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浙江大学学报(理学版)  2020, Vol. 47 Issue (5): 554-558    DOI: 10.3785/j.issn.1008-9497.2020.05.006
数学与计算机科学     
一个R2上含双曲函数核的Hilbert型不等式
有名辉, 孙霞
浙江机电职业技术学院 数学教研室, 浙江 杭州 310053
A Hilbert-type inequality defined on R2 with the kernel involving hyperbolic functions
YOU Minghui, SUN Xia
Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China
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摘要: 通过引入参数,构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开,建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用,通过赋予参数不同的值,建立了一些有意义的特殊结果。
关键词: Gamma函数Hilbert型不等式双曲函数正切函数有理分式展开    
Abstract: By introducing some parameters, we construct a non-homogeneous kernel function including hyperbolic functions on the whole plane. In addition, by using the rational fraction expansion of tangent function, a Hilbert-type integral inequality associated with the best possible constant factor and the higher derivatives of tangent function is presented. Furthermore, some meaningful and special results are presented by specializing the parameters with different values as on application.
Key words: Hilbert-type inequality    tangent function    hyperbolic function    Gamma function    rational fraction expansion
收稿日期: 2019-08-13 出版日期: 2020-09-25
CLC:  O178  
基金资助: 浙江机电职业技术学院科教融合一般项目(A-0271-20-007).
作者简介: 有名辉(1982—),ORCID:http://orcid.org/0000-0002-8000-249X,男,硕士,讲师,主要从事解析不等式研究,E-mail:youminghui@hotmail.com.。
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引用本文:

有名辉, 孙霞. 一个R2上含双曲函数核的Hilbert型不等式[J]. 浙江大学学报(理学版), 2020, 47(5): 554-558.

YOU Minghui, SUN Xia. A Hilbert-type inequality defined on R2 with the kernel involving hyperbolic functions. Journal of Zhejiang University (Science Edition), 2020, 47(5): 554-558.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.05.006        https://www.zjujournals.com/sci/CN/Y2020/V47/I5/554

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