Vol. 8, No. 4, 2019
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A new explicit formula for Bernoulli numbers involving the Euler number

Sumit Kumar Jha
Vol. 8 (2019), No. 4, 385–387
DOI: 10.2140/moscow.2019.8.389
Abstract

We derive a new explicit formula for Bernoulli numbers in terms of the Stirling numbers of the second kind and the Euler numbers. As a corollary of our result, we obtain an explicit formula for the even Euler numbers in terms of the Stirling numbers of the second kind.

Keywords
Bernoulli numbers, Stirling numbers of the second kind, Euler numbers, polylogarithm function
Mathematical Subject Classification 2010
Primary: 11B68
Milestones
Received: 17 June 2019
Revised: 24 July 2019
Accepted: 8 August 2019
Published: 11 October 2019
Authors
Sumit Kumar Jha
International Institute of Information Technology
Hyderabad
India