TY - Type of reference TI - A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials AU - Bakir Farhi AB - 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. DO - 10.21494/ISTE.OP.2022.0886 JF - Advances in Pure and Applied Mathematics KW - Genocchi numbers, Bernoulli numbers, Bernoulli polynomials, formal power series, integer-valued polynomials, Genocchi numbers, Bernoulli numbers, Bernoulli polynomials, formal power series, integer-valued polynomials, L1 - http://openscience.fr/IMG/pdf/iste_apam22v13n4_2.pdf LA - en PB - ISTE OpenScience DA - 2022/10/21 SN - 1869-6090 TT - Une nouvelle géneralisation des nombres de Genocchi et conséquence sur les polynômes de Bernoulli UR - http://openscience.fr/A-new-generalization-of-the-Genocchi-numbers-and-its-consequence-on-the IS - Issue 4 (September 2022) VL - 13 ER -