On some properties of the gamma function

Authors
Elbert, A Laforgia, A
Citation
A. Elbert et A. Laforgia, On some properties of the gamma function, P AM MATH S, 128(9), 2000, pp. 2667-2673
Citations number
5
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
128
Issue
9
Year of publication
2000
Pages
2667 - 2673
Database
ISI
SICI code
0002-9939(2000)128:9<2667:OSPOTG>2.0.ZU;2-V
Abstract
Anderson and Qiu (1997) conjectured that the function log Gamma(x+1)/x log x is concave for x > 1. In this paper we prove this conjecture. We also stu dy the monotonicity of some functions connected with the psi-function (x) a nd derive inequalities for psi(x) and psi'(x).