正项级数审敛法到函数级数一致收敛审敛法的推广  

The Extension of Convergence Criterion of Positive Series to Uniform Convergence Criterion of Function Series

作　　者：徐家斌[1] 

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641100

出　　处：《内江师范学院学报》2010年第10期20-24,共5页Journal of Neijiang Normal University

摘　　要：将正项级数审敛法推广到函数级数一致收敛审敛上去,得到了函数级数一致收敛的D’Alembert判别法、Cauchy判别法、Raabe判别法和它们的极限形式,以及推广的Weierstrass判别法,并揭示了这些判别法的实质是比较两个函数级数通项一致收敛于零的速度的快慢.D＇Alembert criterion,Cauchy criterion,Rabbe criterion, their limit form and generalized Weierstrass criterion were obtained for uniform convergence of funcion series,by extending the convergence criterion of positive series to uniform convergence criterion of function series.The essence of these methods is to compare the speeds when the general terms of the two function series uniformly converge at zero.And finally some mistakes in relevant literatures were pointed out.

关 键 词：函数级数 一致收敛 D’Alembert判别法 Cauchy判别法 RAABE判别法 

分 类 号：O173[理学—数学]