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arXiv · 1712.02255

A new proof for the exact values of $\zeta(2k)$ for $k \in \mathbb{N}$

Marius Costandin
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Abstract

We establish a connection between a function and a series representation using a similar technique with that that Euler used to solve the Basel problem. Our result concerns a more general series from which one can obtain $\zeta(2k)$ as a limit case. We also are able to prove the well known result expressing $\zeta(2k)$ with Bernoulli numbers as an application.

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Marius Costandin. 2017-12-03. A new proof for the exact values of $\zeta(2k)$ for $k \in \mathbb{N}$. https://arxiv.org/abs/1712.02255

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