On further strengthened Hardy-Hilbert's inequality

Zhongxue Lã¼

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-5

Abstract:

We obtain an inequality for the weight coefficient ω ( q , n ) ( q > 1 , 1 / q + 1 / q = 1 , n ∈ ℕ ) in the form ω ( q , n ) = : ∑ m = 1 ∞ ( 1 / ( m + n ) ) ( n / m ) 1 / q < π / sin ( π / p ) − 1 / ( 2 n 1 / p + ( 2 / a ) n − 1 / q ) where 0 < a < 147 / 45 , as n ≥ 3 ; 0 < a < ( 1 − C ) / ( 2 C − 1 ) , as n = 1 , 2 , and C is an Euler constant. We show a generalization and improvement of Hilbert's inequalities. The results of the paper by Yang and Debnath are improved.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:861720

DOI: 10.1155/S0161171204205270

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