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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Integral test
Replies: 17   Last Post: Dec 20, 2012 12:29 PM

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Leon Aigret

Posts: 12
Registered: 12/2/12
Re: Integral test
Posted: Dec 10, 2012 6:56 PM
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On Mon, 10 Dec 2012 23:51:20 GMT, aigret.not@myrealbox.invalid (Leon
Aigret) wrote:

>On Mon, 10 Dec 2012 21:05:31 +0000,
>=?ISO-8859-1?Q?Jos=E9_Carlos_Santos?= <jcsantos@fc.up.pt> wrote:
>
>>Hi all,
>>
>>One of my students asked me today a question that I was unable to
>>answer. Let _f_ be an analytical function from (0,+oo) into [1,+oo) and
>>suppose that the integral of _f_ from 1 to +oo converges. Does it follow
>>that the series sum_n f(n) converges? I don't think so, but I was unable
>>to find a counter-example. Any ideas?
>
>If ïnto" means injectivity then the answer must obviously be yes
>because _f_ is monotonous. Otherwise, f(x) = cos (pi x^2) should work
>if absolute convergence of the integral is not required.

... and tried to concel it one minute later. Please ignore.

Leom

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