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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
