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

 Messages: [ Previous | Next ]
 RGVickson@shaw.ca Posts: 1,677 Registered: 12/1/07
Re: Integral test
Posted: Dec 11, 2012 12:44 PM

On Monday, December 10, 2012 10:45:40 PM UTC-8, José Carlos Santos wrote:
> On 10/12/2012 23:15, Butch Malahide wrote:
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>
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> >> 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
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> >> suppose that the integral of _f_ from 1 to +oo converges.
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> >
>
> > Do you mean from [1,+oo) into (0,+oo)?
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>
>
> Yes! My mistake. :-(
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>
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> Best regards,
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>
>
> Jose Carlos Santos

The function f(x) = sum_{n=1..infinity} exp(-n^3*(x-n)^2) has sum_n f(n) divergent but int_{x=0..inf} f(x) dx convergent. It has continuous derivatives of all orders at any x, but I don't know if it is analytic.

RGV

Date Subject Author
12/10/12 Jose Carlos Santos
12/10/12 Virgil
12/10/12 Jose Carlos Santos
12/10/12 Butch Malahide
12/11/12 Jose Carlos Santos
12/11/12 RGVickson@shaw.ca
12/10/12 Leon Aigret
12/10/12 Rotwang
12/11/12 Jose Carlos Santos
12/18/12 Phil Carmody
12/18/12 Rotwang
12/11/12 Rotwang
12/11/12 David C. Ullrich
12/11/12 George Cornelius
12/12/12 David C. Ullrich
12/18/12 David Petry
12/20/12 David Petry