2016arXiv (Cornell University)Open access

Bernoulli, poly-Bernoulli, and Cauchy polynomials in terms of Stirling and r-Stirling numbers

Khristo N. Boyadzhiev

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Abstract

We review and discuss some results on the representation of Bernoulli, poly-Bernoulli numbers, and Bernoulli and Cauchy polynomials in terms of Stirling numbers of the first or second kind, or in terms of r-Stirling numbers.

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What this paper is about

We review and discuss some results on the representation of Bernoulli, poly-Bernoulli numbers, and Bernoulli and Cauchy polynomials in terms of Stirling numbers of the first or second kind, or in terms of r-Stirling numbers.

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Available abstract

We review and discuss some results on the representation of Bernoulli, poly-Bernoulli numbers, and Bernoulli and Cauchy polynomials in terms of Stirling numbers of the first or second kind, or in terms of r-Stirling numbers.

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

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