International Journal of Mathematics and Mathematical Sciences 
Volume 21 (1998), Issue 2, Pages 403-408
doi:10.1155/S0161171298000556

On new strengthened Hardy-Hilbert's inequality

Bicheng Yang1 and Lokenath Debnath2

 1Department of Mathematics, Guangdong Education College, Guangdong, Guangzhou 510303, China
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA
Received 27 February 1997; Revised 8 September 1997

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.