Bull. Korean Math. Soc. 2019; 56(2): 491-499
Online first article November 7, 2018 Printed March 1, 2019
https://doi.org/10.4134/BKMS.b180347
Copyright © The Korean Mathematical Society.
Mircea Merca
Academy of Romanian Scientists
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
2021; 58(6): 1463-1481
2001; 38(2): 399-412
2005; 42(3): 491-499
2005; 42(3): 617-622
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd