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Re: Is this series uniformly convergent for x != 0 ?
Posted:
Feb 11, 2013 1:46 AM
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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.
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