On lacunary recurrences with gaps of length four and eight for the Bernoulli numbers

Mircea Merca

doi:10.4134/BKMS.b180347

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On lacunary recurrences with gaps of length four and eight for the Bernoulli numbers

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Bernoulli numbers recurrences

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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.

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.

참고문헌 (18)

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