@article{tjant2017545,
author={Lima, F. M. S.},
title={An Elementary Proof of and a Recurrence Formula for ζ(2*k*)},
journal={Turkish Journal of Analysis and Number Theory},
volume={5},
number={4},
pages={143--145},
year={2017},
url={http://pubs.sciepub.com/tjant/5/4/5},
issn={2333-1232},
abstract={In this note, a series expansion technique introduced recently by Dancs and He for generating Euler-type formulae for odd zeta values ζ(2*k*+1), ζ(*s*) being the Riemann zeta function and *k* a positive integer, is modified in a manner to furnish the even zeta values ζ(2*k*). As a result, we find an elementary proof of , as well as a recurrence formula for ζ(2*k*) from which it follows that the ratio ζ(2*k*)/π^{2}^{k} is a rational number, without making use of Euler's formula and Bernoulli numbers.},
doi={10.12691/tjant-5-4-5}
publisher={Science and Education Publishing}
}