论文标题
在整数参数上涉及riemann zeta函数值的统一词根的新系列表示形式
A New Series Representation Involving Root Of Unity For The Values Of Riemann Zeta Function At Integer Arguments
论文作者
论文摘要
在本文中，我们为Riemann Zeta函数的值提供了一个新的系列表示，即：$ ζ(m)=\sum_{n=1}^{\infty}\frac{m(-1)^{n-1}Γ(1-ω_{m}n)...Γ(1-ω_{m}^{m-1}n)}{n!n^m}$, where $n$ is an integer that lager than $1$ and $ω$ is the $ m $ - 团结根。该系列收敛很快。它是由某种无限部分分数分解的技术得出的。通过这种技术，我们还建立了与伽马功能相关的其他有用公式。
In this paper we provide a new series representation for the values of Riemann zeta function at integer arguments, namely: $ ζ(m)=\sum_{n=1}^{\infty}\frac{m(-1)^{n-1}Γ(1-ω_{m}n)...Γ(1-ω_{m}^{m-1}n)}{n!n^m}$, where $n$ is an integer that lager than $1$ and $ω$ is the $m$-th root of unity. This series converges quite fast. It's derived by some technique of infinite partial fraction decomposition. With this technique we also establish other useful formulas related to gamma function.
