A proof that Euler missed: Evaluating \(\zeta\) (2) the easy way

DOI10.1007/BF03026576zbMath0538.10001MaRDI QIDQ793070

Tom M. Apostol

Publication date: 1983

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

zbMATH Keywords

summation of seriesEuler's identityzeta (2)

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Convergence and divergence of series and sequences (40A05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01)

Related Items (12)

A Wilf–Zeilberger–Based Solution to the Basel Problem With Applications ⋮ Hidden lemmas in Euler's summation of the reciprocals of the squares ⋮ Evaluation of harmonic sums with integrals ⋮ Experimental Math for Math Monthly Problems ⋮ Basel Problem: A Solution Motivated by the Power of a Point ⋮ A bridge between unit square and single integrals for real functions of the form \(f(x\cdot y)\) ⋮ A simple proof that \(\zeta (2) = \frac {\pi^{2}}{6}\) ⋮ New definite integrals and a two-term dilogarithm identity ⋮ Piecewise isometries, uniform distribution and 3log 2−π²/8 ⋮ Twin composites, strange continued fractions, and a transformation that Euler missed (Twice) ⋮ Green’s Functions and Euler’s Formula for $$\zeta (2n)$$ ⋮ Stochastic Navier-Stokes equations in unbounded channel domains

Cites Work

• A Note on the Irrationality of ζ(2) and ζ(3)

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