulli Numbers.


The Bernoulli numbers $B_n$ are a sequence of rational numbers defined by:

Generating Function

$\displaystyle \frac x {e^x - 1} = \sum_{n \mathop = 0}^\infty \frac {B_n x^n} {n!}$


Recurrence Relation

$B_n = \begin{cases} 1 & : n = 0 \\ \displaystyle - \sum_{k \mathop = 0}^{n - 1} \binom n k \frac {B_k} {n - k + 1} & : n > 0 \end{cases}$