1Institute of Physics, University of Brasília, P.O. Box 04455, 70919-970, Brasília-DF, Brazil
Turkish Journal of Analysis and Number Theory.
2018,
Vol. 6 No. 2, 49-51
DOI: 10.12691/tjant-6-2-3
Copyright © 2018 Science and Education PublishingCite 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.
Correspondence to: F. M. S. Lima, Institute of Physics, University of Brasília, P.O. Box 04455, 70919-970, Brasília-DF, Brazil. Email:
fabio@fis.unb.brAbstract
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.
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