Titre : 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 : Issue 4 (September 2022)
Volume : 13
Date : 2022/10/21
DOI : 10.21494/ISTE.OP.2022.0886
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