On a Reverse of the Slightly Sharper Hilbert-type Inequality

In this paper, by introducing parameters , and two pairs of conjugate exponents (p;q), (r;s) and applying the improved Euler-Maclaurin's summation formula, we establish a reverse of the slightly sharper Hilbert-type inequality. As applications, the strengthened version and the equivalent form are given. ∑ n=0 ∞ ∑ m=0 ambn m + n + 1 < sin(=p ) ( ∞ ∑ n=0 a p ) 1=p ( ∞ ∑ n=0 b q ) 1=q ;