论文标题
Genocchi数字的新概括及其对Bernoulli多项式的后果
A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials
论文作者
论文摘要
本文提出了Genocchi数字和Genocchi定理的新概括。结果，我们获得了一些与Bernoulli多项式密切相关的整数值多项式的重要家族。用$ {（b_n）} _ {n \ in \ mathbb {n}} $ bernoulli数字的顺序以及$ {（b_n（x））} _ {n \ in \ mathbb {n}}多项式$ \ big（b_n（x）-b_n \ big）$的多项式是整数值。
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.
