Involve: A Journal of Mathematics
- Volume 12, Number 4 (2019), 541-548.
Euler's formula for the zeta function at the positive even integers
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 .
Involve, Volume 12, Number 4 (2019), 541-548.
Received: 12 June 2017
Revised: 30 July 2018
Accepted: 28 October 2018
First available in Project Euclid: 30 May 2019
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Krishnamurthy, Samyukta; Milinovich, Micah B. Euler's formula for the zeta function at the positive even integers. Involve 12 (2019), no. 4, 541--548. doi:10.2140/involve.2019.12.541. https://projecteuclid.org/euclid.involve/1559181651