Erratum à l’article Nombres de Bell et somme de factorielles
Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions
There is a circle of problems concerning the exponential generating function of harmonic numbers. The main results come from Cvijovic, Dattoli, Gosper and Srivastava. In this paper, we extend some of them. Namely, we give the exponential generating function of hyperharmonic numbers indexed by arithmetic progressions; in the sum several combinatorial numbers (like Stirling and Bell numbers) and the hypergeometric function appear.
Extended Bell and Stirling numbers from hypergeometric exponentiation.
Extension of classical sequences to negative integers
We give a method to extend Bell exponential polynomials to negative indices. This generalizes many results of this type such as the extension to negative indices of Stirling numbers or of Bernoulli numbers.