S***p
发帖数: 19902 | 1 Prove of disprove the following claim
suppose Sum_{n=0,1...}f_n converges pointwisely to a function f on a set E
and {f_n} converges uniformly on E
then Sum_{n=0,1...}f_n uniformly on E |
x******i
发帖数: 3022 | 2 E = (0,1]
f_n = cos(n*x)/n
【在 S***p 的大作中提到】
: Prove of disprove the following claim
: suppose Sum_{n=0,1...}f_n converges pointwisely to a function f on a set E
: and {f_n} converges uniformly on E
: then Sum_{n=0,1...}f_n uniformly on E
|
S***p
发帖数: 19902 | 3 but
sum f_n converges?
【在 x******i 的大作中提到】
: E = (0,1]
: f_n = cos(n*x)/n
|
x******i
发帖数: 3022 | 4 http://www.wolframalpha.com/input/?i=
Sum[Cos[n*x]%2Fn%2C{n%2C1%2C%2Binfinity}]
【在 S***p 的大作中提到】
: but
: sum f_n converges?
|
S***p
发帖数: 19902 | 5 ......
【在 x******i 的大作中提到】
: http://www.wolframalpha.com/input/?i=
: Sum[Cos[n*x]%2Fn%2C{n%2C1%2C%2Binfinity}]
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