|
|||||
|
|
Inequalities for the gamma function |
|
| Authors: | Horst Alzer |
| Affiliation: | Morsbacher Str. 10, 51545 Waldbröl, Germany |
| Abstract: | We prove the following two theorems: (i) Let
holds for all (ii) The inequalities
are valid for all |
| Keywords: | Gamma function psi function power mean inequalities |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Proceedings of the American Mathematical Society》下载全文 | |
be the 
th power mean of 
and 
. The inequality 
if and only if 
, where 
denotes Euler's constant. This refines results established by W. Gautschi (1974) and the author (1997). 
if and only if 
and 
, while 
holds for all 
if and only if 
and 
. These bounds for 
improve those given by G. D. Anderson an S.-L. Qiu (1997).