函数项级数的一致收敛性及其应用.doc

函数项级数的一致收敛性及其应用
摘要:随着科学技术的发展,,随着人们对级数的深入研究,,,函数项级数的一致收敛性在应用中起着至关重要的作用,,对函数项级数一致收敛性的判定方法进行梳理、归纳,并举例说明,以一类最简单的函数项级数幂级数为例,说明函数项级数在计算方面的应用.
关键词:函数项级数;一致收敛;幂级数
Uniformly Convergence Series of Functions and Application
Abstract: With the development of science and technology, elementary function has failed to meet the needs of the people. Since the Cauchy gives the definition of infinite series, the theory of series has been developed rapidly with the in-depth study of it. With the infinite series, series of functions came into being. Series of functions has a wide application in mathematics and engineering science. The uniformly convergence of series of functions plays an important role in application. During the application, the uniformly convergence of series of function and its judgment e important. This article describes the concept of the uniformly convergence of series of functions, to sum up the judgment of the uniformly convergence of series of functions. We give many examples and take the series of powers to illustrate the application in calculation of series of functions.
Key words: series of functions; uniformly convergence; series of powers
目录
1 引言……………………………………………………………………………………………………1
2 函数项级数的相关概念介绍…………………………………………………………………………2
函数列及其一致收敛性………………………………………………………………………2
函数项级数及其一致收敛性…………………………………………………………………3
一致收敛函数项级数的性质…………………………………………………………………4
3 函数项级数的一致收敛性判别法……………………………………………………………………5
一般判别法……………………………………………………………………………………5
魏尔斯特拉斯判别法…………………………………………………………………………7
阿贝尔判别法与狄利克雷判别法……………………………………………………………7
阿贝尔判别法……………………………………………………………………… 8
狄利克雷判别法…………………………………………………………………… 8
类似数项级数判别法的函数项级数一致收敛判别法…………………………………… 10
比式判别法…………………………………………………………………………10
根式判别法…………………………………………………………………………11
对数判别法…………………………………………………………………………12
Dini判别法……………………………