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Euler's formula
for the zeta function at the positive even integers
Samyukta Krishnamurthy and Micah B. Milinovich
Vol. 12 (2019), No. 4, 541–548
DOI: 10.2140/involve.2019.12.541
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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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Authors |
| Samyukta Krishnamurthy | |
| Department of Physics University of Mississippi University, MS United States |
Department of Physics University of Massachusetts Amherst, MA United States |
| Micah B. Milinovich | |
| Department of Mathematics University of Mississippi University, MS United States |
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