Sumit Kumar Jha
Abstract
In this brief note, we give, a possibly new, integral expression for the Bernoulli numbers involving the polylogarithm function. We use this to derive two explicit formulas for them in terms of the Stirling numbers of the second kind, and the Eulerian numbers.
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In this brief note, we give, a possibly new, integral expression for the Bernoulli numbers involving the polylogarithm function. We use this to derive two explicit formulas for them in terms of the Stirling numbers of the second kind, and the Eulerian numbers.
Key concepts: Stirling numbers of the second kind, Bernoulli number, Polylogarithm, Expression (computer science), Stirling numbers of the first kind, Bernoulli's principle, Bernoulli polynomials, Mathematics