A shortened recurrence relation for the Bernoulli numbers

F. M. S. Lima

doi:10.12691/tjant-6-2-3

paper

A shortened recurrence relation for the Bernoulli numbers

arXiv:1109.4694 · doi:10.12691/tjant-6-2-3

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 $B_{0}, B_{2}, ..., B_{2 n}$ .

arXiv comment7 pages, no figures. Submitted to "J. Number Theory" (09/22/2011)