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  Volume 1, Issue 2, Article 22
On a strengthened Hardy-Hilbert inequality

    Authors: Bicheng Yang,  
    Keywords: Hardy-Hilbert inequality, weight coefficient, Hölder's inequality  
    Date Received: 08/05/00  
    Date Accepted: 10/06/00  
    Subject Codes:


    Editors: Lokenath Debnath,  

In this paper, a new inequality for the weight coefficient $W(n,r)$ of the form

egin{eqnarray*}Wleft( n,right) &=&sum_{m=0}^{infty }frac{1}{m+n+1}left... ...frac{1}{13left(n+1ight) left( 2n+1ight) ^{1-frac{1}{r}}} end{eqnarray*}n
for $r>1,;nin N_{0}=Ncup left{ 0ight}$ is proved. This is followed by a strengthened version of the more accurate Hardy-Hilbert inequality.

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