On a Strengthened of the More Accurate Hilbert's Inequality
Keywords:
Hilbert's inequality, Weight coefficient, Cauchy’s inequality, Strengthen.Abstract
By deducing the inequality of weight coefficient:$$\omega {\kern 1pt} {\kern 1pt} (n) = \sum\limits_{m = 0}^\infty {\frac{1}{{\kern 1pt} {\kern 1pt} m + {\kern 1pt} {\kern 1pt} n +1}} (\frac{2{\kern 1pt} {\kern 1pt} n + 1}{2{\kern 1pt} {\kern 1pt} m + 1})^{\frac{1}{2}}
 < \pi -\frac{5}{6(\sqrt {2n + 1} + \frac{3}{4}\sqrt {(2n + 1)^{ - 1}} )}, $$
where $n \in N$. We obtain on a strengthened of the more accurate Hilbert's inequality.
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Published
2011-01-30
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Discrete Mathematics
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How to Cite
On a Strengthened of the More Accurate Hilbert’s Inequality. (2011). European Journal of Pure and Applied Mathematics, 4(1), 83-88. https://ejpam.com/index.php/ejpam/article/view/670