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:
- $E_n = \begin {cases} 1 & : n = 0 \\ 0 & : n > 0, n = 2 r + 1 \\ \ds -\sum_{k \mathop = 0}^{n - 1} \binom {2 n} {2 k} E_{2 k} & : n > 0, n = 2 r \end {cases}$
Also see
- Results about the Euler Numbers can be found here.