一个基本的Hilbert型不等式的推广  

On a Generalization of a Basic Hilbert-type Inequality

作　　者：有名辉[1] YOU Minghui(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,China)

机构地区：[1]浙江机电职业技术学院数学教研室

出　　处：《湖州师范学院学报》2019年第10期19-23,共5页Journal of Huzhou University

基　　金：浙江机电职业技术学院科教融合一般项目(A-0271-18-016)

摘　　要：通过构造一个非齐次的核函数,建立一个定义在第一象限的Hilbert型积分不等式,推广一个基本的Hilbert型不等式.利用余切函数的有理分式展开,给出了用余切函数高阶导数表示的最佳常数因子.通过对参数赋予不同的值,给出一些有意义的推论.By constructing a non homogeneous kernel function,we establish a new Hilbert type integral inequality defined in the first quadrant,which generalizes a basic Hilbert type inequality.In addition,by using the rational fraction expansion of cotangent function,the best possible constant factor of the obtained inequality can be represented by the higher derivative of cotangent function.Moreover,giving the parameters different values,some special interesting Hilbert type inequalities are presented at the end of the paper.

关 键 词：HILBERT型不等式 余切函数 有理分式展开 BERNOULLI数 

分 类 号：O178[理学—数学]