A Generalization of a Hilbert-type Inequality with the Best Constant Factor

Hilbet-type inequality is important in analysis and its applications. In recent years,by improving the way of weight coefficient,some research on the extensions and applications of this type of inequalities are developed. In this paper,we give a Hilbert infinite series inequality with the best constant factor whose kernel is a negative quadratic form by applying the method of weight coefficients. And an equivalent form is considered.