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 $\psi ’(x)$.References
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Additional Information
- Árpád Elbert
- Affiliation: Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, Budapest H-1364, Hungary
- Andrea Laforgia
- Affiliation: Department of Mathematics, Largo S. Leonardo Murialdo, 1 00146 Roma, Italy
- Email: laforgia@mat.uniroma3.it
- Received by editor(s): October 23, 1998
- Published electronically: March 1, 2000
- Communicated by: Hal L. Smith
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2667-2673
- MSC (2000): Primary 33B15; Secondary 26A48, 26D07
- DOI: https://doi.org/10.1090/S0002-9939-00-05520-9
- MathSciNet review: 1694859