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给出如下形式的权系数的估计式:ω(r,n)=∞Σk=1/1max{k,n}(n/k)1/r<(r2/r-1)-(r/r-1)(1/n1-1r)(r>1,n∈N)得到一个Hardy-Hilbert型不等式的一个新的改进形式.推广和发展了一些作者近期的结果.
An estimate of the weight coefficient is given as follows: ω (r, n) = ∞ Σ k = 1/1 max {k, n} (n / k) 1 / r <(r2 / r- 1) - (r / r -1) (1 / n1-1r) (r> 1, n∈N) A new improved version of Hardy-Hilbert’s type inequality is obtained. Some recent results of the authors are generalized and developed.