Recurrence Relations for Values of the Riemann Zeta Function in Odd Integers

Tobias Kyrion

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arXiv · 2005.02391

Recurrence Relations for Values of the Riemann Zeta Function in Odd Integers

Tobias Kyrion

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Abstract

It is commonly known that $\zeta(2k) = q_{k}\frac{\zeta(2k + 2)}{\pi^2}$ with known rational numbers $q_{k}$. In this work we construct recurrence relations of the form $\sum_{k = 1}^{\infty}r_{k}\frac{\zeta(2k + 1)}{\pi^{2k}} = 0$ and show that series representations for the coefficients $r_{k} \in \mathbb{R}$ can be computed explicitly.

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Tobias Kyrion. 2020-05-06. Recurrence Relations for Values of the Riemann Zeta Function in Odd Integers. https://arxiv.org/abs/2005.02391

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