Vol. 8, No. 4, 2019

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This article is available for purchase or by subscription. See below.
A new explicit formula for Bernoulli numbers involving the Euler number

Sumit Kumar Jha

Vol. 8 (2019), No. 4, 385–387
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.

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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