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2020•Notes on Number Theory and Discrete MathematicsOpen access

A new explicit formula for the Bernoulli numbers in terms of the Stirling numbers of the second kind

Sumit Kumar Jha

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Abstract

Let B r denote the Bernoulli numbers, and S(r, k) denote the Stirling numbers of the second kind.We prove the following explicit formulaTo the best of our knowledge, the formula is new.

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What this paper is about

Let B r denote the Bernoulli numbers, and S(r, k) denote the Stirling numbers of the second kind.We prove the following explicit formulaTo the best of our knowledge, the formula is new.

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Available abstract

Let B r denote the Bernoulli numbers, and S(r, k) denote the Stirling numbers of the second kind.We prove the following explicit formulaTo the best of our knowledge, the formula is new.

Key concepts: Stirling numbers of the second kind, Stirling numbers of the first kind, Bernoulli number, Stirling number, Bernoulli's principle, Mathematics, Bell polynomials, Stirling engine

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