摘要
通过引入Gamma函数,借助权函数的方法,建立了一个定义在全平面上的Hilbert型积分不等式及其等价形式.特别地,利用余切函数的部分分式展开形式,得到了一个最佳常数因子与余切函数的高阶导数有关的Hilbert型不等式.另外,通过对参数赋值,给出了其它一些特殊的定义在全平面的Hilbert型不等式.
A type of Hilbert-type integral inequality defined in the whole plane as well as its equivalent form of value is established in this paper by means of the introdution of Gamma function and with the help of the weight function method. Particularly, through the partial fraction expansion of cotangent function, a new-type Hilbert inequality whose constant is related to the higher derivative of cotangent function with the best constant factoris also obtained. In addition, a number of special Hilbert-type inequalities defined in the whole plane are oprovided through the different parameters values.
作者
有名辉
YOU Minghui(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou,China 310053)
出处
《温州大学学报（自然科学版）》
2019年第1期9-16,共8页
Journal of Wenzhou University(Natural Science Edition)
基金
浙江省教育厅一般科研项目(Y201737260)
