On lacunary recurrences with gaps of length four and eight for the Bernoulli numbers
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 491-499
https://doi.org/10.4134/BKMS.b180347
Published online 2019 Mar 01
Mircea Merca
Academy of Romanian Scientists
Abstract : The problem of finding fast computing methods for Bernoulli numbers has a long and interesting history. In this paper, the author provides new proofs for two lacunary recurrence relations with gaps of length four and eight for the Bernoulli numbers. These proofs invoked the fact that the $n$th powers of $\pi^2$, $\pi^4$ and $\pi^8$ can be expressed in terms of the $n$th elementary symmetric functions.
Keywords : Bernoulli numbers, recurrences
MSC numbers : 11B68, 11B37, 05E05
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