Apostol, Tom M. A proof that Euler missed: Evaluating \(\zeta\) (2) the easy way. (English) Zbl 0538.10001 Math. Intell. 5, No. 3, 59-60 (1983). 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 Cited in 2 ReviewsCited in 12 Documents 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 PDF BibTeX XML Cite \textit{T. M. Apostol}, Math. Intell. 5, No. 3, 59--60 (1983; Zbl 0538.10001) Full Text: DOI Digital Library of Mathematical Functions: (25.6.7) ‣ §25.6(i) Function Values ‣ §25.6 Integer Arguments ‣ Riemann Zeta Function ‣ Chapter 25 Zeta and Related Functions 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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.