A superadditive property of Hadamard’s gamma function - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

Hadamard’s gamma function is defined by

where Γ denotes the classical gamma function of Euler. H is an entire function, which satisfies H(n)=(n−1)! for all positive integers n. We prove the following superadditive property.

Let α be a real number. The inequality

holds for all real numbers x,y with x,y≥α if and only if α≥α ₀=1.5031…. Here, α ₀ is the only solution of H(2t)=2H(t) in [1.5,∞).

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Authors and Affiliations

1. Morsbacher Str. 10, 51545, Waldbröl, Germany

   Horst Alzer

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Correspondence to Horst Alzer.