Definition:Euler Numbers/Recurrence Relation

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Definition

The Euler numbers $E_n$ are a sequence of rational numbers defined by the recurrence relation:

$E_n = \begin{cases} 1 & : n = 0 \\ 0 & : n > 0, n = 2r + 1 \\ \displaystyle - \sum_{k \mathop = 0}^{n - 1} \binom {2n} {2k} E_{2k} & : n > 0, n = 2r \end{cases}$



Also see

  • Results about the Euler Numbers can be found here.