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2019 Euler's formula for the zeta function at the positive even integers
Samyukta Krishnamurthy, Micah B. Milinovich
Involve 12(4): 541-548 (2019). DOI: 10.2140/involve.2019.12.541

Abstract

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 12.

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Samyukta Krishnamurthy. Micah B. Milinovich. "Euler's formula for the zeta function at the positive even integers." Involve 12 (4) 541 - 548, 2019. https://doi.org/10.2140/involve.2019.12.541

Information

Received: 12 June 2017; Revised: 30 July 2018; Accepted: 28 October 2018; Published: 2019
First available in Project Euclid: 30 May 2019

zbMATH: 07072538
MathSciNet: MR3941597
Digital Object Identifier: 10.2140/involve.2019.12.541

Subjects:
Primary: 11M06
Secondary: 11B37, 11B68

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 4 • 2019
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