JIPAM

Some Inequalities Regarding a Generalization of Euler's Constant  
 
  Authors: Alina Sîntamarian,  
  Keywords: Sequence, Convergence, Euler's constant, Approximation, Estimate, Series.  
  Date Received: 28/11/07  
  Date Accepted: 20/03/08  
  Subject Codes:

11Y60, 40A05.

  
  Editors: László Tóth,  
 
  Abstract:

The purpose of this paper is to evaluate the limit $ gamma(a)$ of the sequence

$displaystyle left(frac{1}{a}+frac{1}{a+1}+cdots+frac{1}{a+n-1}- lnfrac{a+n-1}{a}right)_{ninmathbb{N}},$
where $ ain(0,+infty)$. We give some lower and upper estimates for
$displaystyle frac{1}{a}+frac{1}{a+1}+cdots+frac{1}{a+n-1}- lnfrac{a+n-1}{a}-gamma(a), quad ninmathbb{N}.$
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