学号：0901174099函数项级数一致收敛的判别专业名称： 数学与应用数学 年级班别： 2024 级 1 班 姓 名： 庆明 指导老师： 左红亮 2024 年 04 月河南师范大学新联学院本科毕业论文函数项级数一致收敛的判别摘 要：函数项级数的一致收敛性是函数级数概念当中最基本最重要的问题。 本文则在数项级数的基础上, 分析函数项级数的收敛性定义与其判定, 函数项级数的分析性质和函数的一致收敛有关。而因此本论文中提出了函数级数一致收敛的定义, 柯西一致收敛准则, 尔斯特拉斯判别法(M 判别法), 狄利克雷判别法, 阿贝尔判别法, 余项判别法, 积分判别法。本文对函数项级数一致收敛的判别法进行推广, 主要归纳总结出了对数判别法, 导数判别法, 连续性判别法, 逼敛性判别法以与 M 判别法的推论等几种判别法, 同时并应用函数项级数一致敛的定义, 重要判别法与其充要条件给出了论文中一些结论的证明。关键词：函数项级数；一致收敛性；判别法。 Discrimination of uniform convergence of function seriesAbstract: The uniform convergence of function series is the concept of series of functions are the most basic and most important problem. In this paper, on the basis of a number of series,the definitions of convergence of function series and its decision, uniform convergence analysis of properties and functions related to the function of series. Therefore, this paper proposes a definition of uniform convergence of function series, Cauchy uniform convergence criteria the Weierstrass discrimination method (M identification method), Dirichlet discrimination law, Abel discriminant law, the remainder discriminant method, integration criterion method and article on the function series convergence discriminant method to promote mainly summarized Diagnostic Method derivative test, continuity discrimination law, forcing several discriminant method of convergence discrimination law and M inference of discrimination law, and apply function series consistent definition of convergence, it is...
