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Abstract
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We give a new proof of Euler’s formula for the values of the Riemann
zeta function at the positive even integers. The proof involves estimating
a certain integral of elementary functions two different ways and
using a recurrence relation for the Bernoulli polynomials evaluated at
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Keywords
Riemann zeta function, Euler, Basel problem, Bernoulli
numbers, Bernoulli polynomials
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Mathematical Subject Classification 2010
Primary: 11M06
Secondary: 11B68, 11B37
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Milestones
Received: 12 June 2017
Revised: 30 July 2018
Accepted: 28 October 2018
Published: 16 April 2019
Communicated by Filip Saidak
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