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Research Article | Open Access

Explicit formulae for Bernoulli numbers

Nadia N. Li1, Wenchang Chu2( )
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Via Dalmazio Birago 9/E, Lecce 73100, Italy
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Abstract

By examining the connection coefficients, we systematically review and extend (with an extra integer parameter) several double sum expressions for the Bernoulli numbers. New summation formulae are also established explicitly.

Keywords

Bernoulli numberharmonic numberStirling number of the second kindbinomial coefficientconnection coefficient
CLC number: Primary 11B68, Secondary 05A10

References

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 28170-28194
DOI: 10.3934/math.20241366

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Li NN, Chu W. Explicit formulae for Bernoulli numbers. AIMS Mathematics, 2024, 9(10): 28170-28194. https://doi.org/10.3934/math.20241366

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Received: 10 August 2024
Revised: 16 September 2024
Accepted: 25 September 2024
Published: 15 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)