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


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.



