看板 Math 關於我們 聯絡資訊
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
wickeday :M test應該可以吧? 感覺會被k^(-3/2) bound住 04/26 17:24
keroro321 :gn(x)=Σ(k=1->n) x/(1+(k^2)(x^2)) ?? 04/26 19:31
keroro321 :it doesn't converge uniformly near 0 . 04/26 19:33
keroro321 :for any a>0 ,this sequence of functions converges 04/26 20:07
keroro321 :uniformly on [a,∞) but not on (0,∞) 04/26 20:07
math1209 :So, the limit funtion g is discontinuous on (0,1) 04/27 11:41
math1209 :by Dini' thm. 04/27 11:41