JIPAM logo: Home Link
 
Home Editors Submissions Reviews Volumes RGMIA About Us
 

   
  Volume 8, Issue 1, Article 28
 
Inequalities for the Gamma Function
    Authors: Xin Li, Chao-Ping Chen,  
    Keywords: Gamma function, psi function, inequality.  
    Date Received: 16/10/06  
    Date Accepted: 09/02/07  
    Subject Codes:

Primary 33B15; Secondary 26D07.

  
    Editors: Andrea Laforgia,  
 
    Abstract:

For $ x>1$, the inequalities

$\ displaystyle $\ frac{x^{x-$\ gamma}}{e^{x-1}}<$\ Gamma(x)<$\ frac{x^{x-1/2}}{e^{x-1}} $
hold, and the constants $ $\ gamma$ and $ 1/2$ are the best possible, where $ $\ gamma=0.577215$\ ldots$ is the Euler-Mascheroni constant. For $ 0<x<1$, the left-hand inequality also holds, but the right-hand inequality is reversed. This improves the result given by G. D. Anderson and S. -L. Qiu (1997).

         
       
  Download Screen PDF
  Download Print PDF
  Send this article to a friend
  Print this page
  

      search [advanced search] copyright 2003 terms and conditions login