Abstract
Let Γ be Euler's Gamma function. We prove that, for all α ≠ 0, β > 0, γ > 0, δ > 0, the function (Γ(γ + iαz)/Γ(γ)βi α z) δ, z ∈ R 1, is a self-decomposable characteristic function from the Thorin class \(\mathcal{T}_e \) and derive its explicit canonical form. Similarly to [1], we also describe several classes of Lévy-type stochastic processes related to Γ.
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Grigelionis, B. On the Self-Decomposability of Euler's Gamma Function. Lithuanian Mathematical Journal 43, 295–305 (2003). https://doi.org/10.1023/A:1026141402811
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DOI: https://doi.org/10.1023/A:1026141402811