Titre : [Forthcoming] A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials 

Auteurs : Bakir Farhi,  

Revue : Advances in Pure and Applied Mathematics 

Numéro : Forthcoming papers<br> 

Volume : 13 

Date : 2022/05/16 

DOI :  

ISSN : 1869-6090 

Résumé : This paper presents a new generalization of the Genocchi numbers and the Genocchi theorem. As consequences, we obtain some important families of integer-valued polynomials those are closely related to the Bernoulli polynomials. Denoting by $$${(B_n)}_{n \in \mathbb{N}}$$$ the sequence of the Bernoulli numbers and by $$${(B_n(X))}_{n \in \mathbb{N}}$$$ the sequence of the Bernoulli polynomials, we especially obtain that for any natural number $$$n$$$, the reciprocal polynomial of the polynomial $$$\big(B_n(X) - B_n\big)$$$ is integer-valued. 

Éditeur : ISTE OpenScience