## 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

### Keywords:

zeta (2); summation of series; Euler’s identity
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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 [3] F. Goldscheider (1913)Arch. Math. Phys. 20:323–324.
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