On some properties of the Gamma function

Elbert, Árpád; Laforgia, Andrea

doi:10.1090/S0002-9939-00-05520-9

On some properties of the Gamma function
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by Árpád Elbert and Andrea Laforgia PDF

Proc. Amer. Math. Soc. 128 (2000), 2667-2673 Request permission

Abstract:

Anderson and Qiu (1997) conjectured that the function $\frac {\log \Gamma (x+1)}{{x \log x}}$ is concave for $x>1$. In this paper we prove this conjecture. We also study the monotonicity of some functions connected with the psi-function $\psi (x)$ and derive inequalities for $\psi (x)$ and $\psi ’(x)$.

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