作者ss1132 (景)
看板Math
標題[微積] uniform convergence
時間Tue Apr 26 15:29:46 2011
Discuss the uniform convergence of
gn(x)=sum(k=1,n,x/(1+k^2x^2)) 0<x<infinity
我連該用哪種測試都搞不清楚
M測試失敗
麻煩大家了
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1F：→ wickeday :M test應該可以吧? 感覺會被k^(-3/2) bound住 04/26 17:24
2F：→ keroro321 :gn(x)=Σ(k=1->n) x/(1+(k^2)(x^2)) ?? 04/26 19:31
3F：→ keroro321 :it doesn't converge uniformly near 0 . 04/26 19:33
4F：→ keroro321 :for any a>0 ,this sequence of functions converges 04/26 20:07
5F：→ keroro321 :uniformly on [a,∞) but not on (0,∞) 04/26 20:07
6F：推 math1209 :So, the limit funtion g is discontinuous on (0,1) 04/27 11:41
7F：→ math1209 :by Dini' thm. 04/27 11:41