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arXiv · 1109.4694

A shortened recurrence relation for the Bernoulli numbers

F. M. S. Lima
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Abstract

In this note, starting with a little-known result of Kuo, I derive a recurrence relation for the Bernoulli numbers $B_{2 n}$, $n$ being any positive integer. This new recurrence seems advantageous in comparison to other known formulae since it allows the computation of both $B_{4 n}$ and $B_{4 n +2}$ from only $B_0, B_2,..., B_{2n}$.

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F. M. S. Lima. 2011-09-22. A shortened recurrence relation for the Bernoulli numbers. https://doi.org/10.12691/tjant-6-2-3

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