The values of the high order Bernoulli polynomials at integers and the r-Stirling numbers

Abstract

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.

Some applications of the r-Whitney numbers

“…Recently, Merca [8] gave links of these numbers to the symmetric functions, and Mihoubi et al [10] gave some applications of the r-Stirling numbers to Bernoulli polynomials.…”