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

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.