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Abstract
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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.
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Keywords
Bernoulli numbers, Stirling numbers of the second kind,
Euler numbers, polylogarithm function
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Mathematical Subject Classification 2010
Primary: 11B68
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Milestones
Received: 17 June 2019
Revised: 24 July 2019
Accepted: 8 August 2019
Published: 11 October 2019
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