JIPAM

A Monotonicity Property of the Gamma Function  
 
  Authors: Hendrik Vogt, Jürgen Voigt,  
  Keywords: Gamma function, Strictly completely monotone.  
  Date Received: 11/01/01  
  Date Accepted: 29/07/02  
  Subject Codes:

33B15

  
  Editors: Andrea Laforgia,  
 
  Abstract:

It is shown that the function $x mapsto 1+frac1xlnGamma(x+1)-ln(x+1)$ is strictly completely monotone on $(-1,infty)$ and tends to one as $xto-1$, to zero as $xtoinfty$. This property is derived from a suitable integral representation of $lnGamma(x+1)$.;


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