JIPAM

Monotonicity Results for the Gamma Function  
 
  Authors: Chao-Ping Chen, Feng Qi,  
  Keywords: Gamma function, Monotonicity, Inequality.  
  Date Received: 01/06/02  
  Date Accepted: 01/05/03  
  Subject Codes:

33B15,26D07

  
  Editors: Andrea Laforgia,  
 
  Abstract:

The function $frac {[Gamma(x+1)]^{1/x}}{x+1}$ is strictly decreasing on $% [1,infty)$, the function $fra {[Gamma(x+1)]^{1/x}}{sqrt{x}}$ is strictly increasing on $[2,infty)$, and the function $fra {[Gamma(x+1)]^{1/x}}{% sqrt{x+1}}$ is strictly increasing on $[1,infty)$, respectively. From these, some inequalities, for example, the Minc-Sathre inequality, are deduced, and two open problems posed by the second author are solved partially.;


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