[微積] uniform convergence

看板Math作者 (景)時間14年前 (2011/04/26 15:29), 編輯推噓1(1推 0噓 6→)
留言7則, 3人參與, 最新討論串1/2 (看更多)
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 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.249.180.97
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04/26 17:24, , 1F
M test應該可以吧? 感覺會被k^(-3/2) bound住
04/26 17:24, 1F
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04/26 19:31, , 2F
gn(x)=Σ(k=1->n) x/(1+(k^2)(x^2)) ??
04/26 19:31, 2F
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04/26 19:33, , 3F
it doesn't converge uniformly near 0 .
04/26 19:33, 3F
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04/26 20:07, , 4F
for any a>0 ,this sequence of functions converges
04/26 20:07, 4F
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04/26 20:07, , 5F
uniformly on [a,∞) but not on (0,∞)
04/26 20:07, 5F
推
04/27 11:41, , 6F
So, the limit funtion g is discontinuous on (0,1)
04/27 11:41, 6F
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04/27 11:41, , 7F
by Dini' thm.
04/27 11:41, 7F
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