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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (2): 144-148    DOI: 10.3785/j.issn.1008-9497.2016.02.004
数学与计算机科学     
一个与Euler数有关的Hilbert型不等式的推广
有名辉
浙江机电职业技术学院数学教研室, 浙江杭州 310053
Generalization of a Hilbert-type inequality related to Euler number
YOU Minghui
Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China
 全文: PDF(1328 KB)  
摘要： 通过引入参数,利用实分析技巧,建立最佳常数因子与余割函数有关的Hilbert型积分不等式,推广了与Euler数有关的Hilbert型不等式.作为结论的应用,赋予参数不同的值,给出了一些特殊结果.
关键词： Hilbert型积分不等式;  余割函数;  Euler数;  部分分式展开;  Gamma函数    
Abstract: By introducing parameters and using the method of real analysis, we establish a Hilbert-type integral inequality with the best possible constant factor which is related to cosecant function. We also prove that the obtained inequality is a generalization of Hilbert-type inequality related to Euler number. Furthermore, as applications of the conclusion, some new and special results are presented by giving the parameters different values.
Key words: Hilbert-type integral inequality    cosecant function    Euler number    partial fraction expansion    Gamma function
收稿日期: 2015-04-03 出版日期: 2016-03-12
CLC:  O178  
作者简介: 有名辉(1982-),ORCID:http://orcid.org/0000-0002-1993-9558,男,讲师,硕士,主要从事解析不等式研究,E-mail:youminghui@hotmail.com.
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有名辉

引用本文:

有名辉. 一个与Euler数有关的Hilbert型不等式的推广[J]. 浙江大学学报（理学版）, 2016, 43(2): 144-148.

YOU Minghui. Generalization of a Hilbert-type inequality related to Euler number. Journal of ZheJIang University(Science Edition), 2016, 43(2): 144-148.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.02.004    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I2/144

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