Table 1 Values of \(\zeta (2n)\)
From: An improvement of the Lyapunov inequality for certain higher order differential equations
n | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
ζ(2n) | \(\frac{\pi ^{2}}{6}\) | \(\frac{\pi ^{4}}{90}\) | \(\frac{\pi ^{6}}{945}\) | \(\frac{\pi ^{8}}{9450}\) | \(\frac{\pi ^{10}}{93{,}555}\) | \(\frac{691 \pi ^{12}}{638{,}512{,}875}\) |