[分析] uniform convergence(Apostol)

看板Math作者bineapple (パイナップル)時間15年前 (2011/01/19 23:34)推噓3(3推 0噓 2→)

留言5則, 4人參與討論串1/1

Let {a_n} be a decreasing sequence of positive terms. Prove that the series Σa_nsin(n)x converges uniformly on R if, and only if, na_n→0 as n→∞. 有人能提示一下嗎? Dirichlet和Abel兩種測試好像都派不太上用場... -- Stirling's formula: 1 log(2π) ∞ B_1(t) logΓ(s)=(s-─)logs-s+────-∫────dt, 2 2 0 s+t where B_1 is the first Bernoulli function. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 223.139.118.209

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math1209

01/19 23:38, , 1^F

01/19 23:38, 1^F

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yueayase

01/20 00:03, , 2^F

01/20 00:03, 2^F

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bineapple

01/20 14:21, , 3^F

01/20 14:21, 3^F