Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On some properties of the Gamma function

Author(s): Árpád Elbert; Andrea Laforgia
Journal: Proc. Amer. Math. Soc. 128 (2000), 2667-2673.
MSC (2000): Primary 33B15; Secondary 26A48, 26D07
Posted: March 1, 2000
MathSciNet review: 1694859
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Abstract | References | Similar articles | Additional information

Abstract: Anderson and Qiu (1997) conjectured that the function $\frac{\log \Gamma (x+1)}{{x \log x}}$ is concave for . 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 $\psi '(x)$ .

References:

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[5]: M. E. Muldoon, Some monotonicity properties and characterizations of the gamma function, Aequationes Math. 18 (1978), 54-63. MR 58:11536

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