Further Examples with Moments of Gamma Type

Example A.1 (Rayleigh distribution). The Rayleigh distribution R is the chi distribution χ(2), with density xe−x 2/2. This is a special case of Example 3.6, and we have ER = 2Γ(s/2 + 1), −2 < Re s <∞. (A.1) We have ρ+ =∞, ρ− = −2, γ = γ′ = 1/2, δ = 1/2, κ = 0, C1 = π1/2. Example A.2 (Maxwell distribution). The Maxwell distribution M is the chi distribution χ(3), with density (2/π)1/2x2e−x 2/2. This is a another special case of Example 3.6, and we have