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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1209.5030 |
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Table of Contents:
- We present a new proof of Euler's formulas for $ζ(2k)$, where $k = 1,2,3,...$, which uses only the defining properties of the Bernoulli polynomials, obtaining the value of $ζ(2k)$ by summing a telescoping series. Only basic techniques from Calculus are needed to carry out the computation. The method also applies to $ζ(2k+1)$ and the harmonic numbers, yielding integral formulas for these.