函数项级数敛散性的判别方法及其应用Discrimination Methods of Convergence and Divergence of Series of Functions and Its Application专 业:数学与应用数学作 者: 指导老师: 二○一五年五月 摘 要本文介绍了函数项级数敛散性判别法,如柯西判别法、阿贝尔判别法、达朗贝尔判别法和它们的极限形式,以及多种特别函数项级数敛散性的判别方法. 然后介绍了这些判别法在实际解题中的应用. 本文探究和总结了一些判别函数项级数敛散性的方法, 为今后处理函数项级数敛散性的判别提供理论基础.关键词: 函数项级数; 一致收敛; 判别法; AbstractThis paper introduces discrimination methods of convergence and divergence of series of functions, such as Cauchy criterion, Abel discrimination method, Darren Bell discrimina- tion method and their respective forms, and series of discrimination methods of convergence and divergence of a variety of special functions. Then the paper introduces these disctimina- tion methods in the application of the practical problems. This paper discusses and summari- zes discrimination methods of convergence and divergence of series of functions ,which pro- vide theory for practical problems.Keywords: series of functions, uniform convergence, discrimination method 目 录0 引 言.........................................................................................................................11 预备知识...................................................................................................................12 函数项级数敛散性的判别方法................................................................................23 判别法的一些应用……………………………………….…………………………………………….…...... 6致谢............................................................................................................................11参考文献....................................................................................................................120...