[Calculation 19] Even values of the Zeta Function

zeta-function-even-value

(revision of 2012)  In this post, we evaluate even values of the Riemann zeta function. Calculation 19. For $n\in \N$, we have $$ \zeta(2n) = \frac{|B_{2n}|2^{2n-1} \pi^{2n}}{(2n)!}, $$ where $B_n$’s are Bernoulli numbers.   Proof. We have the general formula for … Continue reading