TY - Type of reference
TI - [Forthcoming] 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 -
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 -
LA - en
PB - ISTE OpenScience
DA - 2022/05/16
SN - 1869-6090
TT - [Forthcoming] Une nouvelle géneralisation des nombres de Genocchi et conséquence sur les polynômes de Bernoulli
UR - https://openscience.fr/A-new-generalization-of-the-Genocchi-numbers-and-its-consequence-on-the
IS - Forthcoming papers

VL - 13
ER -