Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2018, 6(2), 49-51
DOI: 10.12691/tjant-6-2-3
Open AccessArticle

A Shortened Recurrence Relation for Bernoulli Numbers

F. M. S. Lima1,

1Institute of Physics, University of Brasília, P.O. Box 04455, 70919-970, Brasília-DF, Brazil

Pub. Date: April 30, 2018

Cite this paper:
F. M. S. Lima. A Shortened Recurrence Relation for Bernoulli Numbers. Turkish Journal of Analysis and Number Theory. 2018; 6(2):49-51. 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 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.

Keywords:
Bernoulli numbers recurrence relations Riemann zeta function

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