函数项级数一致收敛的判别法摘要函数项级数的一致收敛性在高等数学中是非常重要的，对于求极限、导数等都是有重要的意义，也为以后的学习做了铺垫和基础。为了更好地理解和掌握函数项级数一致收敛的方法，本文对函数项级数一致收敛的几种判别法进行了分析、归纳和总结。举出部分例子。首先在基础知识部分列举了大家熟知的几种基本判别法，然后对基本判别法作了进一步讨论。利用大家己经学过的数列级数的定义和判别法对函数项级数定义进行推广，对比数项级数和函数项级数及判别法，给出了类似数项级数判别法的函数项级数一致收敛判别法一比式判别法和根式判别法。本文还介绍分析了把Guss指标判别法如何应用于正项的函数项级数的一致收敛性的判别，得出了正项的函数项级数一致收敛的另一种判别法，也就是Guss型判别法。本文也拓展了部分知识。考虑函数项级数和含参变量广义积分的一致收敛性的判别问题。关键词：函数项级数：一致收敛：判别法目录引言…基础知识：正文内容5函数项级数的基本一致收敛性判别法.5比式判别法、跟式判别法.6正项级数收敛性Gauss指标判别法.11函数项级数一致收敛柯西准则的改进形式15结语参考文献：.17Discriminant Method For Uniform Convergence Of Series Of Function TermsABSTRACTIn order to better understand and master the method of uniform convergence offunction series,several discriminant methods of uniform convergence of functionseries are analyzed,summarized and summarized.First,the introduction lists severalbasic discriminant methods which are well known,and then discusses the basicdiscriminant methods further.In this paper,the definition of series of functionterms is generalized and compared with series of function terms and discriminantmethod.The discriminant method of uniform convergence of series of function termssimilar to series of number terms is given,which is ratio discriminant method androot discriminant method.This paper also introduces the Gauss index discriminantmethod applied to the discriminant of the uniform convergence of the series of positiveterms,and gives the Gauss type discriminant of the uniform convergence of the seriesof positive terms.In addition,the problem of judging the uniform convergence ofthe series of function terms and the generalized integral with parameter variablesis also considered.Key words:series of function terms;uniform convergence;discriminant method1