Riemann Zeta Function at Even Integers/Also presented as

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Riemann Zeta Function at Even Integers: Also presented 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 $r = 2 n$, $n \ge 1$.


It can also be expressed using the archaic form of the Bernoulli numbers as:

\(\ds \map \zeta {2 n}\) \(=\) \(\ds \dfrac {2^{2 n - 1} \pi^{2 n} {B_n}^*} {\paren {2 n}!}\)


Sources

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