Explicit formulae for Bernoulli numbers

Nadia N. Li; Wenchang Chu; Nadia N. Li; Wenchang Chu

doi:10.3934/math.20241366

AIMS Mathematics

2024, Volume 9, Issue 10: 28170-28194. doi: 10.3934/math.20241366

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Explicit formulae for Bernoulli numbers

Nadia N. Li ¹,
Wenchang Chu ^{2
,
,}

1.
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
2.
Via Dalmazio Birago 9/E, Lecce 73100, Italy

Received: 10 August 2024 Revised: 16 September 2024 Accepted: 25 September 2024 Published: 29 September 2024
MSC : Primary 11B68, Secondary 05A10

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.
- Bernoulli number,
- harmonic number,
- Stirling number of the second kind,
- binomial coefficient,
- connection coefficient
Citation: Nadia N. Li, Wenchang Chu. Explicit formulae for Bernoulli numbers[J]. AIMS Mathematics, 2024, 9(10): 28170-28194. doi: 10.3934/math.20241366

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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.

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