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A new proof for the exact values of $\zeta(2k)$ for $k \in \mathbb{N}$
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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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Cited by 1 Pith paper
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Basel problem: a physicist's solution
A physicist-style proof using Coulomb forces and the digamma function derives zeta(2) equals pi squared over 6, and by extension all even zeta values.
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