论文标题
Riemann Zeta函数在奇数正整数和随之而来的表示形式的有限零件积分表示
Finite-part integral representation of the Riemann zeta function at odd positive integers and consequent representations
论文作者
论文摘要
显示Riemann Zeta功能在奇数正整数中的值，$ζ（2n+1）$，被证明可以接受与发散积分$ \ int_0^{\ int_0^{\ infty} t^{ - 2n-1} { - 2n-1} \ perperatoRatoRAnnAme {csch {csCh} $ {d $ {然后，从有限的部分积分表示中推导出$ζ（2n+1）$的积分表示。同样推导了$ζ（2n+1）$和$ζ'（2n+1）$之间的某些关系，从中获得了$ζ'（2n+1）$的积分表示。
The values of the Riemann zeta function at odd positive integers, $ζ(2n+1)$, are shown to admit a representation proportional to the finite-part of the divergent integral $\int_0^{\infty} t^{-2n-1} \operatorname{csch}t\,\mathrm{d}t$. Integral representations for $ζ(2n+1)$ are then deduced from the finite-part integral representation. Certain relations between $ζ(2n+1)$ and $ζ'(2n+1)$ are likewise deduced, from which integral representations for $ζ'(2n+1)$ are obtained.
