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A proof that Euler missed: Evaluating \(\zeta\) (2) the easy way. (English) Zbl 0538.10001
The author proves Euler’s identity \(\sum^{\infty}_{n=1}n^{- 2}=\pi^ 2/6\) by simply evaluating a certain double integral in two different ways. Contrary to the more standard proofs this approach can be presented in a course in elementary calculus.
Reviewer: F.Beukers

MSC:
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
40A05 Convergence and divergence of series and sequences
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References:
[1] R. Apéry (1979) Irrationalité de \(\zeta\)(2) et \(\zeta\)(3).Astérisque 62.11–13. Paris: Société Mathématique de France.
[2] F. Beukers (1979) A note on the irrationality of \(\zeta\)(2) and \(\zeta\)(3),Bull. Lon. Math. Soc. 11:268–272. · Zbl 0421.10023 · doi:10.1112/blms/11.3.268
[3] F. Goldscheider (1913)Arch. Math. Phys. 20:323–324.
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