论文标题
奇数整数中Riemann Zeta函数值的复发关系
Recurrence Relations for Values of the Riemann Zeta Function in Odd Integers
论文作者
论文摘要
众所周知，$ζ（2k）= q_ {k} \ frac {ζ（2k + 2）} {π^2} $带有已知有理数$ q_ {k {k {k} $。在这项工作中，我们构建了$ \ sum_ {k = 1}^{\ infty} r_ {k {k} \ frac {ζ（2k + 1）} {π^{2k}} = 0 $的复发关系。
It is commonly known that $ζ(2k) = q_{k}\frac{ζ(2k + 2)}{π^2}$ with known rational numbers $q_{k}$. In this work we construct recurrence relations of the form $\sum_{k = 1}^{\infty}r_{k}\frac{ζ(2k + 1)}{π^{2k}} = 0$ and show that series representations for the coefficients $r_{k} \in \mathbb{R}$ can be computed explicitly.
