A proof that Euler missed: Evaluating \(\zeta\) (2) the easy way
type: Item
instance of: scholarly article
title: A proof that Euler missed: Evaluating \(\zeta\) (2) the easy way
zbMATH Open document ID: 0538.10001
DOI: 10.1007/BF03026576
published in: The Mathematical Intelligencer
publication date: 1983-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11-01
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 3855198
zbMATH Keywords: zeta (2)
zbMATH Keywords: summation of series
zbMATH Keywords: Euler's identity
author: Tom M. Apostol
reviewed by: Frits Beukers
MaRDI profile type: Publication
cites work: A Note on the Irrationality of ζ(2) and ζ(3)
description: scientific article; zbMATH DE number 3855198