Limits of Sums for Binomial and Eulerian Numbers and their Associated Distributions.

We provide a probabilistic approach using renewal theory to derive some novel identities involving Eulerian numbers and uniform B-splines. The renewal perspective leads to a unified treatment for the normalized binomial coefficients and the normalized Eulerian numbers when studying their limits of sums, as well as their associated distributions - the binomial distributions (Bernstein polynomials) and the Irwin-Hall distributions (uniform B-splines). We further extend the probabilistic perspective to

Déclaration de conflit d'intérêts

Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.