Riemann Zeta Function at Even Integers

Theorem
The Riemann $\zeta$ function can be calculated for even integers as follows:

where:
 * $B_n$ are the Bernoulli numbers
 * $n$ is a positive integer.

Also rendered as
This can also be seen rendered in the elegant form:


 * $\map \zeta r = \dfrac 1 2 \size {B_r} \dfrac {\paren {2 \pi}^r} {r!}$

for $r = 2 n$, $n \ge 1$.

Also see

 * Basel Problem
 * Riemann Zeta Function at Odd Integers: still unsolved