Bernoulli数的Zagier修正和一个多项式延拓。部件I
The Zagier modification of Bernoulli numbers and a polynomial extension. Part I
摘要：
D.引入的修正B_{n} ^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}，\quad n > 0. Zagier在1998年提出的一种新方法，通过用Bernoulli多项式$B_{r}(x)$代替$B_{r}$，将其推广到多项式情形.这些新的多项式的性质建立使用的阴影方法以及经典的技术。对产生周期性双折射$B_{2n+1}^{*}(x)$的$x$值进行分类。奇怪的6-周期性$B_{2n+1}^{*}$，建立了Zagier，解释了展示这个序列的分解为两个部分的总和与周期2和3，分别。欧拉数的修改类似的结果。
英文摘要：
The modified B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 introduced by D. Zagier in 1998 are extended to the polynomial case by replacing $B_{r}$ by the Bernoulli polynomials $B_{r}(x)$. Properties of these new polynomials are established using the umbral method as well as classical techniques. The values of $x$ that yield periodic subsequences $B_{2n+1}^{*}(x)$ are classified. The strange 6-periodicity of $B_{2n+1}^{*}$, established by Zagier, is explained by exhibiting a decomposition of this sequence as the sum of two parts with periods 2 and 3, respectively. Similar results for modifications of Euler numbers are stated.
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