On new strengthened Hardy-Hilbert's inequality

Abstract

In this paper, a new inequality for the weight coefficient ω(q,n) in the form ω(q,n):=∑m=1∞1m+n(nm)1/q              <πsin(π/p)−12π1/p+n−1/q(q>1,1p+1q=1,n∈N) is proved. This is followed by a strengthened version ofthe Hardy-Hilbert inequality.