By introducing several positive parameters,a new fractional discrete kernel function is con-structed.By means of the method of weight coefficients,a double Hilbert series inequality is established,and the constant factor of the newly obtained inequality is proved to be the best possible.Furthermore,based on the rational fraction expansion of the cosecant function,it is also proved that the optimal constant factor can be represented by the cosecant function.At last,by assigning some specific values to the param-eters,some previously known results are obtained,and some new Hilbert-type inequalities with special kernel functions are also presented at the end of the paper.
关键词
Hilbert型不等式/分式型核函数/有理分式展开/余割函数
Key words
Hilbert-type inequality/fractional kernel function/rational fraction expansion/cosecant function
维普
万方数据