Sumit Kumar Jha
Abstract
We derive an explicit formula for the Bernoulli numbers in terms of Stirling numbers of the second kind. To the best of our knowledge, the formula is new. Additionally, we recover two more explicit formulas from this formula expressing the Bernoulli numbers in terms of Stirling numbers of the second kind.
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We derive an explicit formula for the Bernoulli numbers in terms of Stirling numbers of the second kind. To the best of our knowledge, the formula is new. Additionally, we recover two more explicit formulas from this formula expressing the Bernoulli numbers in terms of Stirling numbers of the second kind.
Key concepts: Stirling numbers of the second kind, Stirling numbers of the first kind, Bernoulli number, Stirling number, Bernoulli's principle, Bell polynomials, Mathematics, Stirling engine