A More Accurate Half-Discrete Hilbert-Type Inequality Involving One Higher-Order Derivative Function

By means of the weight functions, Hermite-Hadamard's inequality and the technique of real analysis, a new more accurate half-discrete Hilbert-type inequality involving one higher-order derivative function is given. The equivalent conditions of the best possible constant factor related to a few parameters, the equivalent forms, several particular inequalities and the operator expressions are considered.