A shortened recurrence relation for the Bernoulli numbers

Details A shortened recurrence relation for the Bernoulli numbers A shortened recurrence relation for the Bernoulli numbers

2011-09-22

arxiv.org/abs/1109.4694v1

Mathematics

Number Theory

7 pages, no figures. Submitted to "J. Number Theory" (09/22/2011)

Scientific paper

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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