Paul Nahin also does it in his book "Interesting integrals". Probably inspired by Apostol. Nahin's book, by the way, that incredibly I have lost...
The most elegant solution to Euler's "Basel Problem" I've ever seen
The LHS can be shown to be π²/6 using standard calculus techniques
(cite: 𝐴 𝑝𝑟𝑜𝑜𝑓 𝑡ℎ𝑎𝑡 𝐸𝑢𝑙𝑒𝑟 𝑚𝑖𝑠𝑠𝑒𝑑: 𝑒𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑛𝑔 ζ(2) 𝑡ℎ𝑒 𝑒𝑎𝑠𝑦 𝑤𝑎𝑦)
https://link.springer.com/content/pdf/10.1007%2FBF03026576.pdf …pic.twitter.com/4htpbetVCf
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That book is quite incredible, I agree. You can get that and all books for free on http://libgen.io .. thank me later
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Still not convinced about the most elegant part Especially after seeing this https://www.quora.com/Whats-the-most-ingenious-way-to-solve-the-basel-problem-displaystyle-sum_-n-1-infty-frac-1-n-2-frac-pi-2-6/answer/Sridhar-Ramesh?ch=10&share=2a7b0e9a&srid=56PwP …
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Looks oddly similar to one of my previous tweets ;)https://twitter.com/InertialObservr/status/1126211658177699840?s=20 …
Was playing around with Fourier series, and found an alternative solution to Euler's Basel problem
∑ 1/n² = π²/6 pic.twitter.com/tViTmJIXlLShow this thread
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I’ll have to check, but I think this is the proof included in “Proofs from THE BOOK”.
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Can it though?
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Keywords Straightforward Manner
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God damnit Dillon, why did I have to learn about that just now, and not like 3 years ago?
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Dammit*
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Euler did not care about finding the easy way. You are confusing him with Gauss?
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