eldorado.tu-dortmund.de/server/api/core/bitstreams/62767894-c1f2-48d5-8900-0734fc97c605/content
()
− ln(ch x) =
∫ 1
0
∫ π
0 ln(|1 + reiϕ tanh(x)|)dmα,−1/2(r, ϕ)
≥ − Γ(α + 1)
Γ(1/2)Γ(α + 1/2)
1
e
∫ 1
0 (1 − r)−1(1 − r2)α−1/2dr
≥ − Γ(α + 1)
Γ(1/2)Γ(α + 1/2)
2
e
∫ 1
0 (1 − r2)α−3/2dr.
After substitution [...] = Σ(2,1),(2,2) · Σ(3,2),(2,1)
π = (1 2 1 2), π(I)1 = {(2, 1), (3, 2)} , π(Σ)I = Σ(2,1),(3,2) · Σ(2,2),(2,1)
π = (1 2 2 1), π(I)1 = {(2, 1), (2, 1)} , π(Σ)I = Σ(2,1),(2,1) · Σ(2,2),(3,2)
π = (2 1 1 2), π(I)1 [...] ř2(α) − r̂1(α)2. (3.4.4)
By using the estimate of m1 in Lemma 3.3.4 we get
E(ξ1,αnξ1,α) = E(m (αn,β) 1 (X1)m
(α,β) 1 (X1)) − r̂1(αn)r̂1(α)
≥ (1 − cβ
αn
)(1 − cβ
α )E(ln(ch X1)
2) − r̂1(αn)r̂1(α)
≥ r2 − …
