Miloud Mihoubi, Meriem Tiachachat
Abstract
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In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the r-Stirling numbers and binomial coefficients.
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In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the r-Stirling numbers and binomial coefficients.
Key concepts: Stirling numbers of the second kind, Bernoulli number, Stirling number, Stirling numbers of the first kind, Bernoulli polynomials, Mathematics, Binomial coefficient, Bell polynomials