Another proof of Euler’s formula for $\zeta(2k)$

DOI10.1090/S0002-9939-2010-10565-8zbMath1223.40001MaRDI QIDQ2997202

Manuel Díaz-Carrillo, Juan Fernández-Sánchez, Enrique de Amo

Publication date: 6 May 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Approximation to limiting values (summation of series, etc.) (40A25)

Related Items (7)

Revisiting the Riemann Zeta function at positive even integers ⋮ Another Proof of the Famous Formula for the Zeta Function at Positive Even Integers ⋮ Series representations for the Apéry constant \(\zeta (3)\) involving the values \(\zeta (2n)\) ⋮ Euler's formula for the zeta function at the positive even integers ⋮ A new proof of Euler's formula for ζ(2n) ⋮ Green’s Functions and Euler’s Formula for $$\zeta (2n)$$ ⋮ A simpler proof of a Katsurada's theorem and rapidly converging series for \(\zeta (2n+1)\) and \(\beta (2n)\)

Cites Work

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• Euler and Infinite Series
• The Series Σ^∞_{k = 1}k^-s, s = 2,3,4,⋯, Once More
• Euler and the Zeta Function
• Elementary Evaluation of ζ(2n)
• Application of the Hurwitz Zeta Function to the Evaluation of Certain Integrals
• Finding ζ(2p) from a Product of Sines
• An Elementary Proof of Euler's Formula for z(2m)
• On ∑^∞_{n = 1} (1/n^2k)
• Another Elementary Proof of Euler's Formula for ζ(2n)
• Elementary Evaluation of ζ(2k )
• A recurrence formula for 𝜁(2𝑛)
• A New Method of Evaluating ζ(2n)

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