English

A shortened recurrence relation for the Bernoulli numbers

Number Theory 2018-05-10 v1

Abstract

In this note, starting with a little-known result of Kuo, I derive a recurrence relation for the Bernoulli numbers B2nB_{2 n}, nn being any positive integer. This new recurrence seems advantageous in comparison to other known formulae since it allows the computation of both B4nB_{4 n} and B4n+2B_{4 n +2} from only B0,B2,...,B2nB_0, B_2,..., B_{2n}.

Keywords

Cite

@article{arxiv.1109.4694,
  title  = {A shortened recurrence relation for the Bernoulli numbers},
  author = {F. M. S. Lima},
  journal= {arXiv preprint arXiv:1109.4694},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-21T19:08:34.167Z