发布时间 : 星期二 文章函数项级数的一致收敛判别论文更新完毕开始阅读
摘 要
函数项级数是数学分析中的一个重要的概念,在工程技术领域也有着重要应用. 关于函数项级数的问题往往是数学分析的重点,又是难点,不易理解和掌握 而函数项级数的一个基本问题就是研究其一致收敛性,但是一致收敛的判别往往比较困难,我们的教材中对于函数项级数?un(x)的收敛判别给出了一些基本方法,然而这些方法却只能解决一些常见的问题,对于很多其它类型的函数项级数,我们需要寻求其它更为方便的方法。例如,我们可以把正项级数的达朗贝尔判别法、柯西判别法、拉贝判别法和它们的极限形式顺利地推广到函数项级数的一致收敛的判别上,此外,还有很多种不常见的判别函数项级数一致收敛的方法,它们在处理某些类型函数项级数一致收敛判别问题上有着很重要的应用。本文旨在对上述函数项级数收敛判别的方法进行全面的总结和探究,为今后在处理函数项级数一致收敛性的判别提供理论基础。
关键词：函数项级数、 一致收敛、函数列、部分和数列
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Abstract
The function series is an important concept in mathematical analysis ,also has its importing application in engineering field. The function of series problems are often the focus of mathematical analysis, it is difficult, difficult to understand and master and one of the basic problems in function series is to study the convergence problems, but consistent convergence is often difficult, our textbooks for the convergence of functional series discriminate gives some basic methods in common use, however these methods can only solve some common problems, for series of function of many other types, we need to find other more convenient method. For example, we can put the positive term series by Darren Bell method, Cauchy method, Abe discriminate method and their limiting forms smoothly to discriminant of uniform convergence of functional series of. In addition, there are many not often the discriminant function series convergence method, in which they some type of uniform convergence the function series problems of discriminant has a very important application. This paper aims to make a comprehensive summary and research method to distinguish the function series convergence, for the future in the processing function of distinguishing uniform convergence of series and provide a theoretical basis.
Keywords: function series, uniform convergence,function,partial sums
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目 录
第1章 引 言 ..................................................................................................... 1 第2章 预备知识 ............................................................................................... 2
2.1函数列及其一致收敛性 .................................................................................................... 2 2.2 函数项级数及其一致收敛性的定义 ............................................................................... 2
第3章 函数项级数一致收敛的判定方法 ............................................................ 4
3.1 常用判别方法 ................................................................................................................. 4
3.1.1 定义法 .................................................................................................................. 4 3.1.2 阿贝尔判别法 .................................................................................................... 5 3.1.3 余项判别法 ........................................................................................................ 5 3.1.4 狄利克雷判别法................................................................................................. 6 3.1.5 比式判别法 ........................................................................................................ 6 3.1.6 根式判别法 ........................................................................................................ 7 3.1.7 对数判别法 ........................................................................................................ 7 3.1.8 端点判别法 ........................................................................................................ 8 3.2 其它判别方法 ................................................................................................................. 9
3.2.1 两边夹判别法 .................................................................................................... 9 3.2.2
单调判别法 ....................................................................................................... 9
3.2.3 一致L条件判别法 .......................................................................................... 10 3.2.4 导数判别法 ...................................................................................................... 11 3.2.5
点列判别法 ..................................................................................................... 12
结束语 ................................................................................................................. 14 致谢 .................................................................................................................... 15 参考文献 ............................................................................................................. 16
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