关于一类函数级数一致收敛性的判别  

The Estimation of Consistent Convergence about a Kind of Function Series

作　　者：宋根壮[1] 周香孔[1] 

机构地区：[1]衡水学院数学与计算机科学系,河北衡水053000

出　　处：《衡水学院学报》2006年第1期8-9,共2页Journal of Hengshui University

摘　　要：对于函数级数,研究其和函数的解析性质很重要,但函数级数必须具有一致收敛性,而判断函数级数的一致收敛性往往是比较困难的.对∞∑n=1(-1)(n+1)u[a,b]上单调减少并收敛于0,则∑∞n=1(-1)(n+1)un(x)型函数级数就一致收敛.It is of great importance to study the analytic quality of sum function in function series. However, this study should be bssed on the fact that the series must have consistent convergence, the judgment of which is rather difficult. So far as the type of series ∑n=1^∞（-1）^（n＋1）un（x） is concerned, only if the function u. （x） （ n =1,2,3 ,…） continues at the interval [ a,b], and the function chain un （x）reduces and converges to 0, the type of series will achieve consistent convergence.

关 键 词：函数级数 一致收敛 一致有界 和函数 

分 类 号：O173.1[理学—数学]