Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


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

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

Advanced Search
Reply to this Topic Reply to this Topic

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
RGVickson@shaw.ca

Posts: 1,595
Registered: 12/1/07
Re: Integral test
Posted: Dec 11, 2012 12:44 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2013. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.