Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 4 (September 2022) > Article
Bakir Farhi
Université de Bejaia
Algeria
Published on 21 October 2022 DOI : 10.21494/ISTE.OP.2022.0886
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 the sequence of the Bernoulli numbers and by the sequence of the Bernoulli polynomials, we especially obtain that for any natural number , the reciprocal polynomial of the polynomial is integer-valued.
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 the sequence of the Bernoulli numbers and by the sequence of the Bernoulli polynomials, we especially obtain that for any natural number , the reciprocal polynomial of the polynomial is integer-valued.
Genocchi numbers Bernoulli numbers Bernoulli polynomials formal power series integer-valued polynomials
Genocchi numbers Bernoulli numbers Bernoulli polynomials formal power series integer-valued polynomials