论文标题
常规整数点的多个Zeta功能
Multiple zeta functions at regular integer points
论文作者
论文摘要
我们显示了Euler-Zagier多个Zeta功能的复发关系，该功能描述了$ r $折叠功能，其中一个变量专门针对非阳性整数作为$（r-1）$ - 折叠功能的合理线性组合，从而扩展了Akiyama-egami-egami-egami-tanigawa和Matsumoto的先前结果。作为一个应用程序，我们获得了一种明确的方法来计算在任何整数点（参数既不是全阳性也不是全阳性的参数）作为多个Zeta值的合理线性求和。
We show the recurrence relations of the Euler-Zagier multiple zeta-function which describes the $r$-fold function with one variable specialized to a non-positive integer as a rational linear combination of $(r-1)$-fold functions, which extends the previous results of Akiyama-Egami-Tanigawa and Matsumoto. As an application, we obtain an explicit method to calculate the special values of the multiple zeta-function at any integer point (the arguments could be neither all-positive nor all-non-positive) as a rational linear summation of the multiple zeta values.
