On further strengthened Hardy-Hilbert's inequality

Lü Zhongxue
2004 International Journal of Mathematics and Mathematical Sciences  
We obtain an inequality for the weight coefficientω(q,n)(q>1,1/q+1/q=1,n∈ℕ) in the formω(q,n)=:∑m=1∞(1/(m+n))(n/m)1/q<π/sin(π/p)−1/(2n1/p+(2/a)n−1/q)where0<a<147/45, asn≥3;0<a<(1−C)/(2C−1), asn=1,2, andCis an Euler constant. We show a generalization and improvement of Hilbert's inequalities. The results of the paper by Yang and Debnath are improved.
doi:10.1155/s0161171204205270 fatcat:kuvwhurgzrg5rlxah5ysi4ifha