which obviously holds for
k = 3 and 4. This concludes the proof.
Similarly to the reasoning for the upper bound and due to (3.2) in order to
show that u(α, k) u
∗
for some u
∗
it is enough to prove that
(6.16) 1 − e
−2
2
u
∗
u
∗ − k + 2√
k
Ek(u
∗
) α.
For the future use we put κ = −2 log (
(1 − e
−2
)/2
)
≈ 1.6771.