@article{tjant2017545,
author={Lima, F. M. S.},
title={An Elementary Proof of <img src=image/tit1.png></img> and a Recurrence Formula for &#950;(2<i>k</i>)},
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 &#950;(2<i>k</i>+1), &#950;(<i>s</i>) being the Riemann zeta function and <i>k</i> a positive integer, is modified in a manner to furnish the even zeta values &#950;(2<i>k</i>). As a result, we find an elementary proof of <img src=image/abs1.png></img>, as well as a recurrence formula for &#950;(2<i>k</i>) from which it follows that the ratio &#950;(2<i>k</i>)/<span style="font-family:Times New Roman; font-size:16px;">&#960;</span><SUP>2</SUP><SUP><i>k</i></SUP> 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}
}