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<br> 
VL  - 13 
ER  -