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bernoulli_number [2014/03/21 11:11] |
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| + | ===== Bernoulli numbers ===== | ||
| + | ==== Function ==== | ||
| + | | @#FFBB00: definiendum | @#FFBB00: $B:\mathbb N\to\mathbb Q$ | | ||
| + | | @#FFFDDD: for all | @#FFFDDD: $z\in \mathbb C$ | | ||
| + | |||
| + | | @#55EE55: postulate | @#55EE55: $\frac{z}{\mathrm{e}^z-1}=\sum_{k=0}^\infty B_k\frac{1}{k!}z^k$ | | ||
| + | |||
| + | ==== Discussion ==== | ||
| + | === Examples === | ||
| + | $B_0=1$ | ||
| + | |||
| + | $B_1=-\tfrac{1}{2}$ | ||
| + | |||
| + | $B_2=\frac{1}{6}$ | ||
| + | |||
| + | $B_4=-\frac{1}{30}$ | ||
| + | |||
| + | $B_6=-\frac{1}{42}$ | ||
| + | ==== Parents ==== | ||
| + | === Subset of === | ||
| + | [[Infinite series]], [[ℚ valued function]] | ||
