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  Volume 9, Issue 2, Article 46
 
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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