Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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: Is this series uniformly convergent for x != 0 ?
Replies: 5   Last Post: Feb 11, 2013 5:28 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
David Bernier

Posts: 3,187
Registered: 12/13/04
Re: Is this series uniformly convergent for x != 0 ?
Posted: Feb 11, 2013 1:46 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 02/10/2013 11:35 PM, vv wrote:
> I'd be grateful if someone can throw light on whether or not the
> following series is uniformly convergent for x not equal to zero:
>
> \sum_{n=1}^infty exp(-ixn)/n
>
> Thanks!
>
> --vv


If x is real, exp(-ixn) = cos(-xn) + i*sin(-xn) .

cos^2(A) + sin^2(A) = 1 if A is real.

If x=0, the series diverges. Also, x = 2kPi , k in Z: divergent.

For x real, it doesn't converge absolutely.

On uniform convergence:

http://en.wikipedia.org/wiki/Uniform_convergence

Suppose X is the set of reals where x in X iff
the series converges.

Do we know what X is?



dave


--
dracut:/# lvm vgcfgrestore
File descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID
993: sh
Please specify a *single* volume group to restore.



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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.