On the sums of series of reciprocals — mentioned by svat

Mon, 02 Jul 2018 19:37:34 GMT

Euler's first major work, the one that brought him fame, was his solution to the Basel problem (https://en.wikipedia.org/wiki/Basel_problem), when he was 28. Namely, he found the sum of the reciprocals of the squares of the integer, i.e. the value of the series (1 + 1/4 + 1/9 + 1/16 + ...), to be π²/6. According to https://faculty.math.illinois.edu/~reznick/sandifer.pdf Euler gave three solutions in his 1736 paper now numbered E41: http://eulerarchive.maa.org/pages/E041.html ("De summis serierum reciprocarum" = "On the sums of series of reciprocals") Here is Jordan Bell's translation…

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On the sums of series of reciprocals — mentioned by scythe

Tue, 05 Jul 2011 20:14:23 GMT

>And it was chosen hastily. It was chosen here: http://arxiv.org/abs/math/0506415 Elegance is found in arguments and proofs, not in results, and so any attempt to look at equations is really missing the point. If you believe Euler's methods might be simplified by using 2pi instead of pi, first consider a look at the methods themselves.

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On the sums of series of reciprocals · HackerPapers discussions

On the sums of series of reciprocals — mentioned by svat

On the sums of series of reciprocals — mentioned by scythe