International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 27, Pages 1423-1427
doi:10.1155/S0161171204205270
On further strengthened Hardy-Hilbert's inequality
1School of Science, Nanjing University of Science & Technology, Nanjing 210094, China
2Department of Basic Science of Technology College, Xuzhou Normal University, Jiangsu , Xuzhou 221011, China
Received 7 May 2002
Copyright © 2004 Lü Zhongxue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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/(2n1/p+(2/a)n−1/q) where 0<a<147/45,
as n≥3; 0<a<(1−C)/(2C−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.