A q-analogue for Euler's $ζ(2k)=\dfrac{(-1)^{k+1}2^{2k}B_{2k}π^{2k}}{2(2k)!}$

Ankush Goswami

Published 2018-03-06Version 1

We give a $q$-analogue of Euler's formula for $\zeta(2k)$ for $k\in\mathbb{Z}^+$. Our main results are stated in Theorems 3.1 and 3.2 below.