On some properties of the gamma function

被引:48
作者
Elbert, A
Laforgia, A
机构
[1] Hungarian Acad Sci, Inst Math, H-1364 Budapest, Hungary
[2] Dept Math, I-00146 Rome, Italy
关键词
gamma function; psi function; monotonicity; inequalities;
D O I
10.1090/S0002-9939-00-05520-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 study the monotonicity of some functions connected with the psi-function (x) and derive inequalities for psi(x) and psi'(x).
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页码:2667 / 2673
页数:7
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