@ARTICLE{10.21494/ISTE.OP.2022.0886,
TITLE={A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials},
AUTHOR={Bakir Farhi, },
JOURNAL={Advances in Pure and Applied Mathematics},
VOLUME={13},
NUMBER={Issue 4 (September 2022)},
YEAR={2022},
URL={https://www.openscience.fr/A-new-generalization-of-the-Genocchi-numbers-and-its-consequence-on-the},
DOI={10.21494/ISTE.OP.2022.0886},
ISSN={1869-6090},
ABSTRACT={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.}}