English

Two new explicit formulas for the Bernoulli Numbers

General Mathematics 2020-03-09 v2

Abstract

In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowledge, these formulas are new. We also derive two more probably known formulas.

Keywords

Cite

@article{arxiv.1905.11216,
  title  = {Two new explicit formulas for the Bernoulli Numbers},
  author = {Sumit Kumar Jha},
  journal= {arXiv preprint arXiv:1905.11216},
  year   = {2020}
}

Comments

Updated to give proofs of some necessary results

R2 v1 2026-06-23T09:26:34.041Z