eng
Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2333-1232
2018-04-09
6
2
49
51
10.12691/tjant-6-2-3
TJANT2018623
article
A Shortened Recurrence Relation for Bernoulli Numbers
F. M. S. Lima
fabio@fis.unb.br
1
Institute of Physics, University of BrasÃlia, P.O. Box 04455, 70919-970, BrasÃlia-DF, Brazil
In this note, starting with a little-known result of Kuo, I derive a recurrence relation for the Bernoulli numbers B2n , n being a positive integer. This formula is shown to be advantageous in comparison to other known formulae for the exact symbolic computation of B2n. Interestingly, it is suitable for large values of n since it allows the computation of both B4n and B4n+2 from only B0, B2, ..., B2n.
http://pubs.sciepub.com/tjant/6/2/3/tjant-6-2-3.pdf
Bernoulli numbers
recurrence relations
Riemann zeta function