quasi
Posts:
12,050
Registered:
7/15/05


Re: Is this series uniformly convergent for x != 0 ?
Posted:
Feb 11, 2013 1:15 AM


quasi wrote: >vv <vanamali@netzero.net> 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 > >I could be wrong, but here's what I think ... > >If k is a nonzero integer then for x = 2*k*Pi, the series >diverges. > >More generally, I think the series diverges for x = (2*k*Pi)/d >where k,d are nonzero integers with d odd and with k,d >relatively prime. Thus, the series is pointwise divergent on a >dense subset of R, so the question of uniform convergence is >silly. > >In fact, going out on a limb, it seems to me that the series >diverges for all real numbers x except for x = 0, x = Pi, >x = Pi.
I meant: except for x = Pi, x = Pi.
quasi

